{"text": "variance <- function(X){\n mean(X^2) - mean(X)^2\n}\n\nstandard_deviation <- function(X){\n variance(X)^(1/2)\n}\n\n\nmu <- mean\nsigma <- standard_deviation\nsigma.2 <- var\n\n\nskewness <- function(X){\n mean(((X - mu(X)) / sigma(X))^3)\n}\n\nkurtosis <- function(X){\n mean(((X - mu(X)) / sigma(X))^4)\n}", "meta": {"hexsha": "7f59f5155e4b2f5967589f46b6127df70d543d13", "size": 299, "ext": "r", "lang": "R", "max_stars_repo_path": "R/sample_moments.r", "max_stars_repo_name": "kevinkevin556/econometrics", "max_stars_repo_head_hexsha": "735a25f3eea03d9d1d1d27d90e7c1ef311604c84", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/sample_moments.r", "max_issues_repo_name": "kevinkevin556/econometrics", "max_issues_repo_head_hexsha": "735a25f3eea03d9d1d1d27d90e7c1ef311604c84", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/sample_moments.r", "max_forks_repo_name": "kevinkevin556/econometrics", "max_forks_repo_head_hexsha": "735a25f3eea03d9d1d1d27d90e7c1ef311604c84", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 14.2380952381, "max_line_length": 36, "alphanum_fraction": 0.5652173913, "num_tokens": 96, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9648551515780319, "lm_q2_score": 0.8289388040954684, "lm_q1q2_score": 0.7998058754744457}} {"text": "#plot likelihood curve----\nn<-10 #set total trials\nx<-0 #set successes\ntheta<- seq(0,1,len=100) #create theta variable, from 0 to 1\nlike <- dbinom(x,n,theta) #create likelihood function\nplot(theta,like,type='l',xlab=expression(theta), ylab='Likelihood', main=\"Likelihood Curve\")\n\n#? Daniel Lakens, 2016. \n# This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. https://creativecommons.org/licenses/by-nc-sa/4.0/\n\n\n\n# Addition to calculate binomial probability given n, x and p\nn<-10\nx<-8\np<-0.5\nr<- choose(n, x) * p^x * (1-p)^(n-x)\nr\n# Wallace Hobbes, 2019.", "meta": {"hexsha": "ce741f2ce542b84ed444c1cdc48f6f129fd4ccca", "size": 614, "ext": "r", "lang": "R", "max_stars_repo_path": "week_2/PlotLikelihood.r", "max_stars_repo_name": "whobbes/improving_statistical_inferences", "max_stars_repo_head_hexsha": "b7ffcc3df42a8257753e533a7b27fa32ee666622", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "week_2/PlotLikelihood.r", "max_issues_repo_name": "whobbes/improving_statistical_inferences", "max_issues_repo_head_hexsha": "b7ffcc3df42a8257753e533a7b27fa32ee666622", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "week_2/PlotLikelihood.r", "max_forks_repo_name": "whobbes/improving_statistical_inferences", "max_forks_repo_head_hexsha": "b7ffcc3df42a8257753e533a7b27fa32ee666622", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 32.3157894737, "max_line_length": 163, "alphanum_fraction": 0.7231270358, "num_tokens": 193, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9597620550745212, "lm_q2_score": 0.8333245911726381, "lm_q1q2_score": 0.7997933221679864}} {"text": "#####################################################################\n# CS638: Applied Machine Learning\n# Copyright 2016 Pejman Ghorbanzade \n# More info: https://github.com/ghorbanzade/beacon\n#####################################################################\n\n# clear workspace\nrm(list = ls())\n\n# enable traceback on error messages\noptions(error=traceback)\n\n# remove all plots if there are any\nif (!is.null(dev.list())) trash <- dev.off()\n\nargs = commandArgs(trailingOnly=TRUE)\nif (0 == length(args)) {\n stop(\"expected path to root directory of course\", call.=FALSE)\n}\npngdir <- args[1]\ncourseNameFull <- \"umb-cs638-2016s\"\n\n# ---------------------------------------------------------\n# function declarations\n# ---------------------------------------------------------\n\n# function to compute sigmoid for logistic regression\nsigmoid <- function(z) {\n\tsigmoid <- 1 / (1 + exp(-z))\n\treturn(sigmoid)\n}\n\n# function to compute cost for logistic regression\ncost <- function(x, y, theta, lambda=0) {\n\tm <- nrow(x)\n\thx <- sigmoid(x %*% theta)\n\tr <- (lambda / (2 * m)) * t(theta) %*% theta\n\tcost <- (1 / m) * sum(-y * log(hx) - (1 - y) * log(1 - hx)) + r\n\treturn(cost)\n}\n\n# function to implement gradient descent algorithm\ngradient_descent <- function(x, y, theta, alpha, iters, lambda=0) {\n\tm <- dim(x)[1]\n\tcosts <- rep(NA, iters)\n\tfor(i in 1:iters) {\n\t\thx <- sigmoid(x %*% theta)\n\t\ttheta[1,1] <- theta[1,1] - alpha * ((1 / m) * t(t(hx - y) %*% x[, 1]))\n\t\ttheta[-1,1] <- theta[-1,1] - alpha * ((1 / m) * t(t(hx - y) %*% x[, -1]) + (lambda / m) * theta[-1, 1])\n\t\tcosts[i] <- cost(x, y, theta, lambda=lambda)\n\t}\n\tout <- list(costs=costs, params=theta)\n\treturn(out)\n}\n\n# function to map features into polynomial terms up to the nth power\nbuild_features <- function(f1, f2, degree) {\n\tout <- matrix(rep(1, length(f1)))\n\tfor (i in 1:degree) {\n\t\tfor (j in 0:i) {\n\t\t\tout <- cbind(out, f1^(i-j) * f2^j)\n\t\t}\n\t}\n\treturn(out)\n}\n\n# ---------------------------------------------------------\n# loading datasets\n# ---------------------------------------------------------\n\n# load dataset 1\ndata1 = read.table(\"dat/hw04/data1.txt\", sep=\",\")\ncolnames(data1) <- c('exam1', 'exam2', 'status')\ndata11 <- data1[data1[, \"status\"] == 1, , drop=FALSE]\ndata12 <- data1[data1[, \"status\"] == 0, , drop=FALSE]\n\n# load dataset 2\ndata2 = read.table(\"dat/hw04/data2.txt\", sep=\",\")\ncolnames(data2) <- c('test1', 'test2', 'status')\ndata21 <- data2[data2[, \"status\"] == 1, , drop=FALSE]\ndata22 <- data2[data2[, \"status\"] == 0, , drop=FALSE]\n\n# ---------------------------------------------------------\n# visualize dataset 1\n# ---------------------------------------------------------\n\npng(filename=file.path(pngdir, paste(courseNameFull, \"-hw04-11\", \".png\", sep=\"\")),\n\theight=768, width=1024, res=150, units=\"px\", bg=\"white\")\n\nxrange <- seq(floor(min(data1$exam1)/5)*5,\n\tceiling(max(data1$exam1)/5)*5,\n\tlength.out=5\n\t)\nyrange <- seq(floor(min(data1$exam2)/5)*5,\n\tceiling(max(data1$exam2)/5)*5,\n\tlength.out=5\n\t)\nplot(0, 0, type=\"n\", axes=F, ann=F,\n\txlim=range(xrange), ylim=range(yrange))\npoints(data11$exam1, data11$exam2, type=\"p\", col=\"blue\", pch=3)\npoints(data12$exam1, data12$exam2, type=\"p\", col=\"red\", pch=1)\naxis(1, at=xrange, labels=round(xrange, 3))\naxis(2, at=yrange, labels=round(yrange, 3))\n\nlegend(\"topright\",\n\tinset=0.01,\n\tlegend = c(expression(\"admitted\"), expression(\"rejected\")),\n\tcol = c(\"blue\", \"red\"),\n\tpch = c(3, 1),\n\tcex = 0.8\n\t);\ngrid(10, 10)\nbox()\ntitle(main=\"Student Admission Results Based on Exam Scores\", font.main=1)\ntitle(xlab=\"Score in Exam 1\", col.lab='black')\ntitle(ylab=\"Score in Exam 2\", col.lab='black')\ntrash <- dev.off()\n\n# ---------------------------------------------------------\n# minimize cost function using gradient descent w/o scaling\n# ---------------------------------------------------------\n\niters <- 1e6\nalpha <- 1e-3\nx <- cbind(1, data1$exam1, data1$exam2)\ny <- data1$status\ntheta <- matrix(0, nrow=ncol(x), ncol=1)\nfit <- gradient_descent(x, y, theta, alpha, iters)\n\n# report final theta coefficients\npaste(\"final theta coefficients:\")\nfit$params\n\n# plot cost function based on number of iterations of gradient descent\n# without feature scaling\npng(filename=file.path(pngdir, paste(courseNameFull, \"-hw04-12\", \".png\", sep=\"\")),\n\theight=768, width=1024, res=150, units=\"px\", bg=\"white\")\n\nxrange <- seq(0, iters, length.out=6)\nyrange <- seq(0, 1, length.out=5)\nplot(0, 0, type=\"n\", axes=F, ann=F, xlim=range(xrange), ylim=range(yrange))\nlines(fit$costs, col=\"blue\", lty=1)\naxis(1, at=xrange, labels=round(xrange, 3))\naxis(2, at=yrange, labels=round(yrange, 3))\n\nlegend(\"topright\", inset=0.01,\n\tlegend = as.expression(bquote(alpha == .(alpha))),\n\tcol = c(\"blue\"),\n\tlty = c(1),\n\tcex = 0.8\n\t);\ngrid(10, 10)\nbox()\ntitle(main=paste(\"Minimizing Cost Function using Gradient Descent Algorithm\\n\",\n\t\"Without Feature Scaling\"), font.main=1)\ntitle(xlab=\"Number of Iterations\", col.lab='black')\ntitle(ylab=\"Cost Function\", col.lab='black')\ntrash <- dev.off()\n\n# ---------------------------------------------------------\n# plot decision boundary\n# ---------------------------------------------------------\n\ntheta <- fit$params\nslope <- - theta[2] / theta[3]\nintercept <- - theta[1] / theta[3]\n\npng(filename=file.path(pngdir, paste(courseNameFull, \"-hw04-13\", \".png\", sep=\"\")),\n\theight=768, width=1024, res=150, units=\"px\", bg=\"white\")\n\nxrange <- seq(floor(min(data1$exam1)/5)*5,\n\tceiling(max(data1$exam1)/5)*5,\n\tlength.out=5\n\t)\nyrange <- seq(floor(min(data1$exam2)/5)*5,\n\tceiling(max(data1$exam2)/5)*5,\n\tlength.out=5\n\t)\nplot(0, 0, type=\"n\", axes=F, ann=F,\n\txlim=range(xrange), ylim=range(yrange))\npoints(data11$exam1, data11$exam2, type=\"p\", col=\"blue\", pch=3)\npoints(data12$exam1, data12$exam2, type=\"p\", col=\"red\", pch=1)\nabline(a=intercept, b=slope, col=\"green\")\naxis(1, at=xrange, labels=round(xrange, 3))\naxis(2, at=yrange, labels=round(yrange, 3))\n\nlegend(\"topright\",\n\tinset=0.01,\n\tlegend = c(\n\t\texpression(\"admitted\"),\n\t\texpression(\"rejected\"),\n\t\texpression(\"decision boundary\")\n\t\t),\n\tcol = c(\"blue\", \"red\", \"green\"),\n\tpch = c(3, 1, NA),\n\tlty = c(NA, NA, 1),\n\tcex = 0.8\n\t);\ngrid(10, 10)\nbox()\ntitle(main=paste(\"Learned Decision Boundary for Student Admissions\\n\",\n\t\"Based on Exam Scores\"\n\t), font.main=1)\ntitle(xlab=\"Score in Exam 1\", col.lab='black')\ntitle(ylab=\"Score in Exam 2\", col.lab='black')\ntrash <- dev.off()\n\n# ---------------------------------------------------------\n# predict result based on learned decision boundary\n# ---------------------------------------------------------\n\n# What is the admission probability of a student with score\n# 100 on exam1 and score 50 on exam2\n\nstudent <- setNames(c(100, 50), c('exam1', 'exam2'))\n\ntheta <- fit$params\nslope <- - theta[2] / theta[3]\nintercept <- - theta[1] / theta[3]\n\nprobability <- sigmoid(c(1, student) %*% theta)\nprint(paste(\"Admission Chance: \", round(probability * 100, 2), \"%\"))\n\n#\n# plot student score relative to decision boundary\n#\npng(filename=file.path(pngdir, paste(courseNameFull, \"-hw04-14\", \".png\", sep=\"\")),\n\theight=768, width=1024, res=150, units=\"px\", bg=\"white\")\n\nxrange <- seq(floor(min(data1$exam1)/5)*5,\n\tceiling(max(data1$exam1)/5)*5,\n\tlength.out=5\n\t)\nyrange <- seq(floor(min(data1$exam2)/5)*5,\n\tceiling(max(data1$exam2)/5)*5,\n\tlength.out=5\n\t)\nplot(0, 0, type=\"n\", axes=F, ann=F,\n\txlim=range(xrange), ylim=range(yrange))\npoints(data11$exam1, data11$exam2, type=\"p\", col=\"blue\", pch=3)\npoints(data12$exam1, data12$exam2, type=\"p\", col=\"red\", pch=1)\nabline(a=intercept, b=slope, col=\"green\")\npoints(student['exam1'], student['exam2'], type=\"p\", col=\"violetred\", pch=2)\naxis(1, at=xrange, labels=round(xrange, 3))\naxis(2, at=yrange, labels=round(yrange, 3))\n\nlegend(\"topright\",\n\tinset=0.01,\n\tlegend = c(\n\t\texpression(\"admitted\"),\n\t\texpression(\"rejected\"),\n\t\texpression(\"student score\"),\n\t\texpression(\"decision boundary\")\n\t\t),\n\tcol = c(\"blue\", \"red\", \"violetred\", \"green\"),\n\tpch = c(3, 1, 2, NA),\n\tlty = c(NA, NA, NA, 1),\n\tcex = 0.8\n\t);\ngrid(10, 10)\nbox()\ntitle(main=paste(\"Decision Boundary for Student Admissions\\n\",\n\t\"Based on Exam Scores\"\n\t), font.main=1)\ntitle(xlab=\"Score in Exam 1\", col.lab='black')\ntitle(ylab=\"Score in Exam 2\", col.lab='black')\ntrash <- dev.off()\n\n# ---------------------------------------------------------\n# visualize dataset 2\n# ---------------------------------------------------------\n\npng(filename=file.path(pngdir, paste(courseNameFull, \"-hw04-21\", \".png\", sep=\"\")),\n\theight=768, width=1024, res=150, units=\"px\", bg=\"white\")\n\nxrange <- seq(floor(min(data2$test1)*4)/4,\n\tceiling(max(data2$test1)*4)/4,\n\tlength.out=4\n\t)\nyrange <- seq(floor(min(data2$test2)*4)/4,\n\tceiling(max(data2$test2)*4)/4,\n\tlength.out=4\n\t)\nplot(0, 0, type=\"n\", axes=F, ann=F,\n\txlim=range(xrange), ylim=range(yrange))\npoints(data21$test1, data21$test2, type=\"p\", col=\"blue\", pch=3)\npoints(data22$test1, data22$test2, type=\"p\", col=\"red\", pch=1)\naxis(1, at=xrange, labels=round(xrange, 3))\naxis(2, at=yrange, labels=round(yrange, 3))\n\nlegend(\"topright\",\n\tinset=0.01,\n\tlegend = c(\n\t\texpression(\"passed\"),\n\t\texpression(\"failed\")\n\t\t),\n\tcol = c(\"blue\", \"red\"),\n\tpch = c(3, 1),\n\tcex = 0.8\n\t);\ngrid(10, 10)\nbox()\ntitle(main=\"Acceptance Based on Test Results\", font.main=1)\ntitle(xlab=\"Test 1\", col.lab='black')\ntitle(ylab=\"Test 2\", col.lab='black')\ntrash <- dev.off()\n\n# ---------------------------------------------------------\n# calculating costs and thetas for different lambda values\n# ---------------------------------------------------------\n\nfeatures <- build_features(data2$test1, data2$test2, degree=7)\nm <- dim(features)[1]\nfeatures <- cbind(rep(1, m), features)\nfeatures <- as.matrix(features)\nn <- dim(features)[2]\ny <- data2$status\ntheta <- matrix(0, ncol=1, nrow=n)\n\nalpha <- 5e-1\niters <- 1e3\nlambdas <- c(0, 1, 10, 100, 1000)\nthetas <- matrix(0, ncol=length(lambdas), nrow=n)\ncosts <- matrix(0, ncol=length(lambdas), nrow=iters)\n\nfor (i in 1:length(lambdas)) {\n\tfit <- gradient_descent(features, y, theta, alpha, iters, lambdas[i])\n\tthetas[,i] <- fit$params\n\tcosts[,i] <- fit$costs\n}\n\n# ---------------------------------------------------------\n# plot cost function for different values of lambda\n# ---------------------------------------------------------\n\n# plot cost function based on number of iterations of gradient descent\n# without feature scaling\npng(filename=file.path(pngdir, paste(courseNameFull, \"-hw04-22\", \".png\", sep=\"\")),\n\theight=768, width=1024, res=150, units=\"px\", bg=\"white\")\n\nxrange <- seq(0, iters, length.out=6)\nyrange <- seq(0, 1, length.out=5)\nplot(0, 0, type=\"n\", axes=F, ann=F, xlim=range(xrange), ylim=range(yrange))\nlines(costs[,1], col=\"blue\", lty=1)\nlines(costs[,2], col=\"red\", lty=1)\nlines(costs[,3], col=\"green\", lty=1)\nlines(costs[,4], col=\"blue\", lty=2)\nlines(costs[,5], col=\"red\", lty=2)\naxis(1, at=xrange, labels=round(xrange, 3))\naxis(2, at=yrange, labels=round(yrange, 3))\n\nlegend(\"topright\", inset=0.01,\n\tlegend = c(\n\t\tas.expression(bquote(lambda == .(lambdas[1]))),\n\t\tas.expression(bquote(lambda == .(lambdas[2]))),\n\t\tas.expression(bquote(lambda == .(lambdas[3]))),\n\t\tas.expression(bquote(lambda == .(lambdas[4]))),\n\t\tas.expression(bquote(lambda == .(lambdas[5])))\n\t\t),\n\tcol = c(\"blue\", \"red\", \"green\", \"blue\", \"red\"),\n\tlty = c(1, 1, 1, 2, 2),\n\tcex = 0.8\n\t);\ngrid(10, 10)\nbox()\ntitle(main=paste(\"Effect of lambda values on Cost Function Minimization\"),\n\tfont.main=1)\ntitle(xlab=\"Number of Iterations\", col.lab='black')\ntitle(ylab=\"Cost Function\", col.lab='black')\ntrash <- dev.off()\n\n# ---------------------------------------------------------\n# compute decision boundary for different lambda values\n# ---------------------------------------------------------\n\nmn1 = mean(data2$test1)\nmn2 = mean(data2$test2)\nr1 = max(data2$test1) - min(data2$test1)\nr2 = max(data2$test2) - min(data2$test2)\n\nnum = 200;\nu <- seq(mn1 - r1 / 2, mn1 + r1 / 2, len=num)\nv <- seq(mn2 - r2 / 2, mn2 + r2 / 2, len=num)\n\nz1 = matrix(0, length(u), length(v))\nz2 = matrix(0, length(u), length(v))\nz3 = matrix(0, length(u), length(v))\nz4 = matrix(0, length(u), length(v))\nfor (i in 1:length(u)) {\n\tfor (j in 1:length(v)) {\n\t\tz1[j, i] <- cbind(1, build_features(u[i], v[j], 7)) %*% thetas[,1]\n\t\tz2[j, i] <- cbind(1, build_features(u[i], v[j], 7)) %*% thetas[,2]\n\t\tz3[j, i] <- cbind(1, build_features(u[i], v[j], 7)) %*% thetas[,3]\n\t\tz4[j, i] <- cbind(1, build_features(u[i], v[j], 7)) %*% thetas[,4]\n\t}\n}\n\n# ---------------------------------------------------------\n# plot decision boundaries for different lambda values\n# ---------------------------------------------------------\n\npng(filename=file.path(pngdir, paste(courseNameFull, \"-hw04-23\", \".png\", sep=\"\")),\n\theight=768, width=1024, res=150, units=\"px\", bg=\"white\")\n\ncontour(u, v, z1, nlevels=0, col=\"green\", lty=2)\n\npoints(data21$test1, data21$test2, type=\"p\", col=\"blue\", pch=3)\npoints(data22$test1, data22$test2, type=\"p\", col=\"red\", pch=1)\n\nlegend(\"topright\",\n\tinset=0.01,\n\tlegend = c(\n\t\texpression(\"passed\"),\n\t\texpression(\"failed\"),\n\t\tas.expression(bquote(lambda == .(lambdas[1])))\n\t\t),\n\tcol = c(\"blue\", \"red\", \"green\"),\n\tpch = c(3, 1, NA),\n\tlty = c(NA, NA, 2),\n\tcex = 0.8\n\t);\ngrid(10, 10)\nbox()\ntitle(main=\"Decision Boundary of Acceptance Based on Test Results\", font.main=1)\ntitle(xlab=\"Test 1\", col.lab='black')\ntitle(ylab=\"Test 2\", col.lab='black')\ntrash <- dev.off()\n\n# plot all contours on the same figure for comparison\npng(filename=file.path(pngdir, paste(courseNameFull, \"-hw04-24\", \".png\", sep=\"\")),\n\theight=768, width=1024, res=150, units=\"px\", bg=\"white\")\n\ncontour(u, v, z1, nlevels=0, col=\"green\", lty=2)\ncontour(u, v, z2, nlevels=0, col=\"orange\", lty=2, add=TRUE)\ncontour(u, v, z3, nlevels=0, col=\"blue\", lty=2, add=TRUE)\ncontour(u, v, z4, nlevels=0, col=\"red\", lty=2, add=TRUE)\n\npoints(data21$test1, data21$test2, type=\"p\", col=\"blue\", pch=3)\npoints(data22$test1, data22$test2, type=\"p\", col=\"red\", pch=1)\n\nlegend(\"topright\",\n\tinset=0.01,\n\tlegend = c(\n\t\texpression(\"passed\"),\n\t\texpression(\"failed\"),\n\t\tas.expression(bquote(lambda == .(lambdas[1]))),\n\t\tas.expression(bquote(lambda == .(lambdas[2]))),\n\t\tas.expression(bquote(lambda == .(lambdas[3]))),\n\t\tas.expression(bquote(lambda == .(lambdas[4])))\n\t\t),\n\tcol = c(\"blue\", \"red\", \"green\", \"orange\", \"blue\", \"red\"),\n\tpch = c(3, 1, NA, NA, NA, NA),\n\tlty = c(NA, NA, 2, 2, 2, 2),\n\tcex = 0.8\n\t);\ngrid(10, 10)\nbox()\ntitle(main=\"Decision Boundary for Acceptance Based on Test Results\", font.main=1)\ntitle(xlab=\"Test 1\", col.lab='black')\ntitle(ylab=\"Test 2\", col.lab='black')\ntrash <- dev.off()\n", "meta": {"hexsha": "3b8eb7ba52c1e6cd9b6820e0fdb8b5c6ba00f34d", "size": 14451, "ext": "r", "lang": "R", "max_stars_repo_path": 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"max_forks_repo_forks_event_max_datetime": "2020-12-06T17:18:05.000Z", "avg_line_length": 31.2792207792, "max_line_length": 105, "alphanum_fraction": 0.5854958134, "num_tokens": 4634, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.905989815306765, "lm_q2_score": 0.8824278556326344, "lm_q1q2_score": 0.7994706499461551}} {"text": "library(pomp)\r\nlibrary(ggplot2)\r\n\r\n## Fake data\r\n\r\nStocSIR <- function(y, pars, T, steps) {\r\n\r\n\tout <- matrix(NA, nrow = (T+1), ncol = 4)\r\n\r\n\tR0 <- pars[['R0']]\r\n\tr <- pars[['r']]\r\n\tN <- pars[['N']]\r\n\teta <- pars[['eta']]\r\n\tberr <- pars[['berr']]\r\n\r\n\tS <- y[['S']]\r\n\tI <- y[['I']]\r\n\tR <- y[['R']]\r\n\r\n\tB0 <- R0 * r / N\r\n\tB <- B0\r\n\r\n\tout[1,] <- c(S,I,R,B)\r\n\r\n\th <- 1 / steps\r\n\r\n\tfor ( i in 1:(T*steps) ) {\r\n\r\n\t\tB <- exp( log(B) + eta*(log(B0) - log(B)) + rnorm(1, 0, berr) )\r\n\r\n\t\tBSI <- B*S*I\r\n\t\trI <- r*I\r\n\r\n\t\tdS <- -BSI\r\n\t\tdI <- BSI - rI\r\n\t\tdR <- rI\r\n\r\n\t\tS <- S + h*dS #newInf\r\n\t\tI <- I + h*dI #newInf - h*dR\r\n\t\tR <- R + h*dR #h*dR\r\n\r\n\t\tif (i %% steps == 0)\r\n\t\t\tout[i/steps+1,] <- c(S,I,R,B)\r\n\r\n\t}\r\n\r\n\treturn(out)\r\n\r\n}\r\n\r\nset.seed(1234)\r\n\r\nT \t\t<- 60\r\ni_infec <- 5\r\nsteps \t<- 7\r\nN \t\t<- 500\r\nsigma \t<- 10\r\nTlim \t<- T\r\n\r\n## Generate true trajecory and synthetic data\r\n##\r\n\r\npars_true <- c(R0 = 3.0, \t# new infected people per infected person\r\n r = 0.1, \t\t# recovery rate\r\n\t\t N = 500, \t\t# population size\r\n\t\t eta = 0.5, \t# geometric random walk\r\n\t\t berr = 0.5) \t# Beta geometric walk noise\r\n\r\ntrue_init_cond <- c(S = N - i_infec,\r\n\t\t\t\t\tI = i_infec,\r\n\t\t\t\t\tR = 0)\r\n\r\nsdeout <- StocSIR(true_init_cond, pars_true, T, steps)\r\ncolnames(sdeout) <- c('S','I','R','B')\r\n\r\ninfec_counts_raw <- sdeout[,'I'] + rnorm(T+1, 0, sigma)\r\ninfec_counts <- ifelse(infec_counts_raw < 0, 0, infec_counts_raw)\r\n\r\ndata <- data.frame(time = 0:T, y = infec_counts)\r\n\r\nsir_step <- Csnippet(\"\r\n B = exp( log(B) + eta*(log(R0*r/500.0) - log(B)) + rnorm(0, berr) );\r\n\tdouble dS = - B*S*I;\r\n\tdouble dI = B*S*I - r*I;\r\n\tdouble dR = r*I;\r\n\tS += dt*dS;\r\n\tI += dt*dI;\r\n\tR += dt*dR;\r\n\")\r\n\r\nsir_init <- Csnippet(\"\r\n\tS = 500.0 - I0;\r\n\tI = I0;\r\n\tR = 0;\r\n\tB = R0*r/500.0;\r\n\")\r\n\r\ndmeas <- Csnippet('\r\n \tlik = dnorm(y, I, sigma, give_log);\r\n \t//Rprintf(\"%lf %lf, %lf, %lf, %d , %lf, %lf, %lf\", lik, y, I, sigma, give_log, S, I, R);\r\n')\r\n\r\nrmeas <- Csnippet('\r\n \ty = rnorm(I, sigma);\r\n')\r\n\r\nlogtrans <- Csnippet(\"\r\n\tTR0 = log(R0);\r\n\tTr = log(r);\r\n\tTsigma = log(sigma);\r\n\tTeta = log(eta);\r\n\tTberr = log(berr);\r\n\tTI0 = log(I0);\r\n\")\r\n\r\nexptrans <- Csnippet(\"\r\n\tTR0 = exp(R0);\r\n\tTr = exp(r);\r\n\tTsigma = exp(sigma);\r\n\tTeta = exp(eta);\r\n\tTberr = exp(berr);\r\n\tTI0 = exp(I0);\r\n\")\r\n\r\noptions(verbose=FALSE) \r\nsir <- pomp(data = data,\r\n time = \"time\",\r\n t0 = 0,\r\n initializer = sir_init,\r\n rprocess = euler.sim(step.fun = sir_step,\r\n delta.t = 1.0/steps),\r\n dmeasure = dmeas,\r\n rmeasure = rmeas,\r\n statenames = c(\"S\",\"I\",\"R\",\"B\"),\r\n paramnames = c(\"R0\",\"r\",\"I0\",\"sigma\",\"eta\",\"berr\"),\r\n toEstimationScale = logtrans,\r\n fromEstimationScale = exptrans)\r\n\r\n#simStates <- simulate(sir,nsim=1,params=c(R0 = 3.0, r = 0.1, I0 = 5.0, sigma = 10.0, eta = 0.5, berr = 0.3),\r\n# states = TRUE, obvs = TRUE, include = FALSE, as = TRUE)\r\n\r\ntransfun <- function(params,...) {\r\n params[c(\"R0\",\"r\",\"I0\",\"sigma\",\"eta\", \"berr\")] <- exp(params[c(\"R0\",\"r\",\"I0\",\"sigma\",\"eta\", \"berr\")])\r\n return(params)\r\n}\r\n\r\ntransfun_inv <- function(params,...) {\r\n params[c(\"R0\",\"r\",\"I0\",\"sigma\",\"eta\", \"berr\")] <- log(params[c(\"R0\",\"r\",\"I0\",\"sigma\",\"eta\", \"berr\")])\r\n return(params)\r\n}\r\n\r\n\r\nm1 <- mif2(sir,\r\n\t Nmif = 300,\r\n\t start = c(R0 = 3.0, r = 0.1, I0 = 5.0, sigma = 10.0, eta = 0.5, berr = 0.3),\r\n\t rw.sd = rw.sd(R0 = 0.3, r = 0.01, I0 = 0.5, sigma = 1.0, eta = 0.05, berr = 0.03),\r\n\t cooling.fraction.50 = 0.90,\r\n\t Np = 3000,\r\n\t toEstimationScale = transfun,\r\n fromEstimationScale = transfun_inv,\r\n\t transform = TRUE\r\n\t )\r\n\r\n#plot(m1)\r\ncoef(m1)\r\n\r\nif2pars <- coef(m1)[-c(grep('sigma', names(coef(m1))),grep('I0', names(coef(m1))))]\r\nif2pars[['N']] <- 500\r\n\r\nnumtraj <- 100\r\n\r\ntrajData <- matrix(NA, nrow = numtraj, ncol = (T+1))\r\nfor(i in 1:numtraj) {\r\n\tsdeout <- StocSIR(true_init_cond, if2pars, T, steps)\r\n\tcolnames(sdeout) <- c('S','I','R','B')\r\n\ttrajData[i,] <- sdeout[,'I']\r\n}\r\n\r\nmeanTraj \t<- colMeans(trajData)\r\nquantTraj \t<- t(apply(trajData, 2, quantile, probs = c(0.025,0.975)))\r\ncolnames(quantTraj) <- c(\"025\",\"975\")\r\n\r\nqplot(1:(T+1), meanTraj, geom = \"line\", xlab = \"Time\", ylab = \"Infection count\") +\r\n\tgeom_ribbon(aes(ymin = quantTraj[,'025'], ymax=quantTraj[,'975']), alpha=0.1) +\r\n\tgeom_line(aes(y = infec_counts)) +\r\n\ttheme_bw()", "meta": {"hexsha": "b2cc1d63e195887895eadb91eb113dd4b57883b4", "size": 4407, "ext": "r", "lang": "R", "max_stars_repo_path": "code/pomp/pompstocsir.r", "max_stars_repo_name": "dbarrows/epidemic-forecasting", "max_stars_repo_head_hexsha": "a0865fa20c992dc4159e79bb332500e3ff2357ae", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "code/pomp/pompstocsir.r", "max_issues_repo_name": "dbarrows/epidemic-forecasting", "max_issues_repo_head_hexsha": "a0865fa20c992dc4159e79bb332500e3ff2357ae", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "code/pomp/pompstocsir.r", "max_forks_repo_name": "dbarrows/epidemic-forecasting", "max_forks_repo_head_hexsha": "a0865fa20c992dc4159e79bb332500e3ff2357ae", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 23.6935483871, "max_line_length": 110, "alphanum_fraction": 0.5069208078, "num_tokens": 1643, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9219218348550491, "lm_q2_score": 0.8670357701094303, "lm_q1q2_score": 0.7993392080642465}} {"text": "# clean\nrm(list = ls())\n\n#setwd(\"Desktop/projects/r-projects/\")\n\n##########\n# Part 1 # Difference in Difference\n########## ========================\n\n# load csv file\nfastfood <- read.csv(\"fastfood.csv\", header = TRUE, row.names = NULL)\nfastfood\n\n# linear model, average difference between fast-food restaurants located \n# in NJ and Pennsylvania in terms of the number of full-time employees \nmodel1 = lm(formula = empft ~ state, data = fastfood)\nsummary(model1) #avg diff = -2.6006\n\n# Difference is not significant at 1% level because the p-value is 0.0188 (null hypothesis says \n# that this difference is 0) and it's greater than 0.01. So we CAN'T reject the null. But we do at 5%.\n\n# same for partial employees\nmodel2 = lm(formula = emppt ~ state, data = fastfood)\nsummary(model2)\n\n# same with wages\nmodel3 = lm(formula = wage_st ~ state, data = fastfood)\nsummary(model3)\n\n# avg starting wage (state=0) = 4.62863\n# avg starting wage (state=1) = b_0 + b_1*S = 4.62863 + (-0.02123)*1 = 4.60707\n# Can we reject the null hypothesis that the avg starting wage is the same in state=1 and state=0?\n# To be the same, b_1 must be 0. So..\n# No, we CAN'T because the p-value of null hypothesis (when b_1 = 0) is 0.638 (big for typical confidence levels)\n\n\n# taking into account pa1 y pa2 for full-time employment\nmodel4 = lm(formula = empft ~ state + pa1 + pa2, data = fastfood)\nsummary(model4) #error, not estimable because state, pa1 and pa2 are collinear\n\n# difference in difference\nmodel5 = lm(formula = empft2 - empft ~ state , data = fastfood)\nsummary(model5) # DiD = 3.443\n\n\n##########\n# Part 2 # Regression Discontinuity\n########## ========================\n\n# clean\nrm(list = ls())\n\n#install.packages(\"rdd\")\nlibrary(rdd)\n\n# load csv file\nindiv_final <- read.csv(\"indiv_final.csv\", header = TRUE, row.names = NULL)\n\n#if difshare > 0, then 1. Create dummy.\nindiv_final$positive_difshare <- as.numeric(indiv_final$difshare > 0)\nmean(indiv_final$positive_difshare)\n\nDCdensity(indiv_final$difshare, ext.out=TRUE)\n# Difference in the log estimate in heights at the cutpoint?\n# ext.out=TRUE to see all the calculated values.\n# log estimate = theta = -0.002470001\n#\n# p-value = 0.9620681 so we CAN'T reject the null (difference in cutoff is 0)\n\n\n# keep only the observations within 50 percentage points of the cutoff\n# this means diffshare between -0.5 and 0.5 (cutoff is 0 by default)\nsubset_indiv_final = subset(indiv_final, -0.5 < difshare & difshare < 0.5)\nDCdensity(subset_indiv_final$difshare, ext.out=TRUE)\n\n# create models to test\nmodel1 = lm(myoutcomenext ~ positive_difshare, \n data=subset_indiv_final)\n\nmodel2 = lm(myoutcomenext ~ positive_difshare + difshare, \n data=subset_indiv_final)\n\nmodel3 = lm(myoutcomenext ~ positive_difshare + difshare + positive_difshare*difshare, \n data=subset_indiv_final)\n\nmodel4 = lm(myoutcomenext ~ positive_difshare + difshare + I(difshare^2), \n data=subset_indiv_final)\n\nmodel5 = lm(myoutcomenext ~ positive_difshare + difshare + I(difshare^2) + \n positive_difshare*difshare + positive_difshare*I(difshare^2), \n data=subset_indiv_final)\n\nmodel6 = lm(myoutcomenext ~ positive_difshare + \n difshare + I(difshare^2)+ I(difshare^3), \n data=subset_indiv_final)\n\nmodel7 = lm(myoutcomenext ~ positive_difshare + \n difshare + I(difshare^2)+ I(difshare^3) + \n positive_difshare*difshare + positive_difshare*I(difshare^2) + positive_difshare*I(difshare^3), \n data=subset_indiv_final)\n\n# From model1 to model4 we see the effects of positive_difshare is greater than 0.6\n# All the models has a p-value (on positive_difshare) < 0.001 so we can reject the null at 99% level.\n# This means we cannot say there's no effect between positive_difshare and the outcome\n\n# estimate the effect non-parametrically. What is the point estimate?\nRDestimate(myoutcomenext ~ difshare, data=subset_indiv_final) #LATE = 0.4707\n# also returns estimates of half and double of the optimal bandwidth\n\n\n# plotting using different bandwith (from smaller to largest)\nsummary(RDestimate(myoutcomenext ~ difshare, data=subset_indiv_final)) #bandwidth = 0.11982\n\nbandwidth <- 0.11982\nm1 <- RDestimate(myoutcomenext ~ difshare, data=indiv_final, subset=abs(indiv_final$difshare) <= 0.5, bw = bandwidth/3) #other option: kernel=\"rectangular\"\nplot(m1)\nm2 <- RDestimate(myoutcomenext ~ difshare, data=indiv_final, subset=abs(indiv_final$difshare) <= 0.5)\nplot(m2)\nm3 <- RDestimate(myoutcomenext ~ difshare, data=indiv_final, subset=abs(indiv_final$difshare) <= 0.5, bw = 3*bandwidth)\nplot(m3)\n", "meta": {"hexsha": "d7805eaa1c7a13b846d22dcaa6192f1b452c99a1", "size": 4806, "ext": "r", "lang": "R", "max_stars_repo_path": "homework9.r", "max_stars_repo_name": "samuxiii/r-projects", "max_stars_repo_head_hexsha": "13a17bdf5a3db2efcf785c4810bb55c86459bfb3", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "homework9.r", "max_issues_repo_name": "samuxiii/r-projects", "max_issues_repo_head_hexsha": "13a17bdf5a3db2efcf785c4810bb55c86459bfb3", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "homework9.r", "max_forks_repo_name": "samuxiii/r-projects", "max_forks_repo_head_hexsha": "13a17bdf5a3db2efcf785c4810bb55c86459bfb3", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 5, "max_forks_repo_forks_event_min_datetime": "2019-06-24T17:18:38.000Z", "max_forks_repo_forks_event_max_datetime": "2020-07-22T03:39:37.000Z", "avg_line_length": 39.7190082645, "max_line_length": 156, "alphanum_fraction": 0.6839367457, "num_tokens": 1370, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9161096158798115, "lm_q2_score": 0.8723473746782093, "lm_q1q2_score": 0.7991658183302164}} {"text": "# <-- encoding UTF-8 -->\n# mathmematical tools\n# ------------------------------------\n## DOC STRING\n# easy math tools (e.g. Lorenz curve, Gini, Theil-I & II)\n# \n# all tools were developed by Tianhao Zhao and require less dependencies (actually, no extra package needed);\n# MIT license;\n# pls acknowledge him when using these functions;\n# \n# Tianhao Zhao (GitHub: Clpr)\n# Dec 2018\n# ------------------------------------\n\n\n\n\n# ------------------------------------\n## function: given x,y vectors, computes trapezium integral (lower & upper bound decided by x iteself); \n# return a real number INT; not support infinite integral; no dependency\nTrapeInt <- function(x,y){\n # get length, validation\n N <- if(length(x)==length(y)) length(x) else stop(\"x,y should have the same length\")\n # sort by x\n chk <- sort(x,index.return=TRUE)$ix\n x <- x[chk]; y <- y[chk]\n # loop and compute\n INT <- 0\n for(idx in 1:(N-1)){\n INT <- INT + 0.5 * ( y[idx+1]+y[idx] ) * ( x[idx+1]-x[idx] )\n }\n return(INT)\n}\n\n\n# ------------------------------------\n## function: compute y's Lorenz Curve & Gini value, sorted by x, weighted by w (popualtion, default all 1); y must be non-negative\nLorenzCurve <- function(y,x=y,w=1+vector(mode=\"numeric\",length=length(y))){\n # input:\n # 1. y: a numeric vector of income (or equivalent value)\n # 2. x: a numeric vector of factor; if y==x, Lorenz Curve & Gini, otherwise, Concentration Curve & Concentration Rate; by default, x == y\n # 3. w: a numeric vector of weights on y (frequencies of each element of y); by default, all 1 (each element of y is an individual but not a representation of a group)\n # output:\n # 1. list:\n # 1.1 LorenzX: X vector to plot Lorenz Curve (or Concentration Curve); in percentile measure, from 0 to 100\n # 1.2 LorenzY: Y vector to plot Lorenz Curve (or Concentration Curve); in percentile measure, from 0 to 100\n # 1.3 GiniIdx: real number in range [0,1]; the Gini index (or concentration index)\n # dependency:\n # 1. TrapeInt(): defined ad hoc, in this module; does trapezium integral for (x,y) pairs\n # -------------------\n # get length\n N <- if(all(y>=0)) length(y) else stop(\"y >=0 required\")\n # sorting & getting index (increasing)\n chk <- sort(x,index.return=TRUE)$ix\n # new y extended by w times\n y <- rep(y[chk],times=w)\n N <- length(y)\n # Lorenz curve (discrete), x in 1:100 (non-constant space), y=1:100(non-constant space)\n LorenzX <- c(0, (1:N)/N * 100) # add a 0 to make two lines(Lorenz & equality line) meet at 0)\n LorenzY <- c(0, cumsum(y) / sum(y) * 100 )\n # using trapezium integral to compute approximated Gini/concentration index\n GiniIdx <- 1 - TrapeInt(LorenzX,LorenzY)/5000\n # return\n return(list(LorenzX=LorenzX,LorenzY=LorenzY,GiniIdx=GiniIdx))\n}\n\n\n# ------------------------------------\n## function: compute non-negative y's Theil-T (a=1) & Theil-L (a=0) index, \nTheil <- function(y,w=1+vector(mode=\"numeric\",length=length(y)), Type = \"T\" ){\n # input:\n # 1. y: non-negative numeric vector, data to compute Theil index (individual-level data or grouped data with frequency w)\n # 2. w: weight/frequency vector\n # 3. Type: type of Theil index, \"T\" or \"L\" allowed (I & II)\n # output:\n # 1. a number, Theil index\n # dependency:\n # 1. NULL\n # ----------------\n # validation\n if(any(y<0)) stop(\"y>=0 required\")\n # expand to micro level data (replicate by population w)\n y <- rep(y,times=w)\n N <- length(y)\n # get Theil index\n ybar <- mean(y)\n if(Type == \"T\"){\n return( mean(y/ybar * log((1E-12) + y/ybar)) ) # a minor is added to avoid y = 0\n }else if(Type == \"L\"){\n return( mean( log((1E-12) + ybar / (y+(1E-12)) ) ) )\n }else{\n stop(\"invalid type of Theil index\")\n }\n # nomial return\n return(NULL)\n}\n\n\n\n# ------------------------------------\n## function: regular descriptive statistics for a dataframe (all variables are numeric)\nfunc_DescrStat <- function(tmpdf){\n return(data.frame(\n Variable = names(tmpdf),\n Observations = apply(tmpdf, 2, length ),\n Mean = apply(tmpdf, 2, mean ),\n Stdev = apply(tmpdf, 2, sd ),\n Min = apply(tmpdf, 2, min ),\n Q1 = apply(tmpdf, 2, quantile, probs = 0.25 ),\n Median = apply(tmpdf, 2, quantile, probs = 0.50 ),\n Q3 = apply(tmpdf, 2, quantile, probs = 0.75 ),\n Max = apply(tmpdf, 2, max )\n ))\n}\n\n\n\n\n\n\n\n\n\n# ------------------------------------\n# function: construct formula objects from Y's name and a vector of X candidates\n# NOTE: not support complex setting, e.g. instrumental variables\nfunc_GetEq <- function(Yname, Xnames, Intercept = TRUE, KeepStr = TRUE ){\n # input:\n # 1. Yname: a string, indicates Y\n # 2. Xnames: a char vec of X names\n # 3. Intercept: bool, indicates if to keep an intercept\n # 4. KeepStr: bool, if TRUE, returns a string formula, if FALSE, returns a formula instance\n # output：\n # 1. Eq: a formla instance\n # ----------\n Eq <- paste(Yname,\"~\", paste(collapse=\" + \",Xnames) )\n if(Intercept){\n Eq <- Eq\n }else{\n Eq <- paste(Eq,\"-1\")\n }\n if(KeepStr){\n return(Eq) \n }else{\n return(formula(Eq))\n }\n \n}\n\n\n\n\n\n\n\n\n# ---------------------------------------\n# function: convert class \"loadings\" to a titled matrix\n# NOTE: thanks: https://stackoverflow.com/questions/53825816/convert-a-loadings-object-to-a-dataframe-r\nfunc_Load2Mat <- function( obj ){\n # input\n # 1. obj: a \"loadings\" instance, usually be pcares$loadings, where pcares is a returned instance by prcomp() or psych::principal()\n # output\n # 1. mat: a numeric matrix (loading matrix), both row & col are named\n # ------------\n df <- data.frame(matrix(as.numeric(obj), attributes(obj)$dim, dimnames=attributes(obj)$dimnames))\n return(df)\n}\n\n\n\n\n\n\n", "meta": {"hexsha": "004be676ea39659c8920e1615d7cfb481d51d2cc", "size": 5900, "ext": "r", "lang": "R", "max_stars_repo_path": "src/mathtools.r", "max_stars_repo_name": "Clpr/HealthInequality2018Dec", "max_stars_repo_head_hexsha": "d88d80c97e46f3e0b10c2c15e83eb0932957e69d", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "src/mathtools.r", "max_issues_repo_name": "Clpr/HealthInequality2018Dec", "max_issues_repo_head_hexsha": "d88d80c97e46f3e0b10c2c15e83eb0932957e69d", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "src/mathtools.r", "max_forks_repo_name": "Clpr/HealthInequality2018Dec", "max_forks_repo_head_hexsha": "d88d80c97e46f3e0b10c2c15e83eb0932957e69d", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 33.7142857143, "max_line_length": 171, "alphanum_fraction": 0.5879661017, "num_tokens": 1700, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9273632856092016, "lm_q2_score": 0.86153820232079, "lm_q1q2_score": 0.7989588979820529}} {"text": "a <- c( 3.0, 4.0, 5.0)\nb <- c( 4.0, 3.0, 5.0)\n\ncross <- function(a, b)\n c(a[2]*b[3] - a[3]*b[2],\n a[3]*b[1] - a[1]*b[3],\n a[1]*b[2] - a[2]*b[1])\n\ncross(a, b)\n# [1] 5 5 -7\n", "meta": {"hexsha": "581fb5577624bb97bd4d839e61ffa9fe81fb4a9c", "size": 187, "ext": "r", "lang": "R", "max_stars_repo_path": "Task/Vector-products/R/vector-products.r", "max_stars_repo_name": "djgoku/RosettaCodeData", "max_stars_repo_head_hexsha": "91df62d46142e921b3eacdb52b0316c39ee236bc", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Task/Vector-products/R/vector-products.r", "max_issues_repo_name": "djgoku/RosettaCodeData", "max_issues_repo_head_hexsha": "91df62d46142e921b3eacdb52b0316c39ee236bc", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Vector-products/R/vector-products.r", "max_forks_repo_name": "djgoku/RosettaCodeData", "max_forks_repo_head_hexsha": "91df62d46142e921b3eacdb52b0316c39ee236bc", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 17.0, "max_line_length": 27, "alphanum_fraction": 0.3582887701, "num_tokens": 122, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9664104933824753, "lm_q2_score": 0.8267117898012104, "lm_q1q2_score": 0.798942948666897}} {"text": "HaversineDistance=function(lat1,lon1,lat2,lon2)\r\n{\r\n\r\n\t#returns the distance in km\r\n\tREarth<-6371\r\n\tlat<-abs(lat1-lat2)*pi/180\r\n\tlon<-abs(lon1-lon2)*pi/180\r\n\tlat1<-lat1*pi/180\r\n\tlat2<-lat2*pi/180\r\n\ta<-sin(lat/2)*sin(lat/2)+cos(lat1)*cos(lat2)*sin(lon/2)*sin(lon/2)\r\n\td<-2*atan2(sqrt(a),sqrt(1-a))\r\n\td<-REarth*d\r\n\r\n\treturn(d)\r\n\t\r\n}\r\n\r\nRMSE<-function(pre,real)\r\n{\r\n\treturn(sqrt(mean((pre-real)*(pre-real))))\r\n}\r\n\r\nmeanHaversineDistance<-function(lat1,lon1,lat2,lon2)\r\n{\r\n\treturn(mean(HaversineDistance(lat1,lon1,lat2,lon2)))\r\n}\r\n\r\n#USAGE\r\n#\r\n#FUNCTION PARAMETERS: @submission,@answers\r\n#@submission: path+filename containing the answers to submit in CSV format\r\n#@answers: path+filename containing the answers to evaluate the submission in CSV format\r\ntravelTime.PredictionEvaluation<-function(submission,answers)\r\n{\r\n\tdt<-read.csv(submission)\r\n\ttt_sub<-dt[,2]\r\n\tdt<-read.csv(answers)\r\n\ttt_real<-dt[,2]\r\n\treturn (RMSE(tt_sub,tt_real))\r\n}\r\n\r\n#USAGE\r\n#\r\n#FUNCTION PARAMETERS: @submission,@answers\r\n#@submission: path+filename containing the answers to submit in CSV format\r\n#@answers: path+filename containing the answers to evaluate the submission in CSV format\r\ndestinationMining.Evaluation<-function(submission,answers)\r\n{\r\n\tdt<-read.csv(submission)\r\n\tlat_sub<-dt[,2]\r\n\tlon_sub<-dt[,3]\r\n\tdt<-read.csv(answers)\r\n\tlat_real<-dt[,2]\r\n\tlon_real<-dt[,3]\r\n\treturn (meanHaversineDistance(lat_sub,lon_sub,lat_real,lon_real))\r\n}", "meta": {"hexsha": "baf790bcf034010f1579b567d397bf2b690f0847", "size": 1417, "ext": "r", "lang": "R", "max_stars_repo_path": "taxi_trajectory/rawdataset/evaluation_script.r", "max_stars_repo_name": "jiangss/mykaggle", "max_stars_repo_head_hexsha": "d9d880bc3bb482fb71960565cb0c351e89e8e6db", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-06-08T22:49:13.000Z", "max_stars_repo_stars_event_max_datetime": "2021-06-08T22:49:13.000Z", "max_issues_repo_path": "taxi_trajectory/rawdataset/evaluation_script.r", "max_issues_repo_name": "jiangss/mykaggle", "max_issues_repo_head_hexsha": "d9d880bc3bb482fb71960565cb0c351e89e8e6db", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "taxi_trajectory/rawdataset/evaluation_script.r", "max_forks_repo_name": "jiangss/mykaggle", "max_forks_repo_head_hexsha": "d9d880bc3bb482fb71960565cb0c351e89e8e6db", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 25.3035714286, "max_line_length": 89, "alphanum_fraction": 0.7155963303, "num_tokens": 413, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9658995703612219, "lm_q2_score": 0.8267117962054049, "lm_q1q2_score": 0.7985205687673547}} {"text": "polylongdiv <- function(n,d) {\n gd <- length(d)\n pv <- vector(\"numeric\", length(n))\n pv[1:gd] <- d\n if ( length(n) >= gd ) {\n q <- c()\n while ( length(n) >= gd ) {\n q <- c(q, n[1]/pv[1])\n n <- n - pv * (n[1]/pv[1])\n n <- n[2:length(n)]\n pv <- pv[1:(length(pv)-1)]\n }\n list(q=q, r=n)\n } else {\n list(q=c(0), r=n)\n }\n}\n\n# an utility function to print polynomial\nprint.polynomial <- function(p) {\n i <- length(p)-1\n for(a in p) {\n if ( i == 0 ) {\n cat(a, \"\\n\")\n } else {\n cat(a, \"x^\", i, \" + \", sep=\"\")\n }\n i <- i - 1\n }\n}\n\nr <- polylongdiv(c(1,-12,0,-42), c(1,-3))\nprint.polynomial(r$q)\nprint.polynomial(r$r)\n", "meta": {"hexsha": "a4e60ab668136a7ddd853cb4a61c38389c7f4b43", "size": 673, "ext": "r", "lang": "R", "max_stars_repo_path": "Task/Polynomial-long-division/R/polynomial-long-division.r", "max_stars_repo_name": "LaudateCorpus1/RosettaCodeData", "max_stars_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Polynomial-long-division/R/polynomial-long-division.r", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Polynomial-long-division/R/polynomial-long-division.r", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 19.2285714286, "max_line_length": 41, "alphanum_fraction": 0.4487369985, "num_tokens": 253, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9416541544761565, "lm_q2_score": 0.847967764140929, "lm_q1q2_score": 0.7984923679651634}} {"text": "## Sample size for equality of means\n## H_0: mu1=mu2\n## two normally distributed samples\n## of equal size (two-sided test)\n\nmu1 = 132.85\ns1 = 15.34\nmu2 = 127.44\ns2 = 18.23\nalpha = 0.05\npower = 0.8\n\n\nzalpha = qnorm(1-alpha/2,0,1)\nzbeta = qnorm(power,0,1)\nn = ((s1*s1 + s2*s2)*(zalpha+zbeta)^2)/(mu2-mu1)^2\n\n\n## -----------------------------------------------\n## Sample size needed to compare two binomial proportions\n## using a two-sided test where one sample is k times\n## as large as the other sample (independent samples)\n\np1 = 0.0015\np2 = 0.0012\nalpha = 0.05\npower = 0.8\nk = 1\n\nq1 = 1-p1\nq2 = 1-p2\nzalpha = qnorm(1-alpha/2,0,1)\nzbeta = qnorm(power,0,1)\np = (p1+k*p2)/(1+k)\nq = 1-p\n\nnum = sqrt(p*q*(1+1/k))*zalpha + sqrt(p1*q1+p2*q2/k)*zbeta\nn = num^2 / (p1-p2)^2\n\n\n## ------------------------------------------\n## Sample size estimation for the comparison of survival curves between\n## two groups under the Cox Proportional-Hazards Model\n## the ratio of participants in the experimental group to control is k\n\nhr = 0.7 ## hazards ratio\nk = 1 \npE = 0.3707\npC = 0.4890\nalpha = 0.05\npower = 0.8\n\nzalpha = qnorm(1-alpha/2,0,1)\nzbeta = qnorm(power,0,1)\nm = (1/k)*((k*hr+1)/(hr-1))^2*(zalpha+zbeta)^2\nn = m/(k*pE + pC)\n", "meta": {"hexsha": "444aea9ee1551f205954c8737ac8549a64121475", "size": 1216, "ext": "r", "lang": "R", "max_stars_repo_path": "sample-size.r", "max_stars_repo_name": "solislemuslab/sample-size-shinyapp", "max_stars_repo_head_hexsha": "5d85798dae4a3a5f07e57fe592b339561c88f2c0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "sample-size.r", "max_issues_repo_name": "solislemuslab/sample-size-shinyapp", "max_issues_repo_head_hexsha": "5d85798dae4a3a5f07e57fe592b339561c88f2c0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "sample-size.r", "max_forks_repo_name": "solislemuslab/sample-size-shinyapp", "max_forks_repo_head_hexsha": "5d85798dae4a3a5f07e57fe592b339561c88f2c0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 21.3333333333, "max_line_length": 71, "alphanum_fraction": 0.6027960526, "num_tokens": 465, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9683812318188366, "lm_q2_score": 0.8244619263765706, "lm_q1q2_score": 0.7983934558522744}} {"text": "# 4.2 b) Use R and plot {ψj, j = 0, . . . , 50} when the parameteres are given by (4.12) (X_t= MA(INF))\n#Consider a causal ARMA(2, 3)\n\nlibrary(itsmr)\nphi = c(1.7,-.9)\ntheta = c(-1.4,.8,.1)\nsigma2 = 1\n#Using a function to check for invertibility and causality\ncheck(list(phi=phi, theta=theta, sigma2 = sigma2))\n## Causal\n## Invertible\n#Checking roots of AR-polynomial\nMod(polyroot(c(1,-phi)))\n## [1] 1.054093 1.054093\n#Checking roots of MA-polynomial\nMod(polyroot(c(1,theta)))\n## [1] 1.022124 1.022124 9.571780\n\n\npsi = numeric(51)\npsi[1] = 1\npsi[2] = phi[1]+theta[1]\npsi[3] = phi[1]*psi[2]+phi[2]*psi[1]+theta[2]\npsi[4] = phi[1]*psi[3]+phi[2]*psi[2]+theta[3]\nfor(k in 5:51){\n psi[k] = phi[1]*psi[k-1]+phi[2]*psi[k-2]\n}\nplot(0:50,psi, xlab = \"k\", ylab = expression(psi[k]), type= \"b\")\n\n\n#4.3 c) \n#Implement the results in R, compute and plotf\n#(h); h = 0; : : : ; 50g with parameter\n#values given by (3). Check your calculations with help of an R-function.\n\nm = 50\nM = matrix(0, ncol=m+1,nrow=m+1)\ndiag(M) = 1\nM[2,2] = 1-phi[2]; M[1,2:3] = -phi; M[m+1,m] = -phi[1]\nfor(i in 1:(m-1)){\n M[seq(i+1,i+2),i] = -phi\n}\n\nM[1:5,1:5]\n## [,1] [,2] [,3] [,4] [,5]\n## [1,] 1.0 -1.7 0.9 0.0 0\n## [2,] -1.7 1.9 0.0 0.0 0\n## [3,] 0.9 -1.7 1.0 0.0 0\n## [4,] 0.0 0.9 -1.7 1.0 0\n## [5,] 0.0 0.0 0.9 -1.7 1\nM[(m-3):(m+1),(m-3):(m+1)]\n## [,1] [,2] [,3] [,4] [,5]\n## [1,] 1.0 0.0 0.0 0.0 0\n## [2,] -1.7 1.0 0.0 0.0 0\n## [3,] 0.9 -1.7 1.0 0.0 0\n## [4,] 0.0 0.9 -1.7 1.0 0\n## [5,] 0.0 0.0 0.9 -1.7 1\ns = c(1+theta[1]*psi[2]+theta[2]*psi[3]+theta[3]*psi[4],\ntheta[1]+theta[2]*psi[2]+theta[3]*psi[3],\ntheta[2]+theta[3]*psi[2],theta[3],rep(0,nrow(M)-4))\ngamma.h = solve(M,s)\nplot(0:m,gamma.h, col = 4, type = \"h\", xlab= \"h\", ylab = \"Autocovariance\")\n\n#4.5\n# Use R and draw the rectangle defined by (4.11) in a φ1φ2-coordinate system\nphi1 = seq(from = -2.5, to = 2.5, length = 51) \nplot(phi1,1+phi1,lty=\"dashed\",type=\"l\",xlab=\"\",ylab=\"\",cex.axis=.8,ylim=c(-1.5,1.5))\nabline(a = -1, b = 0, lty=\"dashed\")\nabline(a = 1, b = -1, lty=\"dashed\")\ntitle(ylab=expression(phi[2]),xlab=expression(phi[1]),cex.lab=.8)\npolygon(x = phi1[6:46], y = 1-abs(phi1[6:46]), col=\"gray\")\nlines(phi1,-phi1^2/4)\ntext(0,-.5,expression(phi[2]1-phi[1]),cex=.7)\ntext(-1.75,.5,expression(phi[2]>1+phi[1]),cex=.7)\n\n# 4.9 a)\ntheta = c(1.8, 0.9)\nMod(polyroot(c(1,theta)))\n#[1] 1.054093 1.054093\n# Hence invertible as roots larger than 1", "meta": {"hexsha": "bdaf09a53f3431b965241b9e75ed4410cf24f2e2", "size": 2429, "ext": "r", "lang": "R", "max_stars_repo_path": "hw4/hw4.r", "max_stars_repo_name": "emoen/Time_Series_stat211", "max_stars_repo_head_hexsha": "f30eb0c6a34c1eab8d347670c3b7a54f2c4c89c0", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2022-01-06T19:14:00.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-06T19:14:00.000Z", "max_issues_repo_path": "hw4/hw4.r", "max_issues_repo_name": "emoen/Time_Series_stat211", "max_issues_repo_head_hexsha": "f30eb0c6a34c1eab8d347670c3b7a54f2c4c89c0", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "hw4/hw4.r", "max_forks_repo_name": "emoen/Time_Series_stat211", "max_forks_repo_head_hexsha": "f30eb0c6a34c1eab8d347670c3b7a54f2c4c89c0", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-11-22T07:40:48.000Z", "max_forks_repo_forks_event_max_datetime": "2021-11-22T07:40:48.000Z", "avg_line_length": 29.987654321, "max_line_length": 103, "alphanum_fraction": 0.5751337999, "num_tokens": 1218, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9207896758909757, "lm_q2_score": 0.8670357494949105, "lm_q1q2_score": 0.7983575667633078}} {"text": "#Preliminaries\nrm(list=ls())\n\n#At an auction, bidders make offers to buy the goods,\n#and a bidder's valuation is how much the bidder offers to pay for the good.\n\n#Uniform Valuations\nnumber_of_bidders <- 2\nnumber_of_simulations <- 1000\n\nset.seed(1)\nvaluations1 <- matrix(runif(\n number_of_bidders * number_of_simulations, min=0, max=1),\n nrow = number_of_simulations\n)\n\n# Defining a price\n#\n# expected profit = price * P(Valuation_bidder >= price for at least one bidder)\n# P(V_bidder >= price) = 1 - CDF nth order statistic from U[0,1] evaluated at price\n# CDF of uniform [0,1] = price^number_of_bidders\n\n# expected_profit = price * (1 - price^number_of_bidders)\n# optimal price: derivative of expected_profit, setting equal to 0 and solving for price\noptimal_price <- (1/(number_of_bidders + 1))^(1/number_of_bidders)\n\n# So expected, optimal profit will be\nexpected_optimal_profit = (number_of_bidders/(number_of_bidders + 1)) * optimal_price\n\n###############\n# Another way # (posted price)\n###############\n\nN <- number_of_bidders\nV <- 1000\n\nset.seed(5) #use another random seed\nvaluations<- matrix(runif(\n N * V, min=0, max=1),\n nrow = V\n)\n\nmaximum_valuation <- apply(valuations, 1, max)\noptimal_price <- 1/((N+1)^(1/N))\nexpected_revenue_posted <- (N/(N+1) * optimal_price)\n\nrevenue <- optimal_price * (maximum_valuation >= optimal_price)\nmean(revenue)\nexpected_revenue_posted\n\n###################\n# English Auction #\n###################\n\n# last person wins the auction, so n-1st order statistic from U[0,1]\n# f(x) = N*(N-1)*(1-x)*x^(N-2) and with integral of f(x) we obtain\nexpected_profit_auction <- (N-1)/(N+1)\n\n####################\n# Comparison #\n####################\nrank_of_valuations <- apply(valuations, 1, rank)\nprice_auction <- apply(valuations, 1, function(x)\n(x[rank(x) == N - 1]))|\nexpected_revenue_auction <- (N-1)/(N+1)\n\nmean(price_auction)\nexpected_revenue_auction\n# IF N > 2, expected_profit_auction does better!!\n", "meta": {"hexsha": "edc5449daded52abce2a8da5f0c73857d34cb8c6", "size": 1943, "ext": "r", "lang": "R", "max_stars_repo_path": "auctions.r", "max_stars_repo_name": "samuxiii/r-projects", "max_stars_repo_head_hexsha": "13a17bdf5a3db2efcf785c4810bb55c86459bfb3", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "auctions.r", "max_issues_repo_name": "samuxiii/r-projects", "max_issues_repo_head_hexsha": "13a17bdf5a3db2efcf785c4810bb55c86459bfb3", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "auctions.r", "max_forks_repo_name": "samuxiii/r-projects", "max_forks_repo_head_hexsha": "13a17bdf5a3db2efcf785c4810bb55c86459bfb3", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 5, "max_forks_repo_forks_event_min_datetime": "2019-06-24T17:18:38.000Z", "max_forks_repo_forks_event_max_datetime": "2020-07-22T03:39:37.000Z", "avg_line_length": 27.7571428571, "max_line_length": 88, "alphanum_fraction": 0.683993824, "num_tokens": 565, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9407897492587141, "lm_q2_score": 0.847967764140929, "lm_q1q2_score": 0.797759380205617}} {"text": "## Author: Sergio García Prado\n## Title: Statistical Inference - Goodness of Fit - Exercise 20\n\n\nrm(list = ls())\n\nobserved <- c(1.5, 2.3, 4.2, 7.1, 10.4, 8.4, 9.3, 6.5, 2.5, 4.6)\n\n(k <- length(observed))\n# 10\n\n(lambda.hat <-1 / mean(observed))\n# 0.176056338028169\n\ntest <- ks.test(observed, pexp, rate = lambda.hat)\n\n(D <- test$statistic[[1]])\n# 0.232976217289659\n\n(criticvalue <- quantile(replicate(1000, ks.test(rexp(k, lambda.hat), pexp, rate = lambda.hat)$statistic), 0.95))\n# 0.4109577865723\n\nD > criticvalue\n# FALSE (H0 no refused)\n", "meta": {"hexsha": "e5eb04e9e4c389e527b5fb13cc8c9dff3d5c78b3", "size": 538, "ext": "r", "lang": "R", "max_stars_repo_path": "statistical-inference/goodness-of-fit/exercise-20.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "statistical-inference/goodness-of-fit/exercise-20.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "statistical-inference/goodness-of-fit/exercise-20.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 21.52, "max_line_length": 113, "alphanum_fraction": 0.656133829, "num_tokens": 210, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9621075690244281, "lm_q2_score": 0.828938806208442, "lm_q1q2_score": 0.7975282997112155}} {"text": "x=c(11.0,11.2,11.2,11.2,11.4,11.5,11.6,11.7,11.8,11.9,11.9,12.1,10.2,10.3,10.4,10.6,10.6,10.7,10.8,10.8,10.9,11.1,11.1,11.3)\r\ny=rank(x)\r\ncbind(x,y)\r\nrep(table(y), table(y))\r\nn1=12\r\nn2=12\r\nmut=n1*(n1+n2+1)/2\r\ns=((n1*n2)/12)*((n1+n2+1)-(48/((n1+n2)*(n1+n2-1))))\r\nsigmat=sqrt(s)\r\nT=216 # sum of ranks of before clean up values\r\nZ=(T-mut)/sigmat\r\nZ\r\n# This value exceeds 1.645, so we reject H0 and conclude that the distribution of before-cleanup measurements is shifted to the right of the corresponding distribution of after-cleanup measurements\r\n# part b\r\nsi=(n1*n2*(n1+n2+1))/n1\r\nsqrt(si)\r\n", "meta": {"hexsha": "be5913ed0144285e937bb86cfbffa1fc394a99c8", "size": 590, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH6/EX6.6/Ex6_6.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH6/EX6.6/Ex6_6.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH6/EX6.6/Ex6_6.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 34.7058823529, "max_line_length": 198, "alphanum_fraction": 0.6610169492, "num_tokens": 265, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9518632288833652, "lm_q2_score": 0.8376199613065411, "lm_q1q2_score": 0.7972996409464036}} {"text": "\n#acceptance ratio = g(u)/q(u*|ui-1) / g(ui-1)/q(ui-1|u*)\n\n#q = candidate drawing function \n\n# g(u) = posterior distribution \n#log(g(u)) = likeyhood*prior \nlg = function(yBar,n,mu){\n mu2 = mu^2\n n*(yBar*mu - mu2/2) - log (1+mu2)\n}\n\n\nmh = function(n, yBar, nIter, muInit, candSd){\n muOut = numeric(nIter)\n accept = 0 \n muNow = muInit\n lgNow = lg(mu=muNow, n=n, yBar=yBar)\n\n\n for (i in 1:nIter){\n #draw candidate from proposal distribution \n #q(u*|ui-1), using a normal distribution\n muCand = rnorm(1,mean=muNow,sd=candSd)\n\n #norm(mean=muNow,sd=candSd)/#norm(mean=muCand|sd=nowSd) -> cancles\n lgCand = lg(yBar=yBar,n=n,mu=muCand)\n lgNow = lg(yBar=yBar,n=n,mu=muNow)\n\n logAlpha = lgCand - lgNow\n\n alpha = exp(logAlpha)\n\n u = runif(1)\n #accept wiht proability alpha, rejects with probability 1-alpha\n if (u < alpha){\n muNow = muCand\n accept = accept + 1\n lgNow = lgCand\n }\n \n muOut[i] = muNow\n\n }\n list(mu=muOut,acceptRate=accept/nIter)\n}\n\n\n## Set up\n# y = c(1.2, 1.4, -0.5, 0.3, 0.9, 2.3, 1.0, 0.1, 1.3, 1.9)\ny = c(-0.2, -1.5, -5.3, 0.3, -0.8, -2.2)\n\n\nyBar = mean(y)\nn= length(y)\n\nhist(y, freq=FALSE, xlim=c(-1.0, 3.0))\npoints(y, rep(0.0, n))\npoints(yBar, 0.0, pch=19)\ncurve(dt(x, df=1), lty=2, add=TRUE)\n\n### posterior sampling \nset.seed(43)\n#want acceptance rate between .23 and .5 with randomwalk MH\npost = mh(n=n, yBar=yBar, nIter=1e3, muInit=1, candSd=1.5)\nstr(post) #find what's in object\n\nlibrary(\"coda\")\n\ntraceplot(as.mcmc(post$mu))\n\n\n### post analysis \npost$muKeep = post$mu[-c(1:100)]\nplot(density(post$muKeep), xlim=c(-1.0,3.0))\nmean(post$mu)\nplot(density(post$mu))", "meta": {"hexsha": "cd80528b457a4c5517869c3a67dab6827aa24aff", "size": 1732, "ext": "r", "lang": "R", "max_stars_repo_path": "montyCarlo/randomWalkMetropolisHastings.r", "max_stars_repo_name": "CharlieShelbourne/algos_practice", "max_stars_repo_head_hexsha": "bf32a739a9ab88f177461057fededb42e2d7fe10", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "montyCarlo/randomWalkMetropolisHastings.r", "max_issues_repo_name": "CharlieShelbourne/algos_practice", "max_issues_repo_head_hexsha": "bf32a739a9ab88f177461057fededb42e2d7fe10", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "montyCarlo/randomWalkMetropolisHastings.r", "max_forks_repo_name": "CharlieShelbourne/algos_practice", "max_forks_repo_head_hexsha": "bf32a739a9ab88f177461057fededb42e2d7fe10", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.4935064935, "max_line_length": 74, "alphanum_fraction": 0.5819861432, "num_tokens": 669, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.956634206181515, "lm_q2_score": 0.8333245911726382, "lm_q1q2_score": 0.7971868087679723}} {"text": "# Time series\n\ndata=read.csv(file=\"http://eric.univ-lyon2.fr/~jjacques/Download/DataSet/varicelle.csv\") \nplot(data$x)\n# We indicate to R the specificity of the timeseries (ts) object \nvaricelle<-ts(data$x,start=c(1931,1),end=c(1972,6),freq=12) \nplot(varicelle)\n\n\ninstall.packages(\"forecast\")\ninstall.packages(\"ggplot2\")\ninstall.packages(\"ffp\")\ninstall.packages(\"ffp2\")\nlibrary(forecast) \nlibrary(ggplot2) \nautoplot(varicelle) +\n ggtitle('Number of varicella per months')+ xlab('year')+\n ylab('Number of varicella')\n\nggseasonplot(varicelle,year.labels= TRUE,year.labels.left=TRUE)\n\nggseasonplot(varicelle,polar=TRUE)\n\nmean(varicelle)\nvar(varicelle)\n\ntmp=acf(varicelle,type=\"cov\",plot = FALSE) \ntmp$acf[1:3,1,1]\n\nplot(tmp)\n\n\ntmp=acf(varicelle,type=\"cor\",plot = FALSE) \ntmp$acf[1:3,1,1]\n\nplot(tmp)\n\nserie=2*(1:100)+4 \npar(mfrow=c(1,2)) \nplot(ts(serie)) \nacf(serie)\n\n\nserie=cos(2*pi/12*(1:100))\npar(mfrow=c(1,2)) \nplot(ts(serie)) \nacf(serie)\n\n\ntmp=pacf(varicelle,type=\"cor\",plot = FALSE) \ntmp$acf[1:3,1,1]\n\nplot(tmp)\n\nx=rep(0,41)\nfor (i in 0:40) \n x[i+1]<-sum(varicelle[(1+12*i):(12*(i+1))]) \nplot(x,type='l',xaxt='n',xlab='')\naxis(1,at = 0:40,labels = 1931:1971)\n\n\n#ex2\nplot.ts(co2)\n\nsanfran <-read.csv(file=\"http://eric.univ-lyon2.fr/~jjacques/Download/DataSet/sanfran.dat\", skip=1) \nView(sanfran)\nsanfran <- scan(file=\"http://eric.univ-lyon2.fr/~jjacques/Download/DataSet/sanfran.dat\", skip=1)\n\nplot(sanfran)\n\nplot(sanfran,type='l',xlim=c(1,120),ylim=c(1,80),xlab='time',ylab='')\n\ndata(\"AirPassengers\")\nautoplot(AirPassengers, series=\"Data\") + \n autolayer(ma(AirPassengers,6), series=\"6-MA\") + \n autolayer(ma(AirPassengers,12), series=\"12-MA\") + \n xlab(\"Year\") + \n ylab(\"AirPassengers concentration\") + \n ggtitle(\"AirPassengers\") + \n scale_colour_manual(values=c(\"Data\"=\"grey50\",\"6-MA\"=\"red\",\"12-MA\"=\"blue\"), breaks=c(\"Data\",\"6-MA\",\"12-MA\"))\n\nautoplot(decompose(AirPassengers,type=\"additive\"))+ xlab('Year')\n\nautoplot(decompose(AirPassengers,type=\"multiplicative\"))+ xlab('Year')\n\n# we can see that there is a dependancy in residuals (trend)\n\ntmp = decompose(co2)\nplot(tmp)\n\n# how to know there is a correlation between residuals? let's see autocorrelation\n\nacf(tmp$random[-which(is.na(tmp$random))])\n\n#there is a correlation in residuals \n\npacf(tmp$random[-which(is.na(tmp$random))])\n\n#still we can see there is autocorrelation if order 1, 3,4,5 etc \n\n\nair = decompose(AirPassengers)\nplot(air)\nacf(air$random[-which(is.na(air$random))])\npacf(air$random[-which(is.na(air$random))])\n#there is autocorrelation in residuals too\n\na= decompose(AirPassengers, type='multi')\n\nacf(a$random[-which(is.na(a$random))])\npacf(a$random[-which(is.na(a$random))])\n\n\ndata(\"AirPassengers\")\n\npar(mfrow=c(2,1))\nplot(AirPassengers) \nplot(diff(AirPassengers,differences=1))\n\npar(mfrow=c(2,1))\nplot(AirPassengers) \nplot(diff(AirPassengers,differences=2))\n\n\npar(mfrow=c(2,1))\nplot(AirPassengers) \nplot(diff(AirPassengers,lag=12,differences=1))\n\n\npar(mfrow=c(3,1))\nplot(AirPassengers) \nplot(diff(AirPassengers,lag=12,differences=1)) \nplot(diff(diff(AirPassengers,lag=12)))\n\nBox.test(diff(AirPassengers,lag=12,differences=1),lag=10,type=\"Ljung-Box\")\n\ninstall('fpp2')\nlibrary(fpp2)\nplot(goog200)\n\n\n#simulate an AR(p) AutoRegression of order p\npar(mfrow=c(3,1)) \nmodel<-list(ar=c(0.8)) \nar1<-arima.sim(model,5000) \nplot.ts(ar1)\nacf(ar1) \npacf(ar1)\n\n\n#simulate an MAq. Observe the auto-correlations (partial or not)\nmodele<-list(ma=c(2)) \nma1<-arima.sim(modele,1000) \nplot.ts(ma1)\nacf(ma1)\npacf(ma1)\n\n\n\n\nautoplot(uschange[,c(\"Income\",\"Unemployment\")])\n\nArima(uschange[,\"Income\"],order=c(2,0,2)) \nArima(uschange[,\"Unemployment\"],order=c(2,0,2))\n\nauto.arima(uschange[,\"Income\"])\nauto.arima(uschange[,\"Unemployment\"])\n\nautoplot(uschange[,\"Income\"]) +\n xlab(\"Year\") + ylab(\"Quarterly percentage change\")\n\nggAcf(uschange[,\"Income\"])\nggPacf(uschange[,\"Income\"])\n\nArima(uschange[,\"Income\"],order=c(0,0,0))\n\nArima(uschange[,\"Income\"],order=c(0,0,3))\n\nArima(uschange[,\"Unemployment\"],order=c(2,0,0))\nArima(uschange[,\"Unemployment\"],order=c(1,0,2))\n\n\nfit=Arima(uschange[,\"Income\"],order=c(0,0,0)) \nautoplot(forecast(fit,h=10))\n\nfit=Arima(uschange[,\"Unemployment\"],order=c(1,0,2)) \nautoplot(forecast(fit,h=10))\n", "meta": {"hexsha": "14f07e1120b124ea1a0bcd2ae11f03078a9eba58", "size": 4181, "ext": "r", "lang": "R", "max_stars_repo_path": "time series playground.r", "max_stars_repo_name": "milxss/R_and_stats", "max_stars_repo_head_hexsha": "67e6f7842e6a22adef636a0891f8681fc646b816", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "time series playground.r", "max_issues_repo_name": "milxss/R_and_stats", "max_issues_repo_head_hexsha": "67e6f7842e6a22adef636a0891f8681fc646b816", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "time series playground.r", "max_forks_repo_name": "milxss/R_and_stats", "max_forks_repo_head_hexsha": "67e6f7842e6a22adef636a0891f8681fc646b816", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.2393617021, "max_line_length": 109, "alphanum_fraction": 0.7067687156, "num_tokens": 1479, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9334308091776496, "lm_q2_score": 0.8539127529517043, "lm_q1q2_score": 0.7970684719548238}} {"text": "#1 ¿Qué es Estadística?\n\n# calculo de n_5\n0.0603*7614\n# 459.1242\n\n# calculo de n_7\n7614 - 145 - 2415 - 3456 - 852 - 459 - 157\n# 130\n\n# Frecuencias absolutas\nnj <- c(145, 2415, 3456, 852, 459, 157, 130)\n\n# Tamaño de la muestra\nn <- 7614\n\n# Sumar de las frecuencias absolutas\nsum(nj)\n\n# Numero de categorias\nm <- length(nj)\n\n# Frecuencias relativas\nhj <- nj/n\n\n# Nombres para la lista nj\nnames(nj) <- 0:6\n\n# grafico de barras de frecuencias absolutas\n# windows() Ejecución en RStudio (En RStudio server genera error)\nbarplot(\n height = nj, \n col = \"lightblue\", \n xlab = \"No. de piezas defectuosas\",\n ylab = \"Frecuencia absoluta\",\n main = \"Ejemplo 1\",\n border = \"blue\"\n )\n\n# grafico de frecuencias relativas \nhj <- prop.table(nj)\nbarplot(\n height = hj, \n col = \"lightblue\", \n xlab = \"No. de piezas defectuosas\",\n ylab = \"Frecuencia relativa\",\n main = \"Ejemplo 2\",\n border = \"blue\"\n )\n\n# EJEMPLO 2\n# datos\nedu <- c(\"B\", \"D\", \"M\", \"B\", \"B\", \"P\", \"B\", \"M\", \"B\", \"B\", \"B\", \"P\", \"B\", \"M\", \n \"B\", \"B\", \"M\", \"B\", \"M\", \"B\", \"B\", \"B\", \"B\", \"B\", \"B\", \"B\", \"P\", \"B\", \n \"B\", \"B\", \"B\", \"M\", \"B\", \"P\", \"B\", \"B\", \"M\", \"B\", \"B\", \"B\", \"D\", \"B\", \n \"M\", \"B\", \"P\", \"B\", \"B\", \"B\", \"P\", \"P\")\n# tamaño de la muestra\nn <- length(edu)\nprint(n)\n\n# frecuencias absolutas\nnj <- table(edu)\nnj <- nj[c(1, 4, 3, 2)]\nprint(nj)\n\n# Suma de las frecuencias absolutas\nsum(nj)\n\n# recuencias relativas\nhj <- nj/n\nprint(hj)\n\n# frecuencias asolutas acumuladas\nNj <- cumsum(nj)\nprint(Nj)\n\n# frecuencias relativas acumuladas\nHj <- cumsum(hj)\nprint(Hj)\n", "meta": {"hexsha": "b4ca4f72be1693dee87c38eb1501828895c90621", "size": 1545, "ext": "r", "lang": "R", "max_stars_repo_path": "01.introduccionEstadistica/01.IntroduccionEstadistica.r", "max_stars_repo_name": "devHectorGa/UNALProbabilidadEstadistica", "max_stars_repo_head_hexsha": "1cd472cc1b39daa8a9b81d40ec128d3d168af0a5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "01.introduccionEstadistica/01.IntroduccionEstadistica.r", "max_issues_repo_name": "devHectorGa/UNALProbabilidadEstadistica", "max_issues_repo_head_hexsha": "1cd472cc1b39daa8a9b81d40ec128d3d168af0a5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "01.introduccionEstadistica/01.IntroduccionEstadistica.r", "max_forks_repo_name": "devHectorGa/UNALProbabilidadEstadistica", "max_forks_repo_head_hexsha": "1cd472cc1b39daa8a9b81d40ec128d3d168af0a5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 19.3125, "max_line_length": 79, "alphanum_fraction": 0.5786407767, "num_tokens": 636, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9399133531922388, "lm_q2_score": 0.847967764140929, "lm_q1q2_score": 0.797016224592626}} {"text": "# Chapter 10 Lab 1: Principal Components Analysis\n\n# This code is quoted from\n# http://faculty.marshall.usc.edu/gareth-james/ISL/code.html\n\nstates=row.names(USArrests)\nstates\nnames(USArrests)\napply(USArrests, 2, mean)\napply(USArrests, 2, var)\npr.out=prcomp(USArrests, scale=TRUE)\nnames(pr.out)\npr.out$center\npr.out$scale\npr.out$rotation\ndim(pr.out$x)\nbiplot(pr.out, scale=0)\npr.out$rotation=-pr.out$rotation\npr.out$x=-pr.out$x\nbiplot(pr.out, scale=0)\npr.out$sdev\npr.var=pr.out$sdev^2\npr.var\npve=pr.var/sum(pr.var)\npve\nplot(pve, xlab=\"Principal Component\", ylab=\"Proportion of Variance Explained\", ylim=c(0,1),type='b')\nplot(cumsum(pve), xlab=\"Principal Component\", ylab=\"Cumulative Proportion of Variance Explained\", ylim=c(0,1),type='b')\na=c(1,2,8,-3)\ncumsum(a)\n\n\n# Chapter 10 Lab 2: Clustering\n\n# K-Means Clustering\n\nset.seed(2)\nx=matrix(rnorm(50*2), ncol=2)\nx[1:25,1]=x[1:25,1]+3\nx[1:25,2]=x[1:25,2]-4\nkm.out=kmeans(x,2,nstart=20)\nkm.out$cluster\nplot(x, col=(km.out$cluster+1), main=\"K-Means Clustering Results with K=2\", xlab=\"\", ylab=\"\", pch=20, cex=2)\nset.seed(4)\nkm.out=kmeans(x,3,nstart=20)\nkm.out\nplot(x, col=(km.out$cluster+1), main=\"K-Means Clustering Results with K=3\", xlab=\"\", ylab=\"\", pch=20, cex=2)\nset.seed(3)\nkm.out=kmeans(x,3,nstart=1)\nkm.out$tot.withinss\nkm.out=kmeans(x,3,nstart=20)\nkm.out$tot.withinss\n\n# Hierarchical Clustering\n\nhc.complete=hclust(dist(x), method=\"complete\")\nhc.average=hclust(dist(x), method=\"average\")\nhc.single=hclust(dist(x), method=\"single\")\npar(mfrow=c(1,3))\nplot(hc.complete,main=\"Complete Linkage\", xlab=\"\", sub=\"\", cex=.9)\nplot(hc.average, main=\"Average Linkage\", xlab=\"\", sub=\"\", cex=.9)\nplot(hc.single, main=\"Single Linkage\", xlab=\"\", sub=\"\", cex=.9)\ncutree(hc.complete, 2)\ncutree(hc.average, 2)\ncutree(hc.single, 2)\ncutree(hc.single, 4)\nxsc=scale(x)\nplot(hclust(dist(xsc), method=\"complete\"), main=\"Hierarchical Clustering with Scaled Features\")\nx=matrix(rnorm(30*3), ncol=3)\ndd=as.dist(1-cor(t(x)))\nplot(hclust(dd, method=\"complete\"), main=\"Complete Linkage with Correlation-Based Distance\", xlab=\"\", sub=\"\")\n\n\n# Chapter 10 Lab 3: NCI60 Data Example\n\n# The NCI60 data\n\nlibrary(ISLR)\nnci.labs=NCI60$labs\nnci.data=NCI60$data\ndim(nci.data)\nnci.labs[1:4]\ntable(nci.labs)\n\n# PCA on the NCI60 Data\n\npr.out=prcomp(nci.data, scale=TRUE)\nCols=function(vec){\n cols=rainbow(length(unique(vec)))\n return(cols[as.numeric(as.factor(vec))])\n }\npar(mfrow=c(1,2))\nplot(pr.out$x[,1:2], col=Cols(nci.labs), pch=19,xlab=\"Z1\",ylab=\"Z2\")\nplot(pr.out$x[,c(1,3)], col=Cols(nci.labs), pch=19,xlab=\"Z1\",ylab=\"Z3\")\nsummary(pr.out)\nplot(pr.out)\npve=100*pr.out$sdev^2/sum(pr.out$sdev^2)\npar(mfrow=c(1,2))\nplot(pve, type=\"o\", ylab=\"PVE\", xlab=\"Principal Component\", col=\"blue\")\nplot(cumsum(pve), type=\"o\", ylab=\"Cumulative PVE\", xlab=\"Principal Component\", col=\"brown3\")\n\n# Clustering the Observations of the NCI60 Data\n\nsd.data=scale(nci.data)\npar(mfrow=c(1,3))\ndata.dist=dist(sd.data)\nplot(hclust(data.dist), labels=nci.labs, main=\"Complete Linkage\", xlab=\"\", sub=\"\",ylab=\"\")\nplot(hclust(data.dist, method=\"average\"), labels=nci.labs, main=\"Average Linkage\", xlab=\"\", sub=\"\",ylab=\"\")\nplot(hclust(data.dist, method=\"single\"), labels=nci.labs, main=\"Single Linkage\", xlab=\"\", sub=\"\",ylab=\"\")\nhc.out=hclust(dist(sd.data))\nhc.clusters=cutree(hc.out,4)\ntable(hc.clusters,nci.labs)\npar(mfrow=c(1,1))\nplot(hc.out, labels=nci.labs)\nabline(h=139, col=\"red\")\nhc.out\nset.seed(2)\nkm.out=kmeans(sd.data, 4, nstart=20)\nkm.clusters=km.out$cluster\ntable(km.clusters,hc.clusters)\nhc.out=hclust(dist(pr.out$x[,1:5]))\nplot(hc.out, labels=nci.labs, main=\"Hier. Clust. on First Five Score Vectors\")\ntable(cutree(hc.out,4), nci.labs)\n\n\n", "meta": {"hexsha": "b1e1001366c2d8b7daaee1915265c0fec61366c1", "size": 3648, "ext": "r", "lang": "R", "max_stars_repo_path": "Chapter 10/R/Chapter 10.r", "max_stars_repo_name": "borisgarbuzov/schulich_data_science_1", "max_stars_repo_head_hexsha": "fd05ec2bbbe35408f90ebfcf10bb4ca588e7871c", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Chapter 10/R/Chapter 10.r", "max_issues_repo_name": "borisgarbuzov/schulich_data_science_1", "max_issues_repo_head_hexsha": "fd05ec2bbbe35408f90ebfcf10bb4ca588e7871c", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Chapter 10/R/Chapter 10.r", "max_forks_repo_name": "borisgarbuzov/schulich_data_science_1", "max_forks_repo_head_hexsha": "fd05ec2bbbe35408f90ebfcf10bb4ca588e7871c", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 6, "max_forks_repo_forks_event_min_datetime": "2020-10-25T05:26:50.000Z", "max_forks_repo_forks_event_max_datetime": "2021-07-07T08:25:58.000Z", "avg_line_length": 29.184, "max_line_length": 119, "alphanum_fraction": 0.7025767544, "num_tokens": 1319, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9099070084811307, "lm_q2_score": 0.8757869916479466, "lm_q1q2_score": 0.7968847216370721}} {"text": "#\n# Exemplo 1\n#\n\n# serie de maclaurin como função\n# que desenvolverá a série até ter\n# erro menor do que 0.001\nmaclaurin <- function(x) {\n n <- 0\n mac <- 0\n valor <- exp(x)\n while (abs(valor - mac) > 0.001) {\n termo <- (x^n) / factorial(n)\n mac <- mac + termo\n n <- n + 1\n }\n cat(\"Maclaurin=\", mac, \"Numero de interacoes=\", n, \"\\n\")\n}\n\n# ponto 1\nb <- 1\n# exponencial em b=1\nexp(b)\n# serie maclaurin em b=1\nmaclaurin(b)", "meta": {"hexsha": "2fc9854b8bff0ae78fb7672c2ee18088d38c4310", "size": 457, "ext": "r", "lang": "R", "max_stars_repo_path": "src/r/aula5/exemplo1.r", "max_stars_repo_name": "EduardoJM/anotacoes-matematica-aplicada", "max_stars_repo_head_hexsha": "75eaa8548ec01cc596e40dc4699fbef06001f20d", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "src/r/aula5/exemplo1.r", "max_issues_repo_name": "EduardoJM/anotacoes-matematica-aplicada", "max_issues_repo_head_hexsha": "75eaa8548ec01cc596e40dc4699fbef06001f20d", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "src/r/aula5/exemplo1.r", "max_forks_repo_name": "EduardoJM/anotacoes-matematica-aplicada", "max_forks_repo_head_hexsha": "75eaa8548ec01cc596e40dc4699fbef06001f20d", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 18.28, "max_line_length": 60, "alphanum_fraction": 0.5536105033, "num_tokens": 171, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9441768620069625, "lm_q2_score": 0.8438951005915208, "lm_q1q2_score": 0.7967862279395521}} {"text": "# Example : 3 Chapter : 2.5 Pageno : 83\n# Inverse of product of matrices\nE<-matrix(c(1,-5,0,0,1,0,0,0,1),ncol=3)\nE1<-solve(E)\nF<-matrix(c(1,0,0,0,1,-4,0,0,1),ncol=3)\nF1<-solve(F)\nprint(F1)\nFE<-F%*%E\nprint(FE)\nprint(\"Inverse of FE \")\nFE1<-solve(FE)\nprint(FE1)\nprint(\"Inverse of FE can also be E-1*F-1 \")\nprint(E1%*%F1)\n", "meta": {"hexsha": "905de16eed77b0fa42956bdf5290a259e133d743", "size": 322, "ext": "r", "lang": "R", "max_stars_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH2/EX2.5.3/Ex2.5_3.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH2/EX2.5.3/Ex2.5_3.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH2/EX2.5.3/Ex2.5_3.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 21.4666666667, "max_line_length": 43, "alphanum_fraction": 0.6242236025, "num_tokens": 155, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9416541561135442, "lm_q2_score": 0.8459424373085146, "lm_q1q2_score": 0.796585211924384}} {"text": "##########################################################################\n# github : https://github.com/jiankaiwang/DetailScience\n# classification : math\n# description : functions related to the combination of elements\n# \n# function description :\n# - getAllCombinationNumber\n# count all combinations without the permutation\n#\n# - getCombination :\n# return the combination set based on the order of the set\n# for example: the 3rd combination order from vector c(1,2,3,4,5) \n# as three elements in the set\n# 1st order : 1,2,3\n# 2nd order : 1,2,4\n# 3rd order : 1,2,5\n# the function would return c(1,2,5)\n# when the input collection is c('a','b','c','d','e'), \n# return would be c('a','b','e')\n#\n# - getRandomSet : \n# return a matrix conserving all combination set\n#\n# function usage :\n# - numeric getAllCombinationNumber(numeric cntEles, numeric eleInSet)\n# (1) cntEles (as integer) : count of total elements\n# (2) eleInSet (as integer) : count of elements selected in the set\n#\n# - vector getCombination(vector eleColl, numeric eleInSet, numeric setOrd)\n# (1) eleColl (as vector) : a collection with all elements\n# (2) eleInSet (as integer) : count of elements selected in the set\n# (3) setOrd (as integer) : the combination order\n#\n# - matrix getRandomSet(vector eleColl, numeric eleCountInSet, numeric getTtlSetNum, logical retByIndex)\n# (1) eleColl (as vector) : a collection with all elements\n# (2) eleCountInSet (as integer) : count of elements selected in the set\n# (3) getTtlSetNum (as integer) : total set count\n# (4) retByIndex (as bool) : return by index or name in the set\n#\n# function example :\n# - allCombNumber <- getAllCombinationNumber(80,4)\n# return 1581580\n#\n# - getEleSet <- getCombination(c('a','b','c','d','e'),3,7)\n# return c(\"b\" \"c\" \"d\")\n#\n# - getRandomSet(c('a','b','c','d','e'),3,2,FALSE)\n# [,1] [,2] [,3]\n# [1,] \"b\" \"c\" \"e\" \n# [2,] \"b\" \"c\" \"d\" \n##########################################################################\n\ngetAllCombinationNumber <- function(setNum, selectedNum) {\n leftNum <- min(setNum - selectedNum, selectedNum)\n res <- 1\n divNum <- 1\n for(i in setNum:(max(setNum - selectedNum, selectedNum)+1)) {\n res <- res * i\n if(res %% divNum == 0) {\n res <- res / divNum\n divNum <- divNum + 1\n }\n }\n divLeftNum <- 1\n if(divNum < leftNum) {\n for(i in divNum : leftNum) {\n divLeftNum <- divLeftNum * i\n }\n }\n return(res/divLeftNum)\n}\n\ngetCombination <- function(getSet, getNum, getWhichCombination) {\n # initial\n # as stack\n retList <- 1:getNum\n count <- 1\n countLast <- 0\n \n # others\n while(count < getWhichCombination) {\n # pop the last one\n popValue <- retList[length(retList)]\n retList <- retList[1:length(retList)-1]\n \n # get new value\n if(popValue + 1 <= length(getSet)) {\n if(countLast == 0) {\n retList <- c(retList,popValue + 1)\n } else {\n if(popValue + 1 == length(getSet)) {\n countLast <- countLast + 1\n next\n }\n retList <- c(retList, (popValue + 1) : (popValue + 1 + countLast))\n } \n \n # initial for next multiple pops\n countLast <- 0\n } else {\n countLast <- countLast + 1\n next\n }\n \n # count add 1\n count <- count + 1\n }\n \n return(getSet[retList])\n}\n\ngetRandomSet <- function(getSet, eleCountInSet, getTtlSetNum, retByIndex) {\n # check parameters\n if(getTtlSetNum > getAllCombinationNumber(length(getSet),eleCountInSet)) {\n return(\"getTtlSetNum is larger than all combination set count\")\n } else if (length(getSet) < eleCountInSet) {\n return(\"total elements in data set is smaller than the getTtlSetNum value\")\n }\n \n # as return matrix\n retSet <- matrix(c(1:eleCountInSet),nrow=1,ncol=eleCountInSet)\n \n tmpList <- c()\n tmpCheckFlag <- 0\n setIndex <- 1\n \n while(setIndex <= getTtlSetNum) {\n # initialization\n tmpList <- sort(sample(c(1:length(getSet)),eleCountInSet))\n tmpCheckFlag <- 0\n \n # check whether the same combination exists\n for(checkIndex in 1:nrow(retSet)) {\n if(length(which((retSet[checkIndex,] == tmpList) == TRUE)) == eleCountInSet) {\n tmpCheckFlag <- 1\n break\n }\n }\n \n if(tmpCheckFlag == 1) {\n # there is one combination same with new set\n next\n }\n \n if(retByIndex == TRUE) {\n retSet <- rbind(retSet, tmpList)\n } else {\n retSet <- rbind(retSet, getSet[tmpList])\n }\n \n setIndex <- setIndex + 1\n }\n \n # the first row is self-assigned for rbinding usage\n retSet <- retSet[-1,]\n \n if(is.numeric(retSet)) {\n return(matrix(retSet,nrow=nrow(retSet),ncol=eleCountInSet))\n } else {\n return(retSet)\n }\n}\n\n\n\n\n", "meta": {"hexsha": "77f356c0b5b23d127634470ea5360013f31468a6", "size": 4724, "ext": "r", "lang": "R", "max_stars_repo_path": "r/combination.r", "max_stars_repo_name": "jiankaiwang/seed", "max_stars_repo_head_hexsha": "b4c1438267a604503819983ef56d52567df2a5ff", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "r/combination.r", "max_issues_repo_name": "jiankaiwang/seed", "max_issues_repo_head_hexsha": "b4c1438267a604503819983ef56d52567df2a5ff", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "r/combination.r", "max_forks_repo_name": "jiankaiwang/seed", "max_forks_repo_head_hexsha": "b4c1438267a604503819983ef56d52567df2a5ff", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2019-01-02T11:02:58.000Z", "max_forks_repo_forks_event_max_datetime": "2019-01-02T11:02:58.000Z", "avg_line_length": 28.2874251497, "max_line_length": 104, "alphanum_fraction": 0.6052074513, "num_tokens": 1429, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9284087965937711, "lm_q2_score": 0.8577681049901036, "lm_q1q2_score": 0.7963594541103816}} {"text": "#R version 3.3.2 \n\ntotal_sum = 0\n \ntotal_list <- 1:999\n# Basic algo with O(n) speed\nfor (i in total_list) {\n if ((i %% 3 == 0) | (i %% 5 == 0)) {\n total_sum <- total_sum + i\n }\n}\n\nprint(total_sum)\n\n\ntotal_sum <- 0\n\ni <- 0\n# Improved algo with O(n/2)\nwhile (i < 997) {\n i <- i + 3\n total_sum <- total_sum + i\n}\n\ni <- 0\n\nwhile (i < 995) {\n i <- i + 5\n if (i %% 3 != 0) {\n total_sum <- total_sum + i\n }\n}\n\nprint(total_sum)\n\n# O(1) solution\nprint(((3*333*(333+1))/2) + ((5*199*(199+1))/2) - ((15*66*(66+1))/2))\n", "meta": {"hexsha": "ba1eda1dac9dfd67bf19037c1778aeb91e862e13", "size": 543, "ext": "r", "lang": "R", "max_stars_repo_path": "R/Problem1.r", "max_stars_repo_name": "ditekunov/projectEuler-research", "max_stars_repo_head_hexsha": "e8f84388045cdc1391d1e363c7b55ff4f85be708", "max_stars_repo_licenses": ["Unlicense"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2018-05-20T08:01:42.000Z", "max_stars_repo_stars_event_max_datetime": "2018-05-20T08:05:07.000Z", "max_issues_repo_path": "R/Problem1.r", "max_issues_repo_name": "ditekunov/ProjectEuler-asymptotics", "max_issues_repo_head_hexsha": "e8f84388045cdc1391d1e363c7b55ff4f85be708", "max_issues_repo_licenses": ["Unlicense"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/Problem1.r", "max_forks_repo_name": "ditekunov/ProjectEuler-asymptotics", "max_forks_repo_head_hexsha": "e8f84388045cdc1391d1e363c7b55ff4f85be708", "max_forks_repo_licenses": ["Unlicense"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 14.2894736842, "max_line_length": 69, "alphanum_fraction": 0.4917127072, "num_tokens": 217, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9304582477806521, "lm_q2_score": 0.855851154320682, "lm_q1q2_score": 0.7963337654102703}} {"text": "#################################\r\n# Example of Rejection Sampling\r\n#################################\r\n\r\nlibrary(ggplot2)\r\n\r\n# Define nasty function\r\nf <- function(x){ x^2/exp(x)}\r\nx <- seq(0,10,0.01)\r\n\r\nxmin <- 0\r\nxmax <- 10\r\n\r\nC <- 15 # garantees that envelope is always higher than f\r\n# Sample from envelop distribution\r\nrenvelope <- function(n){runif(n,xmin,xmax)}\r\ndenvelope <- function(x){C*dunif(x,xmin, xmax)}\r\n\r\ndf <- data.frame(x=x, f=f(x), q=denvelope(x))\r\ngg <- ggplot(df, aes(x=x)) + \r\n geom_line(aes(y=f, color=\"real\")) + \r\n geom_line(aes(y=q, color=\"envelop\")) +\r\n theme(legend.title=element_blank()) +\r\n ggtitle(\"real and envelop distribution\")\r\nprint(gg) \r\n\r\nnsamples <- 10000\r\n\r\n# Sample from envelop distribution\r\nsamples <- renvelope(nsamples)\r\n\r\n# Sample from uniform distribution\r\nu <- runif(nsamples)\r\n\r\naccept <- u < f(samples)/denvelope(samples)\r\naccept <- as.numeric(accept)\r\n\r\ndf = data.frame(sample = samples, accept = factor(accept, levels= c(1,0)))\r\n\r\ngg<- ggplot(df, aes(x=df$sample)) + \r\n geom_histogram(aes(fill = accept), binwidth=0.1) + \r\n ggtitle(\"Samples\")\r\n \r\nprint(gg)\r\n\r\ncat(\"Acceptance ratio:\", sum(accept)/length(accept))", "meta": {"hexsha": "bb49edab57bbfabcda18d36b48839e2c1aaa4c0d", "size": 1205, "ext": "r", "lang": "R", "max_stars_repo_path": "R_scripts/rejection_sampling.r", "max_stars_repo_name": "alumbreras/alumbreras.github.io", "max_stars_repo_head_hexsha": "e96049061ed6e087d6f98fb687cb2ccea9ed6f50", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R_scripts/rejection_sampling.r", "max_issues_repo_name": "alumbreras/alumbreras.github.io", "max_issues_repo_head_hexsha": "e96049061ed6e087d6f98fb687cb2ccea9ed6f50", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2020-02-26T10:06:36.000Z", "max_issues_repo_issues_event_max_datetime": "2022-02-26T01:39:09.000Z", "max_forks_repo_path": "R_scripts/rejection_sampling.r", "max_forks_repo_name": "alumbreras/alumbreras.github.io", "max_forks_repo_head_hexsha": "e96049061ed6e087d6f98fb687cb2ccea9ed6f50", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.1956521739, "max_line_length": 75, "alphanum_fraction": 0.6008298755, "num_tokens": 322, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9553191271831559, "lm_q2_score": 0.8333245932423308, "lm_q1q2_score": 0.7960909230765219}} {"text": "library(deSolve)\n\n\nseir_ode <- function(t,Y,par){\n S <- Y[1]\n E <- Y[2]\n I <- Y[3]\n R <- Y[4]\n \n beta <- par[1]\n sigma <- par[2]\n gamma <- par[3]\n mu <- par[4]\n \n dYdt <- vector(length=3)\n dYdt[1] = mu-beta*I*S-mu*S\n dYdt[2] = beta*I*S-(sigma+mu)*E\n dYdt[3] = sigma*E-(gamma+mu)*I\n \n return(list(dYdt))\n}\n\nbeta <- 520/365;\nsigma <- 1/60;\ngamma <- 1/30;\nmu <- 774835/(65640000*365) # UK birth and population figures 2016\ninit <- c(0.8,0.1,0.1)\nt <- seq(0,365)\npar <- c(beta,sigma,gamma,mu)\n\nsol <- lsoda(init,t,seir_ode,par)\n\n# Plot\nplot(t,sol[,2],type=\"l\",col=\"blue\",ylim=c(0,1),ylab=\"Proportion\")\nlines(t,sol[,3],col=\"orange\")\nlines(t,sol[,4],col=\"red\") \nlines(t,1-rowSums(sol[,2:4]),col=\"green\")\nlegend(300,0.7,legend=c(\"S\",\"E\",\"I\",\"R\"),col=c(\"blue\",\"orange\",\"red\",\"green\"), lty=1, cex=0.8)\n", "meta": {"hexsha": "74217627557ebe1631ec3475a2d68b056e5f69d2", "size": 825, "ext": "r", "lang": "R", "max_stars_repo_path": "models/simple_deterministic_models/seir/seir_desolve.r", "max_stars_repo_name": "epimodels/epicookbook", "max_stars_repo_head_hexsha": "496088ddc8fc913505d92877e0a687c81976c8f2", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "models/simple_deterministic_models/seir/seir_desolve.r", "max_issues_repo_name": "epimodels/epicookbook", "max_issues_repo_head_hexsha": "496088ddc8fc913505d92877e0a687c81976c8f2", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "models/simple_deterministic_models/seir/seir_desolve.r", "max_forks_repo_name": "epimodels/epicookbook", "max_forks_repo_head_hexsha": "496088ddc8fc913505d92877e0a687c81976c8f2", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2020-10-10T12:46:31.000Z", "max_forks_repo_forks_event_max_datetime": "2020-10-10T12:46:31.000Z", "avg_line_length": 21.1538461538, "max_line_length": 94, "alphanum_fraction": 0.5624242424, "num_tokens": 356, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9793540722737478, "lm_q2_score": 0.8128673087708699, "lm_q1q2_score": 0.7960849090629534}} {"text": "require(MASS)\nrbf=function(a,b,l,s=1)s*exp(-((a-b)^2) / (2*l^2))\ncov=function(x1,x2,K)sapply(x2,function(i)sapply(x1,function(j)K(i,j)))\n\nK = function(a,b)rbf(a,b,5)\n\nconditional = function(x1, x2, y2, K){ #x1,x2,y1,u1,u2 are all vectors\t\n\tK11 = cov(x1,x1,K)\n\tK12 = cov(x1,x2,K)\n\tK22_1 = solve(cov(x2,x2,K))\n\tK21 = cov(x2,x1,K)\n\t#mu = u1 + K12 %*% K22_1 %*% (y2 - u2)\n\tmu = K12 %*% K22_1 %*% (y2)\n\tsigma = K11 - K12 %*% K22_1 %*% K21 \n\tlist(sigma,mu,cbind(x2,y2))\n}\n\nrbfGP = function(obs, xs, l, s){\n\tK = function(a,b)rbf(a,b,l,s)\n\tx2 = obs[,1]\n\ty2 = obs[,2]\n\tconditional(xs,x2,y2,K)\n\t\n}\n\nplt = function(res,n,title=\"plt\"){\n\tr2=mvrnorm(n,res[[2]][,1],res[[1]])\n\tquantiles = apply(r2,2,function(i)quantile(i,probs=c(0.05,0.5,0.95)))\t\n\tylim = c(min(quantiles),max(quantiles))\n\tplot(quantiles[2,],xlab=\"GP Dimension\",ylab=\"Y\",ylim=ylim,type=\"l\", lty=2, lwd=2,col=\"red\",main=title)\n\tlines(quantiles[1,],col=\"blue\")\t\n\tlines(quantiles[3,],col=\"blue\")\n\tpoints(res[[3]],col=\"black\")\t\n}\n\npltdraws = function(x,rbfk,n,title){\n\tc1 = cov(x,x,rbfk)\n\tdraws = mvrnorm(n,rep(0,length(x)),c1)\n\tylim = c(min(draws),max(draws))\n\tplot(draws[1,],ylim=ylim,xlab=\"Dimension\",ylab=\"Y\",main=title)\n\tfor(i in 1:nrow(draws)){\n\t\tlines(draws[i,])\n\t}\n}\n\n#Plot random GP draws on an RBF kernel\nplt4GPs = function(){\n\tx = 1:50\n\trbf1 = function(a,b)rbf(a,b,1)\n\trbf5 = function(a,b)rbf(a,b,5)\n\trbf10 = function(a,b)rbf(a,b,10)\n\trbf20 = function(a,b)rbf(a,b,20)\n\tpar(mfrow=c(2,2))\n\tpltdraws(x,rbf1,10,\"L = 1\")\n\tpltdraws(x,rbf5,10,\"L = 5\")\n\tpltdraws(x,rbf10,10,\"L = 10\")\n\tpltdraws(x,rbf20,20,\"L = 20\")\n}\n\n#Fit GPs with defined kernels to data\nplt4FittedGPs = function(){\n\tx = 1:50\n\tobs = cbind(c(5,7,10,15,40),c(3.3,2.1,.5,-1,0))\n\tpar(mfrow=c(2,2))\n\tplt(rbfGP(obs,1:50,1,5),10000,title=\"L = 1\")\n\tplt(rbfGP(obs,1:50,5,5),10000,\"L = 5\")\n\tplt(rbfGP(obs,1:50,10,5),10000, \"L = 15\")\n\tplt(rbfGP(obs,1:50,20,5),10000, \"L = 20\")\n\t\n\t\n}\n\n\n", "meta": {"hexsha": "fc0ed45a465fdc32dbd82aa4fc4f7566312809f9", "size": 1893, "ext": "r", "lang": "R", "max_stars_repo_path": "assets/code/gProcess.r", "max_stars_repo_name": "joshuaar/joshuaar.github.com", "max_stars_repo_head_hexsha": "3a05e1550a3dfcd088dfc15a9fef539424ede2a9", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "assets/code/gProcess.r", "max_issues_repo_name": "joshuaar/joshuaar.github.com", "max_issues_repo_head_hexsha": "3a05e1550a3dfcd088dfc15a9fef539424ede2a9", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "assets/code/gProcess.r", "max_forks_repo_name": "joshuaar/joshuaar.github.com", "max_forks_repo_head_hexsha": "3a05e1550a3dfcd088dfc15a9fef539424ede2a9", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 25.5810810811, "max_line_length": 103, "alphanum_fraction": 0.6122556788, "num_tokens": 846, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.950410972802222, "lm_q2_score": 0.8376199714402812, "lm_q1q2_score": 0.7960832118951271}} {"text": "sample_size=c(5,4,6,5)\r\n#l1=y1bar-y3bar\r\n#l2=y1bar+y2bar+y3bar-3*y4bar\r\n# We can rewrite the contrasts in the following form:\r\n#l1=y1bar+0*y2bar-y3bar+0*y4bar\r\n#l2=l2=y1bar+y2bar+y3bar-3*y4bar\r\n# thus we identify a1 = 1, a2 = 0, a3 =-1, a4 = 0 and b1 =0, b2 = 1, b3 =0, b4 =-1\r\na=c(1,0,-1,0)\r\nb=c(1,1,1,-3)\r\ntest=0\r\ni=1\r\nwhile(i<=length(sample_size)){\r\n test=test+(a[i]*b[1])/sample_size[i]\r\n i=i+1\r\n}\r\nprint(test)\r\nif(test==0){\r\n print(\"hence the contrasts are orthogonal.\")\r\n}else{\r\n print(\"hence the contrasts are not orthogonal\")\r\n}\r\n# part b\r\nsample_size=5\r\na=c(1,0,-1,0)\r\nb=c(1,1,1,-3)\r\ntest=0\r\ni=1\r\nwhile(i<=4){\r\n test=test+(a[i]*b[1])/sample_size\r\n i=i+1\r\n}\r\nprint(test)\r\nif(test==0){\r\n print(\"hence the contrasts are orthogonal.\")\r\n}else{\r\n print(\"hence the contrasts are not orthogonal\")\r\n}\r\n\r\n", "meta": {"hexsha": "38f505c60bf278f94a64c175479b3782fbb0aae5", "size": 812, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH9/EX9.2/Ex9_2.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH9/EX9.2/Ex9_2.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH9/EX9.2/Ex9_2.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 20.8205128205, "max_line_length": 83, "alphanum_fraction": 0.6243842365, "num_tokens": 329, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9362850039701653, "lm_q2_score": 0.8499711832583696, "lm_q1q2_score": 0.7958152726915887}} {"text": "# nice but not suitable for big samples!\nmonteCarloPi <- function(samples) {\n x <- runif(samples, -1, 1) # for big samples, you need a lot of memory!\n y <- runif(samples, -1, 1)\n l <- sqrt(x*x + y*y)\n return(4*sum(l<=1)/samples)\n}\n\n# this second function changes the samples number to be\n# multiple of group parameter (default 100).\nmonteCarlo2Pi <- function(samples, group=100) {\n lim <- ceiling(samples/group)\n olim <- lim\n c <- 0\n while(lim > 0) {\n x <- runif(group, -1, 1)\n y <- runif(group, -1, 1)\n l <- sqrt(x*x + y*y)\n c <- c + sum(l <= 1)\n lim <- lim - 1\n }\n return(4*c/(olim*group))\n}\n\nprint(monteCarloPi(1e4))\nprint(monteCarloPi(1e5))\nprint(monteCarlo2Pi(1e7))\n", "meta": {"hexsha": "310861e44ddb1bc5764f27bc6959fb6accb16acd", "size": 696, "ext": "r", "lang": "R", "max_stars_repo_path": "Task/Monte-Carlo-methods/R/monte-carlo-methods.r", "max_stars_repo_name": "LaudateCorpus1/RosettaCodeData", "max_stars_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Monte-Carlo-methods/R/monte-carlo-methods.r", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Monte-Carlo-methods/R/monte-carlo-methods.r", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 24.8571428571, "max_line_length": 73, "alphanum_fraction": 0.617816092, "num_tokens": 247, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9511422158380862, "lm_q2_score": 0.8354835452961425, "lm_q1q2_score": 0.7946636705692331}} {"text": "## 2. Calculating expected values ##\n\nmales_over50k <- .67 * .241 * 32561\nmales_under50k <- .67 * .759 * 32561\nfemales_over50k <- .33 * .241 * 32561\nfemales_under50k <- .33 * .759 * 32561\n\n## 3. Calculating the chi-squared statistic ##\n\nchisq_gender_income <- 0\nobserved <- c(6662, 1179, 15128, 9592)\nexpected <- c(5257.6, 2589.6, 16558.2, 8155.6)\n\nfor (i in 1:length(observed)) {\n O <- observed[i]\n E <- expected[i]\n chisq_gender_income <- chisq_gender_income + (O - E)^2 / E\n}\n\n## 4. Calculating degrees of freedom ##\n\nr <- 2\nc <- 2\ndf <- (r - 1) * (c - 1)\n\n## 5. Calculating p-value ##\n\npvalue <- 1 - pchisq(1517, 1)\nreject_null <- TRUE\n\n## 6. R's built-in chi-squared test function ##\n\nlibrary(readr)\nincome <- read.csv(\"income.csv\")\nrace_education_table <- table(income$race, income$education)\nchisq.test(race_education_table)\nreject_null <- TRUE", "meta": {"hexsha": "7cc95a918e25b7633aaa854bcf74e0c8ecbc9bfc", "size": 860, "ext": "r", "lang": "R", "max_stars_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/5. Hypothesis Testing in R/4. Multi category chi-squared tests.r", "max_stars_repo_name": "MyArist/Dataquest", "max_stars_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 8, "max_stars_repo_stars_event_min_datetime": "2020-07-27T12:04:54.000Z", "max_stars_repo_stars_event_max_datetime": "2021-03-01T04:39:33.000Z", "max_issues_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/5. Hypothesis Testing in R/4. Multi category chi-squared tests.r", "max_issues_repo_name": "myarist/Dataquest", "max_issues_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/5. Hypothesis Testing in R/4. Multi category chi-squared tests.r", "max_forks_repo_name": "myarist/Dataquest", "max_forks_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 15, "max_forks_repo_forks_event_min_datetime": "2021-03-30T06:45:19.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-17T03:55:02.000Z", "avg_line_length": 23.2432432432, "max_line_length": 62, "alphanum_fraction": 0.6581395349, "num_tokens": 313, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9511422199928904, "lm_q2_score": 0.8354835411997897, "lm_q1q2_score": 0.7946636701442895}} {"text": "# Binomial logistic regression simulation code\n\n# Raymond Viviano\n# rayviviano@gmail.com\n# March 23, 2020\n\n\n#' Inverse Logit Function\ninv.logit <- function(p){\n return(exp(p)/(1+exp(p)))\n}\n\n\n#' Coverage Probability, i.e., the probability that the confidence interval (ci)\n#' for a parameter will contain the true value\n#' Inputs:\n#' b - Estimate\n#' se - Standard Error of the Estimate\n#' true - True value of parameter for data-generating process\n#' cl - Confidence level\n#' dof - Degrees of Freedom\n#' Output:\n#' List containing coverage probability, vect\ncoverage.prob <- function(b, se, true, cl=.95, dof=Inf){\n # Compute quantile based on confidence level\n coverage.quantile <- cl + (1-cl)/2\n\n # Compute confidence interval upper and lower bounds\n ci.lower <- b - qt(coverage.quantile, df=dof)*se\n ci.upper <- b + qt(coverage.quantile, df=dof)*se\n\n # For each ci generated for each b/se pair, eval if true param is in ci\n ci.contain.true <- ifelse(true>=ci.lower & true<=ci.upper, 1, 0)\n\n # Calculate coverage probability\n cp <- mean(ci.contain.true)\n\n # Calculate Monte Carlo Error\n mc.err.lower <- cp - 1.96*sqrt((cp*(1-cp))/length(b))\n mc.err.upper <- cp + 1.96*sqrt((cp*(1-cp))/length(b))\n\n # Return coverage probability and error\n return(list(cp=cp, ci=cbind(mc.err.lower, mc.err.upper)))\n}\n\n\n#' Power to detect any effect at various alpha levels\n#' Takes a vector of p-values and calculates the proportion of modell where the \n#' p-val for the effect of interest was < .5, .01, and .001.\npower.detect.effect <- function(p.val.vec){\n less.than.05 <- ifelse(p.val.vec < .05, 1, 0)\n prop.05 <- sum(less.than.05)/length(less.than.05)\n\n less.than.01 <- ifelse(p.val.vec < .01, 1, 0)\n prop.01 <- sum(less.than.01)/length(less.than.01)\n\n less.than.001 <- ifelse(p.val.vec < .001, 1, 0)\n prop.001 <- sum(less.than.001)/length(less.than.001)\n\n cat(paste0('Power to detect effect at .05: ', prop.05, '\\n'))\n cat(paste0('Power to detect effect at .01: ', prop.01, '\\n'))\n cat(paste0('Power to detect effect at .001: ', prop.001, '\\n'))\n}\n\n\n# Ensure reproducible results\nset.seed(10000)\n\n# Set logistic regression parameters (Can be calculated as log(oddsRatio))\nb0 <- .2 # Set Logistic Regression Intercept True Value\nb1 <- .5 # Set Logistic Regression Slope True Value \n\n# Define sample size\nn <- 16000\n\n# Define number of simulations\nnsims <- 20\n\n# Define matrix to hold simulation data (estimates, std.errors, and pvals)\nsim.prms <- matrix(NA, nrow=nsims, ncol=6)\n\n# Loop through simulations\nfor(i in 1:nsims){\n # Generate independant variable data, uniform random between -1 and 1\n x <- runif(n, -1, 1)\n\n # Generate true data-generation-process Bernoulli trials\n y <- rbinom(n, 1, inv.logit(b0 + b1*x))\n\n # Estimate logit model\n model <- glm(y~x, family=binomial(link=logit))\n\n # Get variance-covariance matrix\n var.covar <- vcov(model)\n\n # Put model paramters in simulation matrix\n sim.prms[i,1] <- model$coef[1] # Estimate for b0\n sim.prms[i,2] <- model$coef[2] # Estimate for b1\n sim.prms[i,3] <- sqrt(diag(var.covar)[1]) # b0 standard error\n sim.prms[i,4] <- sqrt(diag(var.covar)[2]) # b1 standard error\n sim.prms[i,5] <- summary(model)$coefficients[,4][1] # b0 pvalue\n sim.prms[i,6] <- summary(model)$coefficients[,4][2] # b1 pvalue\n}\n\n# Get Covarage probabilities for the parameters\nb0.coverage <- coverage.prob(sim.prms[,1], sim.prms[,3], b0, .95, n-model$rank)\nb1.coverage <- coverage.prob(sim.prms[,2], sim.prms[,4], b1, .95, n-model$rank)\n\n# Print intercept coverage probability and 95% confidence interval\nprint(\"Coverage Probability for b0\")\nprint(b0.coverage)\n\n# Print coefficent on x coverage probability and 95% confidence interval\nprint(\"Coverage Probability for b1\")\nprint(b1.coverage)\n\n# Power for intercept\ncat(\"Power to detect b0\\n\")\npower.detect.effect(sim.prms[,5])\n\ncat(\"\\nPower to detect b1\\n\")\n# Power for coefficient on x\npower.detect.effect(sim.prms[,6])", "meta": {"hexsha": "fe56cc7a93f31edf7ee8359595224b9a31480e1c", "size": 4118, "ext": "r", "lang": "R", "max_stars_repo_path": "scripts/logistic-regress-simulations.r", "max_stars_repo_name": "rviviano/data-tools", "max_stars_repo_head_hexsha": "97ab15584d01ac81ffe4349e337ed2d76a042ece", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "scripts/logistic-regress-simulations.r", "max_issues_repo_name": "rviviano/data-tools", "max_issues_repo_head_hexsha": "97ab15584d01ac81ffe4349e337ed2d76a042ece", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "scripts/logistic-regress-simulations.r", "max_forks_repo_name": "rviviano/data-tools", "max_forks_repo_head_hexsha": "97ab15584d01ac81ffe4349e337ed2d76a042ece", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 33.4796747967, "max_line_length": 80, "alphanum_fraction": 0.6610004857, "num_tokens": 1193, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9263037323284109, "lm_q2_score": 0.8577681031721325, "lm_q1q2_score": 0.7945537954406078}} {"text": "library(DescTools)\r\nx = c(0.90, 0.37, 1.63, 0.83, 0.95, 0.78, 0.86, 0.61, 0.38, 1.97)\r\ny = c(1.46, 1.45, 1.76 ,1.44, 1.11 ,3.07 ,0.98 ,1.27 ,2.56 ,1.32)\r\n \r\ncbind(c(x,y),rank(c(x,y)))\r\n\r\na <- wilcox.test(x,y,correct=FALSE,conf.int = TRUE)\r\nn1 <- length(x)\r\na$statistic <- a$statistic + n1*(n1+1)/2\r\nnames(a$statistic) <- \"T.W\"\r\na\r\n# T<83 so we reject H0 and conclude there is significant evidence that the placebo population has smaller reaction times than the population of alcohol consumers\r\n# p value calculated in book is wrong\r\n# confidence interval for delta (-1.08, -0.25)\r\n \r\n# 95% confidence interval for the placebo population median\r\nMedianCI(x,conf.level = 0.95,na.rm = FALSE, method = \"exact\",R = 10000)\r\n# # 95% confidence interval for the alcohol population median\r\nMedianCI(y,conf.level = 0.95,na.rm = FALSE, method = \"exact\",R = 10000) \r\n \r\n \r\n \r\n", "meta": {"hexsha": "69f10a1311f974d51e93880f97f57c901ae7d54a", "size": 904, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH6/EX6.5/Ex6_5.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH6/EX6.5/Ex6_5.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH6/EX6.5/Ex6_5.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 39.3043478261, "max_line_length": 163, "alphanum_fraction": 0.6316371681, "num_tokens": 319, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9407897525789547, "lm_q2_score": 0.8438950986284991, "lm_q1q2_score": 0.7939278610412982}} {"text": "########################\r\n# R Script for Class 6 #\r\n########################\r\n\r\n# t distribution\r\nx <- seq(-4, 4, length=100)\r\nhx <- dnorm(x)\r\n\r\ndegf <- c(1, 3, 8, 30)\r\ncolors <- c(\"red\", \"blue\", \"darkgreen\", \"gold\", \"black\")\r\nlabels <- c(\"t df=1\", \"t df=3\", \"t df=8\", \"t df=30\", \"normal\")\r\n\r\nplot(x, hx, type=\"l\", lty=2, xlab=\"x value\",\r\n ylab=\"Density\", main=\"Comparison of t and normal Distributions\")\r\n\r\nfor (i in 1:4){\r\n lines(x, dt(x,degf[i]), lwd=2, col=colors[i])\r\n}\r\n\r\nlegend(\"topright\",\r\n labels, lwd=2, lty=c(1, 1, 1, 1, 2), col=colors)\r\n\r\n\r\n# checking p-values\r\n1-pnorm(1.96)\r\n1-pt(1.96, 15)\r\n\r\n# loading data\r\nD = read.csv2('shoesize.csv')\r\nD\r\n\r\n\r\n# exploring height\r\nD$Height\r\nmean(D$Height)\r\nsd(D$Height)\r\nquantile(D$Height)\r\nhist(D$Height)\r\nplot(density(D$Height))\r\n\r\nsd(D$Height)/sqrt(408)\r\n\r\n\r\n# Assumming this data is a random sample of the full school populatio, what is our best estimate of the mean height of all students at this university? Provide a point estimate and 95% confidence interval.\r\n\r\n\r\n\r\n# Assumming this data is a random sample of the full school populatio, what is our best estimate of the mean shoe sizeght of all students at this university? Provide a point estimate and 95% confidence interval.\r\n\r\nhist(D$Size)\r\nmean(D$Size)\r\nsd(D$Size)\r\n\r\nmean(D$Size)+(2*(sd(D$Size)/sqrt(408)))\r\nmean(D$Size)-(2*(sd(D$Size)/sqrt(408)))\r\n\r\n\r\n# What is the relationship between height and shoe size?\r\n\r\nplot(D$Height, D$Size)\r\ncor(D$Height, D$Size)\r\n\r\n\r\nM = lm(D$Height~D$Size)\r\nsummary(M)\r\n\r\nM = lm(D$Height~D$Size+D$Gender)\r\nsummary(M)\r\n\r\nM = lm(D$Height~D$Size+D$Gender + D$Size*D$Gender )\r\nsummary(M)\r\n\r\n# family planning data\r\nlibrary(foreign)\r\nlibrary(calibrate)\r\n\r\nD = read.dta('effort.dta')\r\nhead(D)\r\n\r\nplot(change~effort, data=D, ylab=\"CBR change\", xlab=\"program effort\", pch=20, col=\"#000099dd\", cex=2)\r\n\r\nM = lm(change~effort, data=D)\r\nsummary(M)\r\n\r\nM = lm(change~effort+setting, data=D)\r\nsummary(M)", "meta": {"hexsha": "c15c5faf260919e7879a371d4930c7609cf0b51a", "size": 1946, "ext": "r", "lang": "R", "max_stars_repo_path": "r_demo_class6.r", "max_stars_repo_name": "JohnPalmer/global_studies_research_methods_2017", "max_stars_repo_head_hexsha": "5b6fdf01e2f862863bbae53050987c53d2ed794d", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "r_demo_class6.r", "max_issues_repo_name": "JohnPalmer/global_studies_research_methods_2017", "max_issues_repo_head_hexsha": "5b6fdf01e2f862863bbae53050987c53d2ed794d", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "r_demo_class6.r", "max_forks_repo_name": "JohnPalmer/global_studies_research_methods_2017", "max_forks_repo_head_hexsha": "5b6fdf01e2f862863bbae53050987c53d2ed794d", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.6279069767, "max_line_length": 212, "alphanum_fraction": 0.6305241521, "num_tokens": 609, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9525741281688026, "lm_q2_score": 0.8333245953120233, "lm_q1q2_score": 0.7938034498609708}} {"text": " ############################\n #FORECASTING AIRLINE DELAYS#\n ############################\n# PROBLEM 1 - LOADING THE DATA\nAirlines <- read.csv(\"AirlineDelay.csv\")\nset.seed(15071)\n\nspl = sample(nrow(Airlines), 0.7*nrow(Airlines))\n\nAirlinesTrain = Airlines[spl,]\n\nAirlinesTest = Airlines[-spl,]\n# How many observations are in the training set AirlinesTrain?\nstr(AirlinesTrain)\n# How many observations are in the testing set AirlinesTest?\nstr(AirlinesTest)\n\n# PROBLEM 2 - METHOD OF SPLITTING THE DATA\n# In this class, we have frequently used the sample.split function to randomly split our data. \n# Why do we use a different approach here?\n# Review help(sample.split) of caTools package to find the answer\n \n# PROBLEM 3 - A LINEAR REGRESSION MODEL \n# Build a linear regression model to predict \"TotalDelay\"\nlinFit <- lm(TotalDelay ~ ., data=AirlinesTrain)\n# What is the model's R-squared? \nsummary(linFit)\n\n#PROBLEM 4 - CHECKING FOR SIGNIFICANCE \n# In your linear regression model, which of the independent variables are significant at the\n# p=0.05 level (at least one star)? \nsummary(linFit)\n\n# PROBLEM 5 - CORRELATIONS \n# What is the correlation between NumPrevFlights and PrevFlightGap in the training set?\ncor(AirlinesTrain$NumPrevFlights,AirlinesTrain$PrevFlightGap)\n# What is the correlation between OriginAvgWind and OriginWindGust in the training set?\ncor(AirlinesTrain$OriginAvgWind,AirlinesTrain$OriginWindGust)\n\n# PROBLEM 6 - IMPORTANCE OF CORRELATIONS\n# Why is it imporant to check for correlations between independent variables? Select all that apply.\n# Read article on \"multicollinearity\" to answer the quiz\n\n# PROBLEM 7 - COEFFICIENTS \n# In the model with all of the available independent variables, what is the coefficient for HistoricallyLate?\ncoef(linFit)\n\n# PROBLEM 8 - UNDERSTANDING THE COEFFICIENTS\n# The coefficient for NumPrevFlights is 1.56. What is the interpretation of this coefficient?\n# Read article on \"Coefficient of determination\" to answer the quiz\n\n# PROBLEM 9 - UNDERSTANDING THE MODEL\n# In the linear regression model, given two flights that are otherwise identical, what is the absolute\n# difference in predicted total delay given that \n# -one flight is on Thursday and the other is on Sunday?\n# -one flight is on Saturday and the other is on Sunday?\n# The absolute difference between the coefficients of two dates is the predicted delay\n\n# PROBLEM 10 - PREDICTIONS ON THE TEST SET \n# What is the Sum of Squared Errors (SSE) on the test set?\npredictions <- predict(linFit, newdata=AirlinesTest)\n# What is the Total Sum of Squares (SST) on the test set?\nSSE <- sum((AirlinesTest$TotalDelay - predictions)^2)\n# What is the R-squared on the test set?\nSST <- sum((AirlinesTest$TotalDelay - mean(AirlinesTrain$TotalDelay))^2)\n1-SSE/SST\n\n# PROBLEM 11 - EVALUATING THE MODEL\n# Given what you have seen about this model (the R-squared on the training and test sets, the \n# significance of the coefficients, etc.), which of the following are true?\n# Eliminate wrong choices. Read article on \"R-squared\" to answer the question\n\n# PROBLEM 12 - A CLASSIFICATION PROBLEM\nAirlines$DelayClass = factor(ifelse(Airlines$TotalDelay == 0, \"No Delay\", ifelse\n (Airlines$TotalDelay >= 30, \"Major Delay\", \"Minor Delay\")))\n# How many flights in the dataset Airlines had no delay, minor delay, major delay respectively?\nsummary(Airlines$DelayClass)\nAirlines$TotalDelay = NULL\n# Prepare necessary data for CART model\nlibrary(caTools)\nset.seed(15071)\nsplit <- sample.split(Airlines$DelayClass, SplitRatio=0.7)\nAirlinesNewTrain <- subset(Airlines, split==T)\nAirlinesNewTest <- subset(Airlines, split==F)\n\n# PROBLEM 13 - A CART MODEL\nlibrary(rpart)\nlibrary(rpart.plot)\ncart <- rpart(DelayClass ~., data=AirlinesNewTrain, method=\"class\")\n# How many split are in the resulting tree?\nprp(cart)\n\n# PROBLEM 14 - UNDERSTANDING THE MODEL \n# The CART model you just built never predicts one of the three outcomes. Which one?\nprp(cart)\n\n# PROBLEM 15 - TRAINING SET ACCURACY\nlibrary(caret)\n# Make predictions on the training set, and then create a confusion matrix. \n# What is the overall accuracy of the model?\ncartTrainPredicts <- predict(cart, AirlinesNewTrain, type=\"class\")\nconfusionMatrix(AirlinesNewTrain$DelayClass, cartTrainPredicts)\n\n# PROBLEM 16 - A BASELINE MODEL\n# What is the accuracy on the training set of a baseline model that predicts the most \n# frequent outcome (No Delay) for all observations?\nobs <- max(table(AirlinesNewTrain$DelayClass))\nobs/nrow(AirlinesNewTrain)\n\n# PROBLEM 17 - TESTING SET ACCURACY \n# Make predictions on the testing set, and then create a confusion matrix. What is the \n# overall accuracy of the model on the testing set?\ncartTestPredicts <- predict(cart, newdata=AirlinesNewTest, type=\"class\")\nconfusionMatrix(AirlinesNewTest$DelayClass, cartTestPredicts)\n", "meta": {"hexsha": "91b2e640577cff64224f7cd07dbae956db79d4e5", "size": 5039, "ext": "r", "lang": "R", "max_stars_repo_path": "final/AirlineDelay.r", "max_stars_repo_name": "graphito0/15.071x-The-Analytics-Edge", "max_stars_repo_head_hexsha": "3c09e1d154f3786f6cb24e45a949b2424b5d8fc3", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 8, "max_stars_repo_stars_event_min_datetime": "2016-04-20T18:44:41.000Z", "max_stars_repo_stars_event_max_datetime": "2021-07-09T13:36:48.000Z", "max_issues_repo_path": "final/AirlineDelay.r", "max_issues_repo_name": "graphito0/15.071x-The-Analytics-Edge", "max_issues_repo_head_hexsha": "3c09e1d154f3786f6cb24e45a949b2424b5d8fc3", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "final/AirlineDelay.r", "max_forks_repo_name": "graphito0/15.071x-The-Analytics-Edge", "max_forks_repo_head_hexsha": "3c09e1d154f3786f6cb24e45a949b2424b5d8fc3", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 25, "max_forks_repo_forks_event_min_datetime": "2015-05-28T13:32:41.000Z", "max_forks_repo_forks_event_max_datetime": "2021-01-05T03:51:03.000Z", "avg_line_length": 43.8173913043, "max_line_length": 109, "alphanum_fraction": 0.7297082755, "num_tokens": 1223, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9173026618464796, "lm_q2_score": 0.8652240947405565, "lm_q1q2_score": 0.7936723651992231}} {"text": "#install.packages(\"GA\")\nlibrary(GA)\n\n# https://cran.r-project.org/web/packages/GA/vignettes/GA.html#constrained-optimisation\n# Townsend function (modified)\n# https://en.wikipedia.org/wiki/Test_functions_for_optimization\nfunc3d <- function(x)\n{\n -(cos((x[1]-0.1)*x[2]))^2-x[1]*sin(3*x+x[2])\n}\n\nc1 <- function(x)\n{\n t <- atan2(x[1], x[2])\n x[1]^2+x[2]^2-(2*cos(t)-1/2*cos(2*t)-1/4*cos(3*t)-1/8*cos(4*t))^2-(2*sin(t))^2\n}\n\nx1LBound <- -2.25\nx1RBound <- 2.25\nx2LBound <- -2.5\nx2RBound <- 1.75\n\nngrid <- 20 # 250\nnLevels <- 5\nx1 <- seq(x1LBound, x1RBound, length = ngrid)\nx2 <- seq(x2LBound, x2RBound, length = ngrid)\nx12 <- expand.grid(x1, x2)\ncol <- adjustcolor(bl2gr.colors(4)[2:3], alpha = 0.2)\nplot(x1, x2, type = \"n\", xaxs = \"i\", yaxs = \"i\")\nimage(x1, x2, matrix(ifelse(apply(x12, 1, c1) <= 0, 0, NA), ngrid, ngrid), col = col[1], add = TRUE)\ncontour(x1, x2, matrix(apply(x12, 1, func3d), ngrid, ngrid), nlevels = nLevels, add = TRUE)\n\nfitness <- function(x)\n{\n f <- -func3d(x) # we need to maximise -func3d(x)\n pen <- sqrt(.Machine$double.xmax) # penalty term\n penalty1 <- max(c1(x),0)*pen # penalisation for 1st inequality constraint\n f - penalty1 # fitness function value\n}\n\nGA <- ga(\"real-valued\", fitness = fitness,\n lower = c(x1LBound, x2LBound), upper = c(x1RBound, x2RBound),\n # selection = GA:::gareal_lsSelection_R,\n maxiter = 10000, run = 5000) # seed = 123)\nsummary(GA)\nplot(GA)\n\nfitness(GA@solution)\nfunc3d(GA@solution)\nc1(GA@solution)\n\nplot(x1, x2, type = \"n\", xaxs = \"i\", yaxs = \"i\")\nimage(x1, x2, matrix(ifelse(apply(x12, 1, c1) <= 0, 0, NA), ngrid, ngrid), col = col[1], add = TRUE)\ncontour(x1, x2, matrix(apply(x12, 1, func3d), ngrid, ngrid), nlevels = nLevels, add = TRUE)\npoints(GA@solution[1], GA@solution[2], col = \"dodgerblue3\", pch = 3) # GA solution\n", "meta": {"hexsha": "3f2bf4e249aa8446334817a7ef21d125730588f3", "size": 1856, "ext": "r", "lang": "R", "max_stars_repo_path": "R/ga/func/3d/with_bounds_formula/ga_minimum_of_3d_townsend_func_formula_bounds.r", "max_stars_repo_name": "reyzeer/algorytmy-genetyczne", "max_stars_repo_head_hexsha": "c8803dd19dd5105d35b287fa13efdc130531403f", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/ga/func/3d/with_bounds_formula/ga_minimum_of_3d_townsend_func_formula_bounds.r", "max_issues_repo_name": "reyzeer/algorytmy-genetyczne", "max_issues_repo_head_hexsha": "c8803dd19dd5105d35b287fa13efdc130531403f", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/ga/func/3d/with_bounds_formula/ga_minimum_of_3d_townsend_func_formula_bounds.r", "max_forks_repo_name": "reyzeer/algorytmy-genetyczne", "max_forks_repo_head_hexsha": "c8803dd19dd5105d35b287fa13efdc130531403f", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 33.1428571429, "max_line_length": 100, "alphanum_fraction": 0.619612069, "num_tokens": 721, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9252299632771662, "lm_q2_score": 0.8577681068080749, "lm_q1q2_score": 0.7936327539623595}} {"text": "######################################################################\n# Ratfor program to display emirps\n######################################################################\n\n######### Test if a number is prime #########\nlogical function prime(n)\n integer n # Number to test\n\n # Deal with numbers <= 3\n if (n < 1) goto 200\n if (n == 2 | n == 3) goto 100\n\n # Check if divisible by 2 or 3\n if (mod(n,2) == 0) goto 200\n if (mod(n,3) == 0) goto 200\n \n # See if divisible by 5, 7, ..., up to approx sqrt(n)\n for (i = 5; i < 1000000; i = i + 2) { \n if (I*I > n) goto 100\n if (mod(n,i) == 0) goto 200\n }\n\n 100 prime = .true.\n return\n 200 prime = .false.\n return\nend\n\n######### Reverse an integer's digits #########\ninteger function revrse(n)\n integer n # Number to reverse\n integer m # Copy of n from which we take digits\n integer r # Reversed digits\n m = n\n r = 0\n while (m >= 1) {\n # Take last digit from m and append to r\n r = r * 10\n r = r + mod(m, 10)\n m = m / 10\n }\n revrse = r\n return\nend\n\n######### Test if an integer is an emirp #########\nlogical function emirp(n)\n integer n # Number to test\n integer revrse # External function\n logical prime # External function\n integer r # Reversed digits of n\n r = revrse(n)\n emirp = .false.\n # n and r must both be prime and not the same value\n if (n .ne. r & prime(n) & prime(r)) {\n emirp = .true.\n }\n return\nend\n\n######### Display an integer #########\nsubroutine show(n)\n integer n\n write(6,50) n\n50 format(i10)\n return\nend\n\n######### Show first 20 emirps #########\nsubroutine test1\n logical emirp # External function\n integer i # Count of emirps found\n integer n # Number to test\n n = 0\n for (i = 1; i <= 20; i = i + 1) {\n repeat {\n n = n + 1\n } until (emirp(n))\n call show(n)\n }\n return\nend\n\n######### Show emirps between 7,700 and 8,000 #########\nsubroutine test2\n logical emirp # External function\n integer n # Number to test\n for (n = 7700; n <= 8000; n = n + 1) {\n if (emirp(n)) {\n call show(n)\n }\n }\n return\nend\n\n######### Show 10,000th emirp #########\nsubroutine test3\n logical emirp # External function\n integer i # Count of emirps found\n integer n # Number to test\n n = 0\n for (i = 1; i <= 10000; i = i + 1) {\n repeat {\n n = n + 1\n } until (emirp(n))\n }\n call show(n)\n return\nend\n\n######### Main entry point #########\ncall test1\ncall test2\ncall test3\nstop\nend\n", "meta": {"hexsha": "42ed4b4dd1ce7bc0517848dd9dd5cca587dfb873", "size": 2677, "ext": "r", "lang": "R", "max_stars_repo_path": "ratfor/emirp.r", "max_stars_repo_name": "rupertl/mts-languages", "max_stars_repo_head_hexsha": "ae0a82d54479b098f9627e4400c08895a4e6e2bb", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 7, "max_stars_repo_stars_event_min_datetime": "2017-10-30T17:51:34.000Z", "max_stars_repo_stars_event_max_datetime": "2020-11-23T00:39:28.000Z", "max_issues_repo_path": "ratfor/emirp.r", "max_issues_repo_name": "rupertl/mts-languages", "max_issues_repo_head_hexsha": "ae0a82d54479b098f9627e4400c08895a4e6e2bb", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "ratfor/emirp.r", "max_forks_repo_name": "rupertl/mts-languages", "max_forks_repo_head_hexsha": "ae0a82d54479b098f9627e4400c08895a4e6e2bb", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2019-04-10T20:01:54.000Z", "max_forks_repo_forks_event_max_datetime": "2019-04-10T20:01:54.000Z", "avg_line_length": 22.8803418803, "max_line_length": 70, "alphanum_fraction": 0.4856182294, "num_tokens": 821, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9230391643039738, "lm_q2_score": 0.8596637469145054, "lm_q1q2_score": 0.7935033065343879}} {"text": "### 線形判別分析(2値判別)の例\n### - Biopsy Data on Breast Cancer Patients\n\n## データの読み込み (\"MASS::biopsy\"を用いる)\nrequire(MASS) # パッケージの読み込み (lda/biopsy)\nrequire(tidyverse) \nrequire(ggfortify)\nrequire(GGally)\nrequire(plotROC)\n\n## データの内容を表示\nhelp(biopsy) # 内容の詳細を表示\n## print(biopsy) # データの表示\nhead(biopsy) # 最初の6個を表示\ntail(biopsy) # 最後の6個を表示\n\n## データの散布図: 図(a)\nmydata <- na.omit(biopsy)[-1] # NA，および患者のIDを除く\nggpairs(mydata, lower=list(mapping=aes(colour=class)))\n## ## ggscatmat でも似たことはできるが数値データの散布図のみ\n## ggscatmat(mydata, color=\"class\", alpha=.8) # colour ではない\n\n## 主成分分析による2次元表示: 図(b)\nautoplot(prcomp(mydata[-10]), data=mydata, colour=\"class\") +\n theme(legend.position=c(.9,.9)) \n\n## 判別分析 (ランダムに選んだ300個のサンプルで分析)\n## set.seed(1234) # 実験の再現性を求める場合\nidx <- sample(nrow(mydata),300)\ntrain <- mydata[idx,] # 学習に用いるデータを選択 \nmodel <- lda(class ~ .,data=train) \nprint(model) # モデルの概要を表示\n\n## 線形判別関数の値の分布をクラス毎に表示\npredict.tr <- predict(model) # 学習データの予測\nres.tr <- data.frame(x=as.vector(predict.tr$x), # 学習データの評価用\n class=train$class,\n d=c(benign=0,malignant=1)[train$class]) \n## 判別関数の値の分布 (学習データ): 図(c)\nggplot(res.tr, aes(x)) + xlim(-3,8) + # 値の範囲を指定\n geom_histogram(aes(fill=class)) +\n facet_grid(class ~ .) + theme(legend.position=\"none\") \n\n## AUC (学習データ): 図(d)\ngg <- ggplot(res.tr, aes(m=x, d=d)) + geom_roc(colour=\"red\")\ngg + annotate(\"text\", x=.9, y=.1,\n label=paste(\"AUC =\", round(calc_auc(gg)$AUC,3)))\n\n## 上記の結果を用いて残りのサンプルを予測\ntest <- mydata[-idx,] # 予測対象のデータを選択 \npredict.te <- predict(model,newdata=test[,-10])\ntable(true=test$class,est=predict.te$class) # 判別結果を表示\n\n## 線形判別関数の値の分布をクラス毎に表示\nres.te <- data.frame(x=as.vector(predict.te$x), # 試験データの評価用\n class=test$class,\n d=c(benign=0,malignant=1)[test$class]) \n## 判別関数の値の分布 (試験データ): 図(e)\nggplot(res.te, aes(x)) + xlim(-3,8) + # 値の範囲を指定\n geom_histogram(aes(fill=class)) +\n facet_grid(class ~ .) + theme(legend.position=\"none\") \n\n## AUC (試験データ): 図(f)\ngg <- ggplot(res.te, aes(m=x, d=d)) + geom_roc(colour=\"red\")\ngg + annotate(\"text\", x=.9, y=.1,\n label=paste(\"AUC =\", round(calc_auc(gg)$AUC,3)))\n", "meta": {"hexsha": "6c0b6e1fc1788cadee0b17030c05feef668a7d7d", "size": 2134, "ext": "r", "lang": "R", "max_stars_repo_path": "docs/code/d-biopsy.r", "max_stars_repo_name": "noboru-murata/multivariate-analysis", "max_stars_repo_head_hexsha": "645bff23d3868e5d7c245ef4af7d0ff9fe98e017", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "docs/code/d-biopsy.r", "max_issues_repo_name": "noboru-murata/multivariate-analysis", "max_issues_repo_head_hexsha": "645bff23d3868e5d7c245ef4af7d0ff9fe98e017", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "docs/code/d-biopsy.r", "max_forks_repo_name": "noboru-murata/multivariate-analysis", "max_forks_repo_head_hexsha": "645bff23d3868e5d7c245ef4af7d0ff9fe98e017", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 31.8507462687, "max_line_length": 62, "alphanum_fraction": 0.6433926898, "num_tokens": 1023, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9597620608291781, "lm_q2_score": 0.8267117962054049, "lm_q1q2_score": 0.793446617237891}} {"text": "\nlibrary(astsa)\n\n# read data to R variable\nbirth.data<-read.csv(\"daily-total-female-births-in-cal.csv\")\n\n# pull out number of births column\nnumber_of_births<-birth.data$Daily.total.female.births.in.California..1959\n\n# use date format for dates\nbirth.data$Date <- as.Date(birth.data$Date, \"%m/%d/%Y\")\n\n\n\nplot.ts(number_of_births,main='Daily total female births in california, 1959', ylab = 'Number of births')\n\n# Test for correlation\nBox.test(number_of_births, lag = log(length(number_of_births)))\n\n# Plot the differenced data\nplot.ts(diff(number_of_births), main='Differenced series', ylab = '')\n\n# Test for correlation in the differenced data\nBox.test(diff(number_of_births), lag = log(length(diff(number_of_births))))\n\n# acf and pacf of the differenced data\n\nacf(diff(number_of_births), main='ACF of differenced data', 50)\npacf(diff(number_of_births), main='PACF of differenced data', 50)\n\n# Fit various ARIMA models\n\n\nmodel1<-arima(number_of_births, order=c(0,1,1))\nSSE1<-sum(model1$residuals^2)\nmodel1.test<-Box.test(model1$residuals, lag = log(length(model1$residuals)))\n\nmodel2<-arima(number_of_births, order=c(0,1,2))\nSSE2<-sum(model2$residuals^2)\nmodel2.test<-Box.test(model2$residuals, lag = log(length(model2$residuals)))\n\nmodel3<-arima(number_of_births, order=c(7,1,1))\nSSE3<-sum(model3$residuals^2)\nmodel3.test<-Box.test(model3$residuals, lag = log(length(model3$residuals)))\n\nmodel4<-arima(number_of_births, order=c(7,1,2))\nSSE4<-sum(model4$residuals^2)\nmodel4.test<-Box.test(model4$residuals, lag = log(length(model4$residuals)))\n\ndf<-data.frame(row.names=c('AIC', 'SSE', 'p-value'), c(model1$aic, SSE1, model1.test$p.value), \n c(model2$aic, SSE2, model2.test$p.value), c(model3$aic, SSE3, model3.test$p.value),\n c(model4$aic, SSE4, model4.test$p.value))\ncolnames(df)<-c('Arima(0,1,1)','Arima(0,1,2)', 'Arima(7,1,1)', 'Arima(7,1,2)')\n\n\n\nformat(df, scientific=FALSE)\n\n# Fit a SARIMA model\n\nsarima(number_of_births, 0,1,2,0,0,0)\n\n\n\n", "meta": {"hexsha": "4e4798f954d3faa6ed6f0f2388d11f471ae6091b", "size": 1972, "ext": "r", "lang": "R", "max_stars_repo_path": "Daily+female+birth.r", "max_stars_repo_name": "NicholasN36/R-programming-New-York-University", "max_stars_repo_head_hexsha": "bc7aca4d6399384809b1cfc139a51d261c8b09ad", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-04-07T20:52:48.000Z", "max_stars_repo_stars_event_max_datetime": "2021-04-07T20:52:48.000Z", "max_issues_repo_path": "Daily+female+birth.r", "max_issues_repo_name": "NicholasN36/R-programming-New-York-University", "max_issues_repo_head_hexsha": "bc7aca4d6399384809b1cfc139a51d261c8b09ad", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Daily+female+birth.r", "max_forks_repo_name": "NicholasN36/R-programming-New-York-University", "max_forks_repo_head_hexsha": "bc7aca4d6399384809b1cfc139a51d261c8b09ad", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 30.3384615385, "max_line_length": 105, "alphanum_fraction": 0.724137931, "num_tokens": 631, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9496693674025231, "lm_q2_score": 0.8354835350552604, "lm_q1q2_score": 0.7934331202111529}} {"text": "## Author: Sergio García Prado\n## Title: Statistical Inference - Goodness of Fit - Exercise 14\n\n\nrm(list = ls())\n\nobserved <- c(9, 11, 4, 6)\n\n(k <- length(observed))\n# 4\n\n(n <- sum(observed))\n# 30\n\n## test F(x) is poisson(lambda)\n\nLogLikelihood <- function(lambda, y, k) {\n (sum(y[1:(k - 1)] * dpois(0:(k - 2), lambda = lambda, log = TRUE)) +\n y[k] * ppois(k - 2, lambda = lambda, lower.tail = FALSE, log = TRUE))\n}\n\nNegativeLogLikelihood <- function(...) {\n - LogLikelihood(...)\n}\n\nopt <- optim(1, NegativeLogLikelihood, y = observed, k = k,\n lower = 10e-4, method = 'L-BFGS-B')\n\n(lambda.hat <- opt$par)\n# 1.31334181246836\n\n(expected1 <- n * c(dpois(0:(k-2), lambda = lambda.hat), 1 - ppois(k - 2, lambda = lambda.hat)))\n# 8.06759619945891 10.5955114148602 6.9577640828109 4.37912830286995\n\n(Q1 <- sum((observed - expected1) ^ 2 / expected1))\n# 1.98049899014501\n\n1 - pchisq(Q1, df = (k - 1) - 1)\n# 0.371483996032531\n\n## test F(x) is poisson(1.2)\n(expected2 <- n * c(dpois(0:(k-2), lambda = 1.2), 1 - ppois(k - 2, lambda = 1.2)))\n# 9.03582635736606 10.8429916288393 6.50579497730357 3.61538703649109\n\n(Q2 <- sum((observed - expected2) ^ 2 / expected2))\n# 2.54038357961436\n\n1 - pchisq(Q2, df = (k - 1))\n# 0.468037053437737\n\n## power:\n\n(null <- n * c(dpois(0:(k-2), lambda = 1.2), 1 - ppois(k - 2, lambda = 1.2)))\n# 9.03582635736606 10.8429916288393 6.50579497730357 3.61538703649109\n\n(alternative <- n * c(dnbinom(0:(k-2),size = 2, prob = 2 / 3), 1 - pnbinom(k - 2,size = 2, prob = 2 / 3)))\n# 13.3333333333333 8.88888888888889 4.44444444444445 3.33333333333333\n\n(Q <- sum((alternative - null) ^ 2 / alternative))\n# 2.79465432822941\n\n\n(power <- 1 - pchisq(qchisq(0.95, df = k - 1), df = k - 1, Q))\n# 0.257468163480735\n\n## sample size power >= 0.8\n\nfn <- function(n) {\n null <- n * c(dpois(0:(k-2), lambda = 1.2), 1 - ppois(k - 2, lambda = 1.2))\n alternative <- n * c(dnbinom(0:(k-2),size = 2, prob = 2 / 3), 1 - pnbinom(k - 2,size = 2, prob = 2 / 3))\n\n Q <- sum((alternative - null) ^ 2 / alternative)\n power <- 1 - pchisq(qchisq(0.95, df = k - 1), df = k - 1, Q)\n}\n\n\n(n.exact <- uniroot(function(n) {fn(n) - 0.8}, c(1, 500))$root)\n# 117.036620884611\n\nceiling(n.exact)\n# 118\n", "meta": {"hexsha": "d8276f717131f026bff95c6a248c5cf99ba9765f", "size": 2194, "ext": "r", "lang": "R", "max_stars_repo_path": "statistical-inference/goodness-of-fit/exercise-14.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "statistical-inference/goodness-of-fit/exercise-14.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "statistical-inference/goodness-of-fit/exercise-14.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.756097561, "max_line_length": 106, "alphanum_fraction": 0.6066545123, "num_tokens": 934, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9334308184368928, "lm_q2_score": 0.8499711756575749, "lm_q1q2_score": 0.793389290141818}} {"text": "N <- 1e6\nb <- 10\n\nX <- runif(n = N, min = 0, max = b)\nY <- runif(n = N, min = 0, max = b)\n\n\nU <- (X-b/2)^2\nV <- (Y-b/2)^2\nW <- U + V\n\necc <- ecdf(W)\n\nhist(W)\n\nF_T <- function(t){\n b <- b + 0i\n t <- t + 0i\n Re(\n (b*sqrt(4*t-b^2) - 4*t*atan(sqrt(4*t-b^2)/b) + 2*pi*t)/(2*b^2)\n )\n}\n\nr <- runif(1, 0, b/2)\necc(r^2)\nF_T(r^2)\n(pi*r^2)/b^2\n\nthN <- sample(1:N, min(1000, N), replace = FALSE)\nplot(X[thN], Y[thN], col = as.numeric(W[thN] <= r^2) + 1)\nplotrix::draw.circle(x = b/2, y = b/2, radius = r, lwd = 4)\n\nvar_delta <- function(A, u, n){\n sapply(A, function(x) {\n x*(u^2-x)/n \n })\n}\n# var_delta <- Vectorize(var_delta)\nuu <- 1\ncurve(var_delta(x, u = uu, n = 10), 0, pi*uu^2/4, lwd = 3,\n ylab = expression(Var(delta[1])), xlab = expression(A))\ncurve(var_delta(x, u = uu, n = 30), 0, pi*uu^2/4,\n lty = 2, lwd = 3, add = TRUE)\ncurve(var_delta(x, u = uu, n = 100), 0, pi*uu^2/4,\n lwd = 3, lty = 4, add = TRUE)\nabline(v = uu^2/2, lwd = 2, lty = 5)\nlegend(x = \"topleft\",\n legend = c(\"n=10\", \"n=30\", \"n=100\"),\n lwd = 2, lty = 1:4, col = 1, bty = 'n')\n\n", "meta": {"hexsha": "ccaab42e0932e2dc42b3327ca749a9fd94381eb4", "size": 1082, "ext": "r", "lang": "R", "max_stars_repo_path": "code/Q_1_P1_2021.r", "max_stars_repo_name": "jlduim/Statistical_Inference_BSc", "max_stars_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 33, "max_stars_repo_stars_event_min_datetime": "2020-08-03T15:42:28.000Z", "max_stars_repo_stars_event_max_datetime": "2021-11-30T15:43:10.000Z", "max_issues_repo_path": "code/Q_1_P1_2021.r", "max_issues_repo_name": "jlduim/Statistical_Inference_BSc", "max_issues_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 23, "max_issues_repo_issues_event_min_datetime": "2020-08-16T23:02:47.000Z", "max_issues_repo_issues_event_max_datetime": "2021-11-07T14:34:43.000Z", "max_forks_repo_path": "code/Q_1_P1_2021.r", "max_forks_repo_name": "jlduim/Statistical_Inference_BSc", "max_forks_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 10, "max_forks_repo_forks_event_min_datetime": "2020-08-13T00:53:42.000Z", "max_forks_repo_forks_event_max_datetime": "2021-12-10T07:35:56.000Z", "avg_line_length": 21.2156862745, "max_line_length": 66, "alphanum_fraction": 0.4944547135, "num_tokens": 512, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9207896780646392, "lm_q2_score": 0.8615382147637196, "lm_q1q2_score": 0.7932954954126693}} {"text": "#install.packages(\"GA\")\nlibrary(GA)\n\n# https://cran.r-project.org/web/packages/GA/vignettes/GA.html#constrained-optimisation\n # Simionescu function\n# https://en.wikipedia.org/wiki/Test_functions_for_optimization\nfunc3d <- function(x)\n{\n 0.1*x[1]*x[2]\n}\n\nc1 <- function(x)\n{\n r_t <- 1\n r_s <- 0.2\n n <- 8\n x[1]^2+x[2]^2-(r_t+r_s*cos(n*atan(x[1]/x[2])))^2\n}\n\nx1LBound <- -1.25\nx1RBound <- 1.25\nx2LBound <- -1.25\nx2RBound <- 1.25\n\nngrid <- 250 # 250\nnLevels <- 21\nx1 <- seq(x1LBound, x1RBound, length = ngrid)\nx2 <- seq(x2LBound, x2RBound, length = ngrid)\nx12 <- expand.grid(x1, x2)\ncol <- adjustcolor(bl2gr.colors(4)[2:3], alpha = 0.2)\nplot(x1, x2, type = \"n\", xaxs = \"i\", yaxs = \"i\")\nimage(x1, x2, matrix(ifelse(apply(x12, 1, c1) <= 0, 0, NA), ngrid, ngrid), col = col[1], add = TRUE)\ncontour(x1, x2, matrix(apply(x12, 1, func3d), ngrid, ngrid), nlevels = nLevels, add = TRUE)\n\nfitness <- function(x)\n{\n f <- -func3d(x) # we need to maximise -func3d(x)\n pen <- sqrt(.Machine$double.xmax) # penalty term\n penalty1 <- max(c1(x),0)*pen # penalisation for 1st inequality constraint\n f - penalty1 # fitness function value\n}\n\nGA <- ga(\"real-valued\", fitness = fitness,\n lower = c(x1LBound, x2LBound), upper = c(x1RBound, x2RBound),\n # selection = GA:::gareal_lsSelection_R,\n maxiter = 10000, run = 1000) # seed = 123)\nsummary(GA)\nplot(GA)\n\nfitness(GA@solution)\nfunc3d(GA@solution)\nc1(GA@solution)\n\nplot(x1, x2, type = \"n\", xaxs = \"i\", yaxs = \"i\")\nimage(x1, x2, matrix(ifelse(apply(x12, 1, c1) <= 0, 0, NA), ngrid, ngrid), col = col[1], add = TRUE)\ncontour(x1, x2, matrix(apply(x12, 1, func3d), ngrid, ngrid), nlevels = nLevels, add = TRUE)\npoints(GA@solution[1], GA@solution[2], col = \"dodgerblue3\", pch = 3) # GA solution\n", "meta": {"hexsha": "db500775eb93cc472a43a076ffa3367bc1108aad", "size": 1799, "ext": "r", "lang": "R", "max_stars_repo_path": "R/ga/func/3d/with_bounds_formula/ga_minimum_of_3d_simionescu_func_formula_bounds.r", "max_stars_repo_name": "reyzeer/algorytmy-genetyczne", "max_stars_repo_head_hexsha": "c8803dd19dd5105d35b287fa13efdc130531403f", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/ga/func/3d/with_bounds_formula/ga_minimum_of_3d_simionescu_func_formula_bounds.r", "max_issues_repo_name": "reyzeer/algorytmy-genetyczne", "max_issues_repo_head_hexsha": "c8803dd19dd5105d35b287fa13efdc130531403f", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/ga/func/3d/with_bounds_formula/ga_minimum_of_3d_simionescu_func_formula_bounds.r", "max_forks_repo_name": "reyzeer/algorytmy-genetyczne", "max_forks_repo_head_hexsha": "c8803dd19dd5105d35b287fa13efdc130531403f", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 31.0172413793, "max_line_length": 100, "alphanum_fraction": 0.6231239578, "num_tokens": 698, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9111797100118214, "lm_q2_score": 0.8705972667296309, "lm_q1q2_score": 0.7932705650357894}} {"text": "library(rstudioapi)\nlibrary(ellipse)\nlibrary(ggplot2)\nlibrary(readr)\nlibrary(psych)\nlibrary(nFactors)\nlibrary(polycor)\nthis.dir <- dirname(rstudioapi::getActiveDocumentContext()$path)\nsetwd(this.dir)\n\n####### 9.28 ##########\ne8_18 <- read_delim(\"e8_18.txt\", \" \", escape_double = FALSE, trim_ws = TRUE)\nnation = e8_18[,1]\nX = as.matrix(e8_18[,2:8])\nR = cor(X)\nS = cov(X)\n# Number of Factor for covariance\nev <- eigen(S) # get eigenvalues\nap <- parallel(subject=nrow(X),var=ncol(X),\n rep=100,cent=.05)\nnS <- nScree(x=ev$values, aparallel=ap$eigen$qevpea)\nplotnScree(nS)\n\n# Number of Factor for correlation\nev <- eigen(R) # get eigenvalues\nap <- parallel(subject=nrow(X),var=ncol(X),\n rep=100,cent=.05)\nnS <- nScree(x=ev$values, aparallel=ap$eigen$qevpea)\nplotnScree(nS)\n\n\n## Unrotated PC Analysis with S\nfit1 <- principal(S, nfactors=2, rotate=\"none\",scores = TRUE,covar = TRUE)\nfit1 \n\n## Varimax Rotation PC Analysis with S\nfit2 <- principal(S, nfactors=2, rotate=\"varimax\",scores = TRUE,covar = TRUE)\nfit2 \n\n## Unrotated PC Analysis with R\nfit3 <- principal(R, nfactors=2, rotate=\"none\",scores = TRUE,covar = TRUE)\nfit3 \nscore <- factor.scores(X,fit3)\nscore$weights\n## Varimax Rotation PC Analysis with R\nfit4 <- principal(R, nfactors=2, rotate=\"varimax\",scores = TRUE,covar = TRUE)\nfit4 \nscore <- factor.scores(X,fit4)\nscore$weights\n## Outlier\nscore <- factor.scores(X,fit4)\nplotscore = as.data.frame(score$scores)\nggplot(data = plotscore, aes(x = RC1, y = RC2)) + geom_point()+ggtitle(\"Scatterplot of Factor Score of PC\")+\n geom_text(aes(label=nation),hjust=0, vjust=0)\n## ML Unrotated PC Analysis with R\nfit5 <- factanal(X, 2, rotation=\"none\")\nfit5 \n## ML Varimax Rotation PC Analysis with R\nfit6 <- factanal(X, 2, rotation=\"varimax\")\nfit6 \nscore <- factor.scores(X,fit6)\nscore$weights\n## Outlier\nscore <- factor.scores(X,fit6)\nplotscore = as.data.frame(score$scores)\nggplot(data = plotscore, aes(x = Factor1, y = Factor2)) + geom_point()+ggtitle(\"Scatterplot of Factor Score of Maximum Likelihood\")+\n geom_text(aes(label=nation),hjust=0, vjust=0)\n\n####### 9.34 ##########\nT7_7 <- read_delim(\"T7-7.dat\", \"\\t\", escape_double = FALSE, col_names = FALSE, trim_ws = TRUE)\nX = T7_7[1:62,1:4]\ncolnames(X) = c(\"BL\",\"EM\",\"SF\",\"BS\")\nX = as.matrix(X)\nR = cor(X)\nS = cov(X)\n\n# Number of Factor for covariance\nev <- eigen(S) # get eigenvalues\nap <- parallel(subject=nrow(X),var=ncol(X),\n rep=100,cent=.05)\nnS <- nScree(x=ev$values, aparallel=ap$eigen$qevpea)\nplotnScree(nS)\n\n# Number of Factor for correlation\nev <- eigen(R) # get eigenvalues\nap <- parallel(subject=nrow(X),var=ncol(X),\n rep=100,cent=.05)\nnS <- nScree(x=ev$values, aparallel=ap$eigen$qevpea)\nplotnScree(nS)\n## Unrotated PC Analysis with S\nfit1 <- principal(S, nfactors=1, rotate=\"none\",scores = TRUE,covar = TRUE)\nfit1 \n\n\nfit2 <- principal(R, nfactors=1, rotate=\"none\",scores = TRUE,covar = TRUE)\nfit2 \n\n\nfit3 <- factanal(X, 1, rotation=\"none\")\nfit3 \n\n\nfit4 <- principal(R, nfactors=2, rotate=\"varimax\",scores = TRUE,covar = TRUE)\nfit4 \nscore <- factor.scores(X,fit4)\nscore$weights\n## Outlier\nscore <- factor.scores(X,fit4)\nplotscore = as.data.frame(score$scores)\nggplot(data = plotscore, aes(x = RC1, y = RC2)) + geom_point()+ggtitle(\"Scatterplot of Factor Score of PC\")+\n geom_text(aes(label=c(1:62)),hjust=0, vjust=0)\n\n\n####### 9.35 ##########\nX = T7_7[1:62,5:8]\ncolnames(X) = c(\"AFL\",\"LFF\",\"FFF\",\"ZST\")\nX = as.matrix(X)\nR = cor(X)\nS = cov(X)\n\n# Number of Factor for covariance\nev <- eigen(S) # get eigenvalues\nap <- parallel(subject=nrow(X),var=ncol(X),\n rep=100,cent=.05)\nnS <- nScree(x=ev$values, aparallel=ap$eigen$qevpea)\nplotnScree(nS)\n\n# Number of Factor for correlation\nev <- eigen(R) # get eigenvalues\nap <- parallel(subject=nrow(X),var=ncol(X),\n rep=100,cent=.05)\nnS <- nScree(x=ev$values, aparallel=ap$eigen$qevpea)\nplotnScree(nS)\n\n## Unrotated PC Analysis with S\nfit1 <- principal(S, nfactors=1, rotate=\"none\",scores = TRUE,covar = TRUE)\nfit1 \n\n\nfit2 <- principal(R, nfactors=1, rotate=\"none\",scores = TRUE,covar = TRUE)\nfit2 \n\n\nfit3 <- factanal(X, 1, rotation=\"none\")\nfit3 \n\n\nfit4 <- principal(R, nfactors=2, rotate=\"varimax\",scores = TRUE,covar = TRUE)\nfit4 \nscore <- factor.scores(X,fit4)\nscore$weights\n## Outlier\nscore <- factor.scores(X,fit4)\nplotscore = as.data.frame(score$scores)\nggplot(data = plotscore, aes(x = RC1, y = RC2)) + geom_point()+ggtitle(\"Scatterplot of Factor Score of PC\")+\n geom_text(aes(label=c(1:62)),hjust=0, vjust=0)\n\n\n\n", "meta": {"hexsha": "a244fe09f5fca9a2b473e1d51b0bc1dd61f917ec", "size": 4517, "ext": "r", "lang": "R", "max_stars_repo_path": "Statistics/STA 135/hw6/hw6.r", "max_stars_repo_name": "HaozheGuAsh/Undergrate", "max_stars_repo_head_hexsha": "2b75ef3ae06b6c2350edc4b0b03f516a194cca99", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Statistics/STA 135/hw6/hw6.r", "max_issues_repo_name": "HaozheGuAsh/Undergrate", "max_issues_repo_head_hexsha": "2b75ef3ae06b6c2350edc4b0b03f516a194cca99", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Statistics/STA 135/hw6/hw6.r", "max_forks_repo_name": "HaozheGuAsh/Undergrate", "max_forks_repo_head_hexsha": "2b75ef3ae06b6c2350edc4b0b03f516a194cca99", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 28.23125, "max_line_length": 132, "alphanum_fraction": 0.6769980075, "num_tokens": 1488, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9518632329799585, "lm_q2_score": 0.8333246015211009, "lm_q1q2_score": 0.7932110493256107}} {"text": "library(deSolve)\r\nlibrary(rstan)\r\nlibrary(shinystan)\r\nlibrary(ggplot2)\r\nlibrary(RColorBrewer)\r\nlibrary(reshape2)\r\nlibrary(gridExtra)\r\n\r\n# NOTE: to save plots, uncomment the ggsave lines\r\n\r\nSIR <- function(Time, State, Pars) {\r\n \r\n with(as.list(c(State, Pars)), {\r\n \r\n B <- R0*r/N\r\n BSI <- B*S*I\r\n rI <- r*I\r\n \r\n dS = -BSI\r\n dI = BSI - rI\r\n dR = rI\r\n \r\n return(list(c(dS, dI, dR)))\r\n \r\n })\r\n \r\n}\r\n\r\nStocSIR <- function(y, pars, T, steps) {\r\n\r\n\tout <- matrix(NA, nrow = (T+1), ncol = 4)\r\n\r\n\tR0 <- pars[['R0']]\r\n\tr <- pars[['r']]\r\n\tN <- pars[['N']]\r\n\teta <- pars[['eta']]\r\n\tberr <- pars[['berr']]\r\n\r\n\tS <- y[['S']]\r\n\tI <- y[['I']]\r\n\tR <- y[['R']]\r\n\r\n\tB0 <- R0 * r / N\r\n\tB <- B0\r\n\r\n\tout[1,] <- c(S,I,R,B)\r\n\r\n\th <- 1 / steps\r\n\r\n\tfor ( i in 1:(T*steps) ) {\r\n\r\n\t\tB <- exp( log(B0) + eta*(log(B) - log(B0)) + rnorm(1, 0, berr) )\r\n\r\n\t\tBSI <- B*S*I\r\n\t\trI <- r*I\r\n\r\n\t\tdS <- -BSI\r\n\t\tdI <- BSI - rI\r\n\t\tdR <- rI\r\n\r\n\t\tS <- S + h*dS #newInf\r\n\t\tI <- I + h*dI #newInf - h*dR\r\n\t\tR <- R + h*dR #h*dR\r\n\r\n\t\tif (i %% steps == 0)\r\n\t\t\tout[i/steps+1,] <- c(S,I,R,B)\r\n\r\n\t}\r\n\r\n\treturn(out)\r\n\r\n}\r\n\r\nset.seed(1001)\r\n\r\nT \t\t<- 60\r\ni_infec <- 5\r\nsteps \t<- 7\r\nN \t\t<- 500\r\nsigma \t<- 10\r\nTlim \t<- 25\r\n\r\npars <- c(R0 = 3.0, \t# new infected people per infected person\r\n r = 0.1, \t\t# recovery rate\r\n gam = 2, \t\t# new infected shock intensity\r\n\t\t N = 500, \t\t# population size\r\n\t\t eta = 0.5, \t# geometric random walk\r\n\t\t berr = 0.5) \t# Beta geometric walk noise\r\n\r\ntrue_init_cond <- c(S = N - i_infec,\r\n\t\t\t\t\tI = i_infec,\r\n\t\t\t\t\tR = 0)\r\n\r\nsdeout <- StocSIR(true_init_cond, pars, T, steps)\r\ncolnames(sdeout) <- c('S','I','R','B')\r\n\r\ninfec_counts_raw <- sdeout[,'I'] + rnorm(T+1, 0, sigma)\r\ninfec_counts <- ifelse(infec_counts_raw < 0, 0, infec_counts_raw)\r\n\r\ndatapart <- c(infec_counts[1:(Tlim+1)],rep(NA,T-Tlim))\r\n\r\nplotdata <- data.frame(times = 0:T, true = sdeout[,'I'], data = datapart)\r\n\r\ng <- ggplot(plotdata, aes(times)) +\r\n geom_line(aes(y = true, colour = \"True\")) + \r\n geom_point(aes(y = data, colour = \"Data\")) +\r\n labs(x = \"Time\", y = \"Infection count\", color = \"\") +\r\n scale_color_brewer(palette=\"Paired\") +\r\n theme(panel.background = element_rect(fill = \"#F0F0F0\"))\r\n\r\nquartz()\r\nprint(g)\r\n#ggsave(g, filename=\"dataplot.pdf\", height=4, width=6.5)\r\n\r\ndatlen <- T*7 + 1\r\n\r\ndata <- matrix(data = -1, nrow = T+1, ncol = steps)\r\ndata[,1] <- infec_counts\r\nstandata <- as.vector(t(data))[1:datlen]\r\n\r\nsir_data <- list( T = datlen, \t# simulation time\r\n y = standata, \t# infection count data\r\n N = 500, \t# population size\r\n h = 1/steps ) \t# step size per day \r\n \r\nrstan_options(auto_write = TRUE)\r\noptions(mc.cores = parallel::detectCores())\r\n\r\nstan_options <- list( chains = 1, \t\t# number of chains\r\n iter = 5000, \t\t# iterations per chain\r\n warmup = 1000, \t\t# warmup interations\r\n thin = 10, \t\t# thinning number\r\n verbose = TRUE,\r\n refresh = 50)\r\n\r\nfit <- with(stan_options,\r\n stan(file \t= \"sirode_euler.stan\",\r\n\t data = sir_data,\r\n\t chains = chains,\r\n\t iter = iter,\r\n\t warmup = warmup,\r\n\t thin = thin,\r\n\t verbose = verbose,\r\n\t refresh = refresh )\r\n \t)\r\n\r\n# traceplots\r\nif (stan_options$chains > 1) {\r\n\r\n\texfit <- extract(fit, permuted = FALSE, inc_warmup = FALSE)\r\n\tplotdata <- melt(exfit[,,'R0'])\r\n\ttracefitR0 <- ggplot() +\r\n\t geom_line(data = plotdata,\r\n\t aes(x = iterations,\r\n\t y = value,\r\n\t color = factor(chains, labels = 1:stan_options$chains))) +\r\n\t labs(x = \"Sample\", y = expression(R[0]), color = \"Chain\") +\r\n\t scale_color_brewer(palette=\"Paired\") +\r\n\t theme(panel.background = element_rect(fill = \"#F0F0F0\"))\r\n\r\n\tquartz()\r\n\tprint(tracefitR0)\r\n\t#ggsave(tracefitR0, filename=\"traceplotR0.pdf\", height=4, width=6.5)\r\n\r\n\texfit <- extract(fit, permuted = FALSE, inc_warmup = TRUE)\r\n\tplotdata <- melt(exfit[,,2])\r\n\ttracefitR0 <- ggplot() +\r\n\t geom_line(data = plotdata,\r\n\t aes(x = iterations,\r\n\t y = value,\r\n\t color = factor(chains, labels = 1:stan_options$chains))) +\r\n\t labs(x = \"Sample\", y = expression(R[0]), color = \"Chain\") +\r\n\t scale_color_brewer(palette=\"Paired\") +\r\n\t theme(panel.background = element_rect(fill = \"#F0F0F0\"))\r\n\r\n\tquartz()\r\n\tprint(tracefitR0)\r\n\t#ggsave(tracefitR0, filename=\"traceplotR0_inc.pdf\", height=4, width=6.5)\r\n\r\n}\r\n\r\nexfit <- extract(fit, permuted = FALSE, inc_warmup = FALSE)\r\nparamdata <- data.frame(R0 = melt(exfit[,,'R0'])$value,\r\n \t\t\tr = melt(exfit[,,'r'])$value,\r\n \t\t\tsigma = melt(exfit[,,'sigma'])$value,\r\n \t\t\teta = melt(exfit[,,'eta'])$value,\r\n \t\t\tberr = melt(exfit[,,'berr'])$value,\r\n \t\t\tSinit = melt(exfit[,,4])$value,\r\n \t\t\tIinit = melt(exfit[,,5])$value,\r\n \t\t\tRinit = melt(exfit[,,6])$value )\r\n\r\n# sample from parameter distributions\r\nsdeout_true <- sdeout\r\n\r\nnTraj \t<- 100\r\ndatlen \t<- dim(paramdata)[1]\r\ninds \t<- sample.int(datlen,nTraj,replace = TRUE)\r\nparams \t<- paramdata[inds,]\r\n\r\nbootstrapdata <- matrix(NA, nrow = nTraj, ncol = T+1)\r\n\r\nfor (i in 1:nTraj) {\r\n\r\n\tinit_cond <- c(S = params$Sinit[i],\r\n\t I = params$Iinit[i],\r\n\t R = params$Rinit[i])\r\n\tpars <- c(R0 = params$R0[i],\r\n\t r = params$r[i],\r\n\t N = 500.0,\r\n\t eta = params$eta[i],\r\n\t berr = params$berr[i])\r\n\r\n\tsdeout <- StocSIR(init_cond, pars, T, steps)\r\n\tcolnames(sdeout) <- c('S','I','R','B')\r\n\r\n\tbootstrapdata[i,] <- sdeout[,'I']\r\n\r\n}\r\n\r\nmeanTraj \t<- colMeans(bootstrapdata)\r\nquantTraj \t<- apply(bootstrapdata, 2, quantile, probs = c(0.025,0.975))\r\n\r\nplotdata <- data.frame(times=0:T,true=sdeout_true[,'I'],est=meanTraj,quants=t(quantTraj),datapart=datapart)\r\n\r\ng <- ggplot(plotdata, aes(times)) +\r\n\t\tgeom_ribbon(aes(ymin = quants.2.5., ymax=quants.97.5.), alpha=0.1) +\r\n geom_line(aes(y = true, colour = \"True\")) + \r\n geom_line(aes(y = est, colour = \"IF2\")) +\r\n geom_point(aes(y = datapart, color = \"Data\")) +\r\n labs(x = \"Time\", y = \"Infection count\", color = \"\") +\r\n scale_color_brewer(palette=\"Paired\") +\r\n theme(panel.background = element_rect(fill = \"#F0F0F0\"))\r\n\r\nquartz()\r\nprint(g)\r\n\r\n# kernel plots\r\n\r\nf <- function(pal) brewer.pal(brewer.pal.info[pal, \"maxcolors\"], pal)\r\nkcolours <- f(\"Paired\")\r\n\r\n\r\ntrueval.R0 \t\t<- 3.0\r\ntrueval.r \t\t<- 0.1\r\ntrueval.sigma \t<- 10.0\r\ntrueval.Iinit \t<- 5\r\ntrueval.eta \t<- 0.5\r\ntrueval.berr \t<- 0.5\r\n\r\nmeanval.R0 \t\t<- mean(paramdata$R0)\r\nmeanval.r \t\t<- mean(paramdata$r)\r\nmeanval.sigma \t<- mean(paramdata$sigma)\r\nmeanval.Iinit \t<- mean(paramdata$Iinit)\r\nmeanval.eta \t<- mean(paramdata$eta)\r\nmeanval.berr \t<- mean(paramdata$berr)\r\n\r\n\r\nlinecolour <- \"grey50\"\r\nlineweight <- 0.5\r\n\r\nkerdataR0 <- data.frame(R0points = paramdata$R0)\r\nR0kernel <- ggplot(kerdataR0, aes(x = R0points, y = ..scaled..)) +\r\n geom_density(color = kcolours[1], fill = kcolours[1]) +\r\n theme(panel.background = element_rect(fill = \"#F0F0F0\")) +\r\n scale_color_brewer(palette=\"Paired\") +\r\n labs(x = expression(R[0]), y = \"Density\", color = \"\") +\r\n geom_vline(aes(xintercept=trueval.R0), linetype=\"solid\", size=lineweight, color=linecolour) +\r\n geom_vline(aes(xintercept=meanval.R0), linetype=\"dashed\", size=lineweight, color=linecolour)\r\n\r\nkerdatar <- data.frame(rpoints = paramdata$r)\r\nrkernel <- ggplot(kerdatar, aes(x = rpoints, y = ..scaled..)) +\r\n geom_density(color = kcolours[2], fill = kcolours[2]) +\r\n theme(panel.background = element_rect(fill = \"#F0F0F0\")) +\r\n scale_color_brewer(palette=\"Paired\") +\r\n labs(x = \"r\", y = \"\", color = \"\") +\r\n geom_vline(aes(xintercept=trueval.r), linetype=\"solid\", size=lineweight, color=linecolour) +\r\n geom_vline(aes(xintercept=meanval.r), linetype=\"dashed\", size=lineweight, color=linecolour)\r\n\r\nkerdatasigma <- data.frame(sigmapoints = paramdata$sigma)\r\nsigmakernel <- ggplot(kerdatasigma, aes(x = sigmapoints, y = ..scaled..)) +\r\n geom_density(color = kcolours[3], fill = kcolours[3]) +\r\n theme(panel.background = element_rect(fill = \"#F0F0F0\")) +\r\n scale_color_brewer(palette=\"Paired\") +\r\n labs(x = expression(sigma), y = \"Density\", color = \"\") +\r\n geom_vline(aes(xintercept=trueval.sigma), linetype=\"solid\", size=lineweight, color=linecolour) +\r\n geom_vline(aes(xintercept=meanval.sigma), linetype=\"dashed\", size=lineweight, color=linecolour)\r\n\r\nkerdatainfec <- data.frame(infecpoints = paramdata$Iinit)\r\ninfeckernel <- ggplot(kerdatainfec, aes(x = infecpoints, y = ..scaled..)) +\r\n geom_density(color = kcolours[4], fill = kcolours[4]) +\r\n theme(panel.background = element_rect(fill = \"#F0F0F0\")) +\r\n scale_color_brewer(palette=\"Paired\") +\r\n labs(x = \"Initial infected\", y = \"\", color = \"\") +\r\n geom_vline(aes(xintercept=trueval.Iinit), linetype=\"solid\", size=lineweight, color=linecolour) +\r\n geom_vline(aes(xintercept=meanval.Iinit), linetype=\"dashed\", size=lineweight, color=linecolour)\r\n\r\nkerdataeta <- data.frame(etapoints = paramdata$eta)\r\netakernel <- ggplot(kerdataeta, aes(x = etapoints, y = ..scaled..)) +\r\n geom_density(color = kcolours[5], fill = kcolours[5]) +\r\n theme(panel.background = element_rect(fill = \"#F0F0F0\")) +\r\n scale_color_brewer(palette=\"Paired\") +\r\n labs(x = expression(eta), y = \"\", color = \"\") +\r\n geom_vline(aes(xintercept=trueval.eta), linetype=\"solid\", size=lineweight, color=linecolour) +\r\n geom_vline(aes(xintercept=meanval.eta), linetype=\"dashed\", size=lineweight, color=linecolour)\r\n\r\nkerdataberr <- data.frame(berrpoints = paramdata$berr)\r\nberrkernel <- ggplot(kerdataberr, aes(x = berrpoints, y = ..scaled..)) +\r\n geom_density(color = kcolours[6], fill = kcolours[6]) +\r\n theme(panel.background = element_rect(fill = \"#F0F0F0\")) +\r\n scale_color_brewer(palette=\"Paired\") +\r\n labs(x = expression(beta[err]), y = \"\", color = \"\") +\r\n geom_vline(aes(xintercept=trueval.berr), linetype=\"solid\", size=lineweight, color=linecolour) +\r\n geom_vline(aes(xintercept=meanval.berr), linetype=\"dashed\", size=lineweight, color=linecolour)\r\n\r\n# show grid\r\nquartz()\r\ngrid.arrange(R0kernel, rkernel, sigmakernel, infeckernel, etakernel, berrkernel, ncol = 3, nrow = 2)\r\n\r\n# Shiny Stan!!!\r\n\r\nsso <- as.shinystan(fit)\r\nsso <- launch_shinystan(sso)", "meta": {"hexsha": "175490070777c29a39f503606775ed1bf72a2817", "size": 11150, "ext": "r", "lang": "R", "max_stars_repo_path": "code/hmc/sir_stan.r", "max_stars_repo_name": "dbarrows/epidemic-forecasting", "max_stars_repo_head_hexsha": "a0865fa20c992dc4159e79bb332500e3ff2357ae", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "code/hmc/sir_stan.r", "max_issues_repo_name": "dbarrows/epidemic-forecasting", "max_issues_repo_head_hexsha": "a0865fa20c992dc4159e79bb332500e3ff2357ae", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "code/hmc/sir_stan.r", "max_forks_repo_name": "dbarrows/epidemic-forecasting", "max_forks_repo_head_hexsha": "a0865fa20c992dc4159e79bb332500e3ff2357ae", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 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YES\n2. YES", "lm_q1_score": 0.9353465116437761, "lm_q2_score": 0.8479677583778258, "lm_q1q2_score": 0.7931436847850918}} {"text": "## L(D|theta)^a_0 pi(theta)\n\nalpha <- 10\nbeta <- 10\nyy <- 20\nNN <- 50\na_0 <- 0\n###########################\n\npower_post <- function(p, y, N, a0){\n lp <- a0 * ( y* log(p) + (N-y) * log(1-p) ) + dbeta(x = p, shape1 = alpha, shape2 = beta, log = TRUE)\n return(exp(lp)) \n}\npower_post <- Vectorize(power_post)\n\ncurve(power_post(p = x, y = yy, N = NN, a0 = a_0))\n\nlog_sq_lik <- function(p, y, N){\n ( y* log(p) + (N-y) * log(1-p) )^2\n}\ncurve(log_sq_lik(p = x, y = yy, N = NN))\n\nexpect <- function(p, y, N, a0){\n ans <- power_post(p = p, y = y, N = N, a0 = a0) * log_sq_lik(p = p, y = y, N = N)\n return(ans)\n}\nexpect <- Vectorize(expect)\ncurve(expect(p = x, y = yy, N = NN, a0 = a_0))\nintegrate(function(x) expect(p = x, y = yy, N = NN, a0 = a_0), 0, 1)\n\n## 1/X^2\none_over_x_sq <- function(p, y, N){\n exp(\n - 2*(y* log(p) + (N-y) * log(1-p)) \n )\n}\n## test that code for 1/L(D|theta)^2 is correct\n# pp <- .2\n# L <- pp^yy * (1-pp)^{NN-yy}\n# 1/L^2\n# one_over_x_sq(p = pp, y = yy, N = NN)\n\nexpect2 <- function(p, y, N, a0){\n ans <- power_post(p = p, y = y, N = N, a0 = a0) * one_over_x_sq(p = p, y = y, N = N)\n return(ans)\n}\nexpect2 <- Vectorize(expect2)\n\ncurve(expect2(p = x, y = yy, N = NN, a0 = a_0))\n\nintegrate(function(x) expect2(p = x, y = yy, N = NN, a0 = a_0), 0, 1)\n\n\n## -log(X)/X\n\nminus_logX_over_X <- function(p, y, N){\n logX <- y* log(p) + (N-y) * log(1-p)\n return(\n -logX/exp(logX)\n )\n}\n\nexpect3 <- function(p, y, N, a0){\n ans <- power_post(p = p, y = y, N = N, a0 = a0) * minus_logX_over_X(p = p, y = y, N = N)\n return(ans)\n}\nexpect3 <- Vectorize(expect3)\n\ncurve(expect3(p = x, y = yy, N = NN, a0 = a_0))\n\nintegrate(function(x) expect3(p = x, y = yy, N = NN, a0 = a_0), 0, 1)\n", "meta": {"hexsha": "035a9f6eeddbf23b50e26a5c2e928a42c18d5fd2", "size": 1698, "ext": "r", "lang": "R", "max_stars_repo_path": "code/extra/test_integrability_binomial.r", "max_stars_repo_name": "maxbiostat/propriety_power_priors", "max_stars_repo_head_hexsha": "43a9dc7bd007d5647bc453cd8a875e82c16ad6eb", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "code/extra/test_integrability_binomial.r", "max_issues_repo_name": "maxbiostat/propriety_power_priors", "max_issues_repo_head_hexsha": "43a9dc7bd007d5647bc453cd8a875e82c16ad6eb", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 7, "max_issues_repo_issues_event_min_datetime": "2020-05-29T19:11:11.000Z", "max_issues_repo_issues_event_max_datetime": "2020-08-29T15:58:08.000Z", "max_forks_repo_path": "code/extra/test_integrability_binomial.r", "max_forks_repo_name": "maxbiostat/propriety_power_priors", "max_forks_repo_head_hexsha": "43a9dc7bd007d5647bc453cd8a875e82c16ad6eb", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 23.5833333333, "max_line_length": 103, "alphanum_fraction": 0.5276796231, "num_tokens": 708, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9539660989095221, "lm_q2_score": 0.8311430415844384, "lm_q1q2_score": 0.7928822850161015}} {"text": "#02. 포아송분포(Poisson distribution) : 램덤하게 선택한 일정단위시간(시, 분, 초)나 공간 등 내에 발생하는 사건의 개수를 설명\n # 보통 단위시간 당 도착에 대한 모델이 많이 사용되므로 시간이 주로 사용 / 하루 사고 건수, 10분간 민원 전화 건수 등 \n # <=> 지수분포 : 도착에 따른 시간 측정에 활용 : 건과 건 사이의 시간\n\n# 확률밀도함수: d~\n# 누적분포함수(점수): p~\n# 누적분포함수(확률): q~\n\n# 포아송분포 확률밀도함수 \n# dpois(발생건수, lambda(단위시간당 평균발생 건수)\n# 서비스센터 사례\n# 서비스 센터에서 단위 시간 당(시간은 임의로 정하는 것) 평균발생건수: 1.5회\n# P(X = a) 확률 계산\ndpois(x=0, lambda = 1.5)\ndpois(x=1, lambda = 1.5)\ndpois(x=2, lambda = 1.5)\ndpois(x=3, lambda = 1.5)\ndpois(x=4, lambda = 1.5)\ndpois(x=5, lambda = 1.5)\n\n# 포아송분포 확률밀도함수 graph \nplot(dpois(x=c(0:10), lambda = 1.5), # 평균을 기준으로 가장 높고 평균을 넘어가면 확률이 낮아지는 개념 \n type='h',\n lwd=10, \n col=\"red\", \n xlab=\"성공확률 X\",\n main = \"포아송분포\")\n\n\n# 포아송분포 누적확률계산 - 사건을 알때 확률 계산\n# 이하 : P(X <= a) lower.tail = TRUE\n# 초과: P(X > a) lower.tail = FALSE\n# 2회이상(x>=2) 받을 확률: P(X > 1) 확률 계산 -> R에서는 이상이 없으니까 초과 개념으로 해서 2회 이상이면 1을 입력한다. \nppois(q=1, lambda = 1.5, lower.tail = FALSE)\n\n# 포아송분포 누적확률 graph\nplot(ppois(0:10, lambda = 1.5), \n type='h', \n lwd=10, \n col=\"red\", \n main = \"누적포아송분포\")\n\n## 퀴즈 K 서비스 센터 10분에 평균 2회 전화, 10분 동안 2회 이하로 전화 받을 확률?\n\n# P(X <= 2)이하로 받을 확률\nppois(q=2, lambda = 2, lower.tail = TRUE)\n\n\n\n", "meta": {"hexsha": "e417cbc25f16745b2a39fff07b16eb266447921a", "size": 1188, "ext": "r", "lang": "R", "max_stars_repo_path": "ch06 - 확률분포/02.포아송분포.r", "max_stars_repo_name": "Lee-changyul/Rstudy_Lee", "max_stars_repo_head_hexsha": "837a88d6cb4c0e223b42ca18dc5a469051b48533", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "ch06 - 확률분포/02.포아송분포.r", "max_issues_repo_name": "Lee-changyul/Rstudy_Lee", "max_issues_repo_head_hexsha": "837a88d6cb4c0e223b42ca18dc5a469051b48533", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "ch06 - 확률분포/02.포아송분포.r", "max_forks_repo_name": "Lee-changyul/Rstudy_Lee", "max_forks_repo_head_hexsha": "837a88d6cb4c0e223b42ca18dc5a469051b48533", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 23.76, "max_line_length": 84, "alphanum_fraction": 0.5824915825, "num_tokens": 838, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9416541561135441, "lm_q2_score": 0.8418256452674008, "lm_q1q2_score": 0.792708617589014}} {"text": "#Mann-Whitney-Wilcoxon\n#Si dos muestras son independientes, entonces\n#provenen de poblaciones distintas y no se afectan entre si\n\n#Usando Mann-White-Wilcoxon, podemos decidir si las \n#distribuciones poblacionales son identicas sin asumir una distribucion\n#normal\n\n#Without assuming the data to have normal distribution, decide at .05 significance level if the gas mileage data of manual and automatic transmissions in mtcars have identical data distribution.\n\nwilcox.test(mpg ~ am,data=mtcars)\n\n'''\n\tWilcoxon rank sum test with continuity\n\tcorrection\n\ndata: mpg by am\nW = 42, p-value = 0.001871\nalternative hypothesis: true location shift is not equal to 0\n'''", "meta": {"hexsha": "d15d50c3f2068c0f8e8e0507365a5b2cf921f585", "size": 661, "ext": "r", "lang": "R", "max_stars_repo_path": "Parcial/5. Metodos no parametricos/MannWhitneyWilcoxon.r", "max_stars_repo_name": "jchudb93/Exp-Numerica", "max_stars_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Parcial/5. Metodos no parametricos/MannWhitneyWilcoxon.r", "max_issues_repo_name": "jchudb93/Exp-Numerica", "max_issues_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Parcial/5. Metodos no parametricos/MannWhitneyWilcoxon.r", "max_forks_repo_name": "jchudb93/Exp-Numerica", "max_forks_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 33.05, "max_line_length": 194, "alphanum_fraction": 0.7942511346, "num_tokens": 174, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9304582632076909, "lm_q2_score": 0.851952809486198, "lm_q1q2_score": 0.7927065314494406}} {"text": "# Mergesort implementation in R\n# Author: Carlos Abraham Hernandez\n# github.com/abranhe\n\n\nmerge <- function(x, start, middle, end){\n \n x.left <- c(x[start:middle], Inf)\n x.right <- c(x[(middle+1):end], Inf)\n \n index.left <- 1\n index.right <- 1\n \n for(index.x in start:end){\n if(x.left[index.left] <= x.right[index.right]){\n x[index.x] <- x.left[index.left]\n index.left <- index.left + 1\n }\n else{\n x[index.x] <- x.right[index.right]\n index.right <- index.right + 1\n }\n }\n \n return(x)\n}\n\nmergeSort <- function(x, start, end){\n \n if(start < end){\n middle <- floor((start + end)/2)\n x <- mergeSort(x, start, middle)\n x <- mergeSort(x, middle+1, end)\n x <- merge(x, start, middle, end)\n }\n \n return(x)\n}\n\nx <- c(7,19,3,15,22,4,9,100)\n\nprint(x)\nprint(mergeSort(x, 1, length(x)))\n", "meta": {"hexsha": "b84cf100551d7dcd5b6fb3f41fc9a15c61e1d5e2", "size": 837, "ext": "r", "lang": "R", "max_stars_repo_path": "algorithms/sorting/mergesort.r", "max_stars_repo_name": "AllAlgorithms/R", "max_stars_repo_head_hexsha": "cab248e8b6e1f150364c5df14f2b3a7162215312", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 4, "max_stars_repo_stars_event_min_datetime": "2018-10-02T06:05:20.000Z", "max_stars_repo_stars_event_max_datetime": "2018-10-09T06:57:51.000Z", "max_issues_repo_path": "algorithms/sorting/mergesort.r", "max_issues_repo_name": "AllAlgorithms/r", "max_issues_repo_head_hexsha": "cab248e8b6e1f150364c5df14f2b3a7162215312", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2018-10-02T06:06:38.000Z", "max_issues_repo_issues_event_max_datetime": "2018-10-02T06:06:38.000Z", "max_forks_repo_path": "algorithms/sorting/mergesort.r", "max_forks_repo_name": "AllAlgorithms/R", "max_forks_repo_head_hexsha": "cab248e8b6e1f150364c5df14f2b3a7162215312", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2018-10-13T19:50:47.000Z", "max_forks_repo_forks_event_max_datetime": "2019-11-20T14:28:06.000Z", "avg_line_length": 19.0227272727, "max_line_length": 51, "alphanum_fraction": 0.5710872162, "num_tokens": 266, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.894789452074398, "lm_q2_score": 0.8856314753275019, "lm_q1q2_score": 0.7924537025481361}} {"text": "library(quaternions)\n\nq <- Q(1, 2, 3, 4)\nq1 <- Q(2, 3, 4, 5)\nq2 <- Q(3, 4, 5, 6)\nr <- 7.0\n\ndisplay <- function(x){\n e <- deparse(substitute(x))\n res <- if(class(x) == \"Q\") paste(x$r, \"+\", x$i, \"i+\", x$j, \"j+\", x$k, \"k\", sep = \"\") else x\n cat(noquote(paste(c(e, \" = \", res, \"\\n\"), collapse=\"\")))\n invisible(res)\n}\n\ndisplay(norm(q))\ndisplay(-q)\ndisplay(Conj(q))\ndisplay(r + q)\ndisplay(q1 + q2)\ndisplay(r*q)\ndisplay(q*r)\nif(display(q1*q2) == display(q2*q1)) cat(\"q1*q2 == q2*q1\\n\") else cat(\"q1*q2 != q2*q1\\n\")\n\n## norm(q) = 5.47722557505166\n## -q = -1+-2i+-3j+-4k\n## Conj(q) = 1+-2i+-3j+-4k\n## r + q = 8+2i+3j+4k\n## q1 + q2 = 5+7i+9j+11k\n## r * q = 7+14i+21j+28k\n## q * r = 7+14i+21j+28k\n## q1 * q2 = -56+16i+24j+26k\n## q2 * q1 = -56+18i+20j+28k\n## q1*q2 != q2*q1\n", "meta": {"hexsha": "dc46f9219a8f29f7eca20c9231adf7635610768c", "size": 766, "ext": "r", "lang": "R", "max_stars_repo_path": "Task/Quaternion-type/R/quaternion-type.r", "max_stars_repo_name": "LaudateCorpus1/RosettaCodeData", "max_stars_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Quaternion-type/R/quaternion-type.r", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Quaternion-type/R/quaternion-type.r", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 22.5294117647, "max_line_length": 93, "alphanum_fraction": 0.5195822454, "num_tokens": 380, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9559813513911654, "lm_q2_score": 0.828938806208442, "lm_q1q2_score": 0.7924500401797256}} {"text": "## Dale W.R. Rosenthal, 2018\n## You are free to distribute and use this code so long as you attribute\n## it to me or cite the text.\n## The legal disclaimer in _A Quantitative Primer on Investments with R_\n## applies to this code. Use or distribution without these comment lines\n## is forbidden.\n\n## No prepayments\nprincipal <- 300000 # mortgage principal\nn.peryr <- 12 # monthly = 12 payments per year\nT <- 30 # 30-year mortgage\nr <- 0.0625 # 6.25%\nt <- 1:(n.peryr*T)\npmt.level <- principal*r/(n.peryr*(1-1/(1+r/n.peryr)^(n.peryr*T)))\npmt.principal <- pmt.level/(1+r/n.peryr)^(n.peryr*T-t+1)\npmt.interest <- pmt.level-pmt.principal\n\nareaplot(t, data.frame(pmt.interest, pmt.principal), col=c(\"red\",\"blue\"),\n ylim=c(0,pmt.level), border=FALSE)\n\n## With prepayments\nprincipal.start <- 300e3 # mortgage principal\nn.peryr <- 12 # monthly = 12 payments per year\nT <- 30 # 30-year mortgage\nr <- 0.0625 # 6.25%\nt <- 1:(n.peryr*T)\n## calculate level monthly payment\npmt.level <- principal.start*r/(n.peryr*(1-1/(1+r/n.peryr)^(n.peryr*T)))\n\n## Prepay an extra 5\\% each payment\npmt.prepay.plan <- 0.05*pmt.level\n\n## In production code, this would be more elegant; however,\n## a for loop shows the intuition better than other approaches\nnum.pmts <- n.peryr*T\nprincipal.left <- c(principal.start, rep(0,num.pmts-1))\npmt.interest <- pmt.principal <- pmt.prepays <- rep(0, num.pmts)\nfor (i in 1:num.pmts) {\n pmt.interest[i] <- principal.left[i]*r/n.peryr\n pmt.principal[i] <- pmt.level - pmt.interest[i]\n if (pmt.principal[i] > principal.left[i]) {\n ## do not repay more than principal remaining\n pmt.principal[i] <- principal.left[i]\n ## stop the loop; mortgage is paid off\n break\n } else {\n ## do not prepay more than principal remaining after normal payment\n pmt.prepays[i] <- pmt.prepay.plan\n if ((pmt.principal[i] + pmt.prepays[i]) > principal.left[i]) {\n pmt.prepays[i] <- principal.left[i] - pmt.principal[i]\n ## stop the loop; mortgage is paid off\n break\n }\n }\n if (i < num.pmts) {\n principal.left[i+1] <- principal.left[i] - pmt.principal[i] - pmt.prepays[i]\n }\n}\n\nareaplot(t,data.frame(pmt.interest, pmt.principal, pmt.prepays),\n ylim=c(0,pmt.level+max(pmt.prepays)), col=c(\"red\",\"blue\",\"orange\"),\n border=FALSE)\n", "meta": {"hexsha": "630a9c2ff491ea438894497d671e99e8fc1648a9", "size": 2361, "ext": "r", "lang": "R", "max_stars_repo_path": "Quantitative Primer/samples/ch23-mortgages.r", "max_stars_repo_name": "bmoretz/Quantitative-Investments", "max_stars_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 7, "max_stars_repo_stars_event_min_datetime": "2020-03-26T05:47:30.000Z", "max_stars_repo_stars_event_max_datetime": "2022-02-18T21:50:54.000Z", "max_issues_repo_path": "Quantitative Primer/samples/ch23-mortgages.r", "max_issues_repo_name": "bmoretz/Quantitative-Investments", "max_issues_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Quantitative Primer/samples/ch23-mortgages.r", "max_forks_repo_name": "bmoretz/Quantitative-Investments", "max_forks_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2020-11-03T09:23:54.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-18T21:50:55.000Z", "avg_line_length": 37.4761904762, "max_line_length": 84, "alphanum_fraction": 0.6446421008, "num_tokens": 738, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9390248242542283, "lm_q2_score": 0.8438950966654772, "lm_q1q2_score": 0.7924384448353048}} {"text": "# two tailed test\r\nybar = 178.2 # sample mean \r\nmu0 = 190 # hypothesized value \r\nsigma = 45.3 # population standard deviation \r\nn = 100 # sample size \r\n# We compute the critical value at .025 significance level.\r\nalpha = .05 \r\nz.half.alpha = qnorm(1-alpha/2) \r\n# critical values\r\nlr=mu0-(z.half.alpha*sigma)/sqrt(n)\r\nur=mu0+(z.half.alpha*sigma)/sqrt(n)\r\npaste0(\" lower rejection = \",lr)\r\npaste0(\"upper rejection = \",ur)\r\nz = (ybar- mu0)/(sigma/sqrt(n))\r\nprint(z) # test statistic\r\n\r\n print(\"The test statistic doesnot lies between the critical values(i.e. |z|>critical value). Hence, at .025 significance level, we reject the null hypothesis\")\r\n", "meta": {"hexsha": "f79bca1ca1e2ce494b4f62b9a2d74e52ba8ad223", "size": 695, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH5/EX5.6/Ex5_6.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH5/EX5.6/Ex5_6.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH5/EX5.6/Ex5_6.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 38.6111111111, "max_line_length": 162, "alphanum_fraction": 0.6446043165, "num_tokens": 192, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9719924785827002, "lm_q2_score": 0.8152324960856177, "lm_q1q2_score": 0.7923998544914209}} {"text": "# 기본함수\nn <- 6 \nr <- 3 \nfactorial(n)\nfactorial(n)/factorial(n-r)\nchoose(n,r)\n\n\n# 패키지 이용\ninstall.packages(\"gtools\")\nlibrary(gtools)\n\nnrow(permutations(6,3))\nnrow(combinations(6,3))\n\n# 야구경기 (9명-9개)\nfactorial(9)\n\n# 집배원(4군데)\nfactorial(4)\n\n# 12명중 8개\nnrow(permutations(12,8))\n\nn <- 12 \nr <- 8 \nfactorial(n)/factorial(n-r)\n\n# 20명중 2명씩 짝\nchoose(20,2)\n\n# 45개 숫자중 6개 고름\nchoose(45,6)\n\n# 1등 당첨확률\n# 지수표기법 환원 1.2e+10->0.00000000012\noptions(\"scipen\" = 20) # 통계치 유의확률 0.05\nlot <- choose(45,6)\n1/lot\n\n# 5등 당첨확률(3개만)\noptions(\"scipen\" = 20)\nlot5 <- (choose(6,3)*choose(39,3))\nlot5/lot\n\n", "meta": {"hexsha": "e045910c3edfcb73779115d7cf2024ecf27618a6", "size": 566, "ext": "r", "lang": "R", "max_stars_repo_path": "ch06 - 확률분포/b_01.순열과 조합.r", "max_stars_repo_name": "Lee-changyul/Rstudy_Lee", "max_stars_repo_head_hexsha": "837a88d6cb4c0e223b42ca18dc5a469051b48533", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "ch06 - 확률분포/b_01.순열과 조합.r", "max_issues_repo_name": "Lee-changyul/Rstudy_Lee", "max_issues_repo_head_hexsha": "837a88d6cb4c0e223b42ca18dc5a469051b48533", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "ch06 - 확률분포/b_01.순열과 조합.r", "max_forks_repo_name": "Lee-changyul/Rstudy_Lee", "max_forks_repo_head_hexsha": "837a88d6cb4c0e223b42ca18dc5a469051b48533", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 12.3043478261, "max_line_length": 38, "alphanum_fraction": 0.6466431095, "num_tokens": 317, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9664104982195785, "lm_q2_score": 0.8198933425148213, "lm_q1q2_score": 0.7923535336266639}} {"text": "paint_data=c(28, 35, 27, 21,21, 36, 25 ,18,26, 38, 27, 17,16, 25, 22, 18)\r\nybar=sum(paint_data)/length(paint_data)\r\nprint(ybar)\r\n# total sum of squares \r\nTSS=0\r\ni=1\r\nwhile(i<=length(paint_data)){\r\n TSS=TSS+(paint_data[i]-ybar)^2\r\n i=i+1\r\n}\r\nprint(TSS)\r\n# between treatment sum of squares\r\n \r\nyi=c(mean(paint_data[1:4]),mean(paint_data[5:8]),mean(paint_data[9:12]),mean(paint_data[13:16]))\r\n \r\nSST=0\r\nj=1\r\nwhile(j<=length(paint_data)/4){\r\n SST=SST+4*((yi[j]-ybar)^2)\r\n j=j+1\r\n}\r\nprint(SST)\r\n# sum of squares for error\r\nSSE=TSS-SST\r\nprint(SSE)", "meta": {"hexsha": "ca5872e913c358e0b3a4f978e4bb1e7929ef728a", "size": 546, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH14/EX14.2/Ex14_2.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH14/EX14.2/Ex14_2.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH14/EX14.2/Ex14_2.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 21.84, "max_line_length": 97, "alphanum_fraction": 0.6465201465, "num_tokens": 223, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9433475778774728, "lm_q2_score": 0.8397339656668287, "lm_q1q2_score": 0.7921610025732477}} {"text": "#Q4. The following iterative sequence is defined for the set of positive integers:\r\n#n → n/2 (n is even)\r\n#n → 3n + 1 (n is odd)\r\n\r\n#Using the rule above and starting with 13, we generate the following sequence:\r\n#13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1\r\n#It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.\r\n#Which starting number, under one thousand, produces the longest chain?\r\n\r\ncollatz.length <- vector(length = 1E6)\r\ncollatz.length[1] <- 0\r\nfor (n in 2:1E6) {\r\n x <- n\r\n count <- 0 \r\n while (x != 1 & x >= n) {\r\n if (x %% 2 == 0) {\r\n x <- x / 2\r\n count <- count + 1\r\n }\r\n else {\r\n x <- (3 * x + 1) / 2\r\n count <- count + 2\r\n }\r\n }\r\n count <- count + collatz.length[x]\r\n collatz.length[n] <- count\r\n}\r\nanswer <- which.max(collatz.length)\r\nprint(answer)", "meta": {"hexsha": "c722237bb7e946cc7c6b024838ea4dd0bb36655e", "size": 996, "ext": "r", "lang": "R", "max_stars_repo_path": "Q.4.r", "max_stars_repo_name": "Subr1ata/D.A.-Lab-Assignments", "max_stars_repo_head_hexsha": "75e9eab3483e8650bd0396b0e102c89d0533b1eb", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Q.4.r", "max_issues_repo_name": "Subr1ata/D.A.-Lab-Assignments", "max_issues_repo_head_hexsha": "75e9eab3483e8650bd0396b0e102c89d0533b1eb", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Q.4.r", "max_forks_repo_name": "Subr1ata/D.A.-Lab-Assignments", "max_forks_repo_head_hexsha": "75e9eab3483e8650bd0396b0e102c89d0533b1eb", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 34.3448275862, "max_line_length": 198, "alphanum_fraction": 0.5702811245, "num_tokens": 301, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9744347823646073, "lm_q2_score": 0.8128673246376009, "lm_q1q2_score": 0.7920861945745413}} {"text": "library(tidyverse)\n\n\n##########################\n######### T-test #########\n##########################\n\n# Two-tailed t-test (unpaired)\n# assumptions: independent, normally distributed, homogeneous variance\n\ntreatment1 <- PlantGrowth[PlantGrowth$group == 'trt1',]$weight\ntreatment2 <- PlantGrowth[PlantGrowth$group == 'trt2',]$weight\n\nshapiro.test(treatment1)\nshapiro.test(treatment2)\n\n# check if variances are equal\nvar.test(treatment1, treatment2)\n\nt.test(\n treatment1, \n treatment2, \n alternative = \"two.sided\", \n var.equal = FALSE\n)\n\n# Two-tailed t-test (paired)\n\nage5 <- Loblolly[Loblolly$age == 5,]$height\nage20 <- Loblolly[Loblolly$age == 20,]$height\nage25 <- Loblolly[Loblolly$age == 25,]$height\n\nshapiro.test(age20)\nshapiro.test(age25)\n\n# near equal variance\nvar.test(age20, age25)\n\nt.test(\n age20, \n age25, \n alternative = \"two.sided\", \n paired = TRUE\n)\n\n# change alternative to \"less\" or \"greater\" for one-tailed test\n\n\n##########################\n######### F-test #########\n##########################\n\nvar.test(\n age20, \n age25,\n ratio = 1,\n conf.level = 0.95,\n alternative = \"two.sided\"\n)\n\n\n\n#########################\n######### ANOVA #########\n#########################\nmtcars\n\nlm1 <- lm(mpg ~ hp , mtcars)\nlm2 <- lm(mpg ~ hp + gear, mtcars)\n\nsummary(lm1)\nsummary(lm2)\n\nanova(lm1, lm2)\n", "meta": {"hexsha": "4294d8064fbd571c47fc0a4a815c01fbb539938f", "size": 1309, "ext": "r", "lang": "R", "max_stars_repo_path": "d822d03b4767dbdb526c15d74191908c/script.r", "max_stars_repo_name": "researchdata-sheffield/dataviz-hub2-qa", "max_stars_repo_head_hexsha": "bd746b5859a1e26f732663eb288b3bad8212c1f2", "max_stars_repo_licenses": ["0BSD", "Apache-2.0", "MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "d822d03b4767dbdb526c15d74191908c/script.r", "max_issues_repo_name": "researchdata-sheffield/dataviz-hub2-qa", "max_issues_repo_head_hexsha": "bd746b5859a1e26f732663eb288b3bad8212c1f2", "max_issues_repo_licenses": ["0BSD", "Apache-2.0", "MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "d822d03b4767dbdb526c15d74191908c/script.r", "max_forks_repo_name": "researchdata-sheffield/dataviz-hub2-qa", "max_forks_repo_head_hexsha": "bd746b5859a1e26f732663eb288b3bad8212c1f2", "max_forks_repo_licenses": ["0BSD", "Apache-2.0", "MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 17.4533333333, "max_line_length": 70, "alphanum_fraction": 0.577540107, "num_tokens": 379, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9553191284552529, "lm_q2_score": 0.8289388104343892, "lm_q1q2_score": 0.7919011019269148}} {"text": "n <- 10\np0 <- 1/2\nalpha0 <- 0.2\n\n# c(p0)\n# delta_c é um teste de tamanho alpha0=0.05\n\ntamanho_c <- function(c){\n ## Pr(Y >= c | p = p0)\n res <- 1- sum(dbinom(0:(c-1), n, p0))\n return(res)\n}\ntamanho_c <- Vectorize(tamanho_c)\n\n# Agora vamos plotar para tentar achar c* tal que Pr(Y >= c | p = p0) <= alpha0\n\ncurve(tamanho_c, 1, n, lwd = 2, xlab = expression(c))\nabline(h = alpha0, lty = 2)\n\n## Agora vamos expressar o poder como função da probabilidade postulada p0\n\nY <- 5\n\npoder_p <- function(p){\n res <- 1- sum(dbinom(0:(Y-1), n, p))\n return(res)\n}\npoder_p <- Vectorize(poder_p)\n\ncurve(poder_p, xlab = expression(p[0]))\nabline(h = alpha0, lty = 2)\n\n# LRT: razão de verossimilhanças\n\nLambda <- function(y, log = FALSE){\n l1 <- y * (log(n*p0)-log(y))\n if(y==0) l1 <- 0\n l2 <- (n-y)*(log(n*(1-p0))-log(n-y))\n if(y==n) l2 <- 0\n ans <- l1 + l2\n if(!log) ans <- exp(ans) \n return(ans)\n}\nLambda <- Vectorize(Lambda)\n\ntabProb <- data.frame(y = 0:n, Lambda = Lambda(0:n), Pr = dbinom(x = 0:n, size = n, prob = p0))\nround(tabProb, 3)\nplot(0:n, Lambda(0:n), xlab = expression(y), ylab = expression(Lambda(y)))\n\n\nfindSet <- function(tab, level = alpha0){\n K <- nrow(tab)\n set <- NA\n accpr <- 0\n for(i in 1:K){\n accpr.tent <- accpr + tab$Pr[i]\n if(accpr.tent < level){\n accpr <- accpr.tent\n set <- c(set, tab$y[i])\n }else{\n next\n }\n }\n set <- na.omit(set)\n return(\n list(\n confidence_set = as.vector(set),\n test_size = accpr\n )\n )\n}\nfindSet(tab = tabProb)", "meta": {"hexsha": "730703dbafeeaf16de0114cbac026bc404e69045", "size": 1508, "ext": "r", "lang": "R", "max_stars_repo_path": "code/teste_binomial_rascunho.r", "max_stars_repo_name": "jlduim/Statistical_Inference_BSc", "max_stars_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 33, "max_stars_repo_stars_event_min_datetime": "2020-08-03T15:42:28.000Z", "max_stars_repo_stars_event_max_datetime": "2021-11-30T15:43:10.000Z", "max_issues_repo_path": "code/teste_binomial_rascunho.r", "max_issues_repo_name": "jlduim/Statistical_Inference_BSc", "max_issues_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 23, "max_issues_repo_issues_event_min_datetime": "2020-08-16T23:02:47.000Z", "max_issues_repo_issues_event_max_datetime": "2021-11-07T14:34:43.000Z", "max_forks_repo_path": "code/teste_binomial_rascunho.r", "max_forks_repo_name": "jlduim/Statistical_Inference_BSc", "max_forks_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 10, "max_forks_repo_forks_event_min_datetime": "2020-08-13T00:53:42.000Z", "max_forks_repo_forks_event_max_datetime": "2021-12-10T07:35:56.000Z", "avg_line_length": 20.9444444444, "max_line_length": 95, "alphanum_fraction": 0.5789124668, "num_tokens": 571, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9314625012602593, "lm_q2_score": 0.8499711832583695, "lm_q1q2_score": 0.7917162843569832}} {"text": "dist <- \"beta\"\n\n## Beta\nalpha <- 3\nbeta <- 2\n\n## Log-normal\nmu <- 0\nsigma <- 2\n\nif(dist == \"ln\"){\n EX <- exp(mu + sigma^2/2) \n}else{\n EX <- alpha / (alpha + beta)\n}\n\ncomputa_media <- function(n){\n if(dist == \"ln\"){\n mean(rlnorm(n = n, meanlog = mu, sdlog = sigma))\n }else{\n mean(rbeta(n = n, shape1 = alpha, shape2 = beta))\n }\n}\nns <- seq(2, 1E5, by = 500)\nmedias <- sapply(ns, computa_media)\n\nlibrary(ggplot2)\n\nforplot <- data.frame(n = ns, x_bar = medias)\n\nggplot(forplot, aes(x = n, y = x_bar))+\n geom_line() +\n scale_x_continuous(\"Tamanho de amostra\", expand = c(0, 0)) + \n scale_y_continuous(expression(bar(X[n])), expand = c(0, 0)) +\n geom_hline(yintercept = EX, linetype = \"longdash\", size = 2) +\n theme_bw(base_size = 16)\n\n", "meta": {"hexsha": "c9beed888ae69397645a3cee626cfa10285fb47c", "size": 748, "ext": "r", "lang": "R", "max_stars_repo_path": "code/LGN.r", "max_stars_repo_name": "jlduim/Statistical_Inference_BSc", "max_stars_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 33, "max_stars_repo_stars_event_min_datetime": "2020-08-03T15:42:28.000Z", "max_stars_repo_stars_event_max_datetime": "2021-11-30T15:43:10.000Z", "max_issues_repo_path": "code/LGN.r", "max_issues_repo_name": "jlduim/Statistical_Inference_BSc", "max_issues_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 23, "max_issues_repo_issues_event_min_datetime": "2020-08-16T23:02:47.000Z", "max_issues_repo_issues_event_max_datetime": "2021-11-07T14:34:43.000Z", "max_forks_repo_path": "code/LGN.r", "max_forks_repo_name": "jlduim/Statistical_Inference_BSc", "max_forks_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 10, "max_forks_repo_forks_event_min_datetime": "2020-08-13T00:53:42.000Z", "max_forks_repo_forks_event_max_datetime": "2021-12-10T07:35:56.000Z", "avg_line_length": 19.6842105263, "max_line_length": 64, "alphanum_fraction": 0.5949197861, "num_tokens": 264, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.94499471015743, "lm_q2_score": 0.8376199694135332, "lm_q1q2_score": 0.7915464402180172}} {"text": "#Copyright (c) 2016 Riccardo Francescato\na <- c(16.85,16.40,17.21,16.35,16.52,17.04,16.96,17.15,16.59,16.57)\nb <- c(16.62,16.75,17.37,17.12,16.98,16.87,17.34,17.02,17.08,17.27)\n#confidency level\nalpha = .05 \n#type of test: 0 left tail 1 double tail 2 right tail\ntype = 1\n#calculations....\nn0 = length(a)\t\t# number of reps for sample 0\nn1 = length(b)\t\t# number of reps for sample 1\nxbar0 = mean(a)\t\t# sample 0 mean \nxbar1 = mean(b)\t\t# sample 1 mean \ns0 = sd(a)\t\t\t# sample 0 standard deviation \ns1 = sd(b)\t\t\t# sample 1 standard deviation \nsp2 = ((n0-1)*s0^2 + (n1-1)*s1^2)/(n0+n1-2)\nt = (xbar0−xbar1)/(sqrt(sp2)*sqrt((1/n0) + (1/n1))) \nif(type == 0){\n\tt.alpha = qt(1−alpha, df=n0−1) \n\tpval = pt(t, df=n0−1) \n\tcat(\"Results of lower tail\\n\")\n\tcat(\"First sample\\n\")\n\tcat(paste(\"# of elements: \", n0, \" Mean: \", xbar0, \" St Dev: \",s0))\n\tcat(\"\\nSecond sample\\n\")\n\tcat(paste(\"# of elements: \", n1, \" Mean: \", xbar1, \" St Dev: \",s1))\n\tcat(paste(\"\\nEstimate of common variance Sp: \",sqrt(sp2)))\n\tcat(paste(\"\\nt0: \",t))\n\tcat(paste(\"\\ntalpha: \",−t.alpha))\n\tcat(paste(\"\\np-value: \",pval))\n\tif(t<−t.alpha) cat(\"\\nREJECT H0\\n\") else cat(\"\\nACCEPT H0\\n\")\n}else if(type == 1){\n\tt.half.alpha = qt(1−alpha/2, df=n0−1) \n\tpval = 2 * pt(t, df=n0−1)\n\tcat(\"Results of 2-tail tail\\n\")\n\tcat(\"First sample\\n\")\n\tcat(paste(\"# of elements: \", n0, \" Mean: \", xbar0, \" St Dev: \",s0))\n\tcat(\"\\nSecond sample\\n\")\n\tcat(paste(\"# of elements: \", n1, \" Mean: \", xbar1, \" St Dev: \",s1))\n\tcat(paste(\"\\nEstimate of common variance Sp: \",sqrt(sp2)))\n\tcat(paste(\"\\nt0: \",t))\n\tcat(paste(\"\\ntalpha +: \",t.half.alpha))\n\tcat(paste(\"\\ntalpha -: \",-t.half.alpha))\n\tcat(paste(\"\\np-value: \",pval))\n\tif(t<-t.half.alpha || t>t.half.alpha) cat(\"\\nREJECT H0\\n\") else cat(\"\\nACCEPT H0\\n\")\n\n}else if(type == 2){\n\tt.alpha = qt(1−alpha, df=n0−1) \n\tpval = pt(t, df=n0−1, lower.tail=FALSE) \n\tcat(\"Results of upper tail\\n\")\n\tcat(\"First sample\\n\")\n\tcat(paste(\"# of elements: \", n0, \" Mean: \", xbar0, \" St Dev: \",s0))\n\tcat(\"\\nSecond sample\\n\")\n\tcat(paste(\"# of elements: \", n1, \" Mean: \", xbar1, \" St Dev: \",s1))\n\tcat(paste(\"\\nEstimate of common variance Sp: \",sqrt(sp2)))\n\tcat(paste(\"\\nt0: \",t))\n\tcat(paste(\"\\ntalpha: \",t.alpha))\n\tcat(paste(\"\\np-value: \",pval))\n\tif(t>t.alpha) cat(\"\\nREJECT H0\\n\") else cat(\"\\nACCEPT H0\\n\")\n}\n", "meta": {"hexsha": "ba6d351bce55996a6bbb8648acf29fa2017c1b71", "size": 2262, "ext": "r", "lang": "R", "max_stars_repo_path": "Test_of_hp_2_series_of_data.r", "max_stars_repo_name": "RiccardoFrancescato/DataDesignScrips", "max_stars_repo_head_hexsha": "92d19d1cd5da9fb1486d53bc97c444714a3e5aa1", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Test_of_hp_2_series_of_data.r", "max_issues_repo_name": "RiccardoFrancescato/DataDesignScrips", "max_issues_repo_head_hexsha": "92d19d1cd5da9fb1486d53bc97c444714a3e5aa1", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Test_of_hp_2_series_of_data.r", "max_forks_repo_name": "RiccardoFrancescato/DataDesignScrips", "max_forks_repo_head_hexsha": "92d19d1cd5da9fb1486d53bc97c444714a3e5aa1", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 38.3389830508, "max_line_length": 85, "alphanum_fraction": 0.6052166225, "num_tokens": 886, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9449947132556618, "lm_q2_score": 0.8376199633332891, "lm_q1q2_score": 0.7915464370673595}} {"text": "readings=c(203.1, 184.5, 206.8 ,211.0 ,218.3, 174.2, 193.2 ,201.9 ,199.9 ,194.3,\r\n 199.4, 193.6, 194.6 ,187.2 ,197.8 ,184.3, 196.1, 196.4 ,197.5 ,187.9)\r\nn=length(readings)\r\nybar=mean(readings)\r\ns=sd(readings)\r\nmuo=5\r\n# test static\r\nX=(n-1)*(s^2)/(muo^2)\r\nprint(X)\r\n#critical value\r\nalpha=0.05\r\nX.alpha=qchisq(1-0.05,df=19)\r\n \r\n# the null hypothesis, H0 is rejected if the value of the X is greater than X.alpha\r\n#Since the computed value of the X., 74.61, is greater than the\r\n# critical value 30.14, there is sufficient evidence to reject H0\r\n# The upper-tail chi-square value\r\nXU=qchisq(.975, df=19)\r\n# The lower-tail chi-square value\r\nXL=qchisq(1-.975, df=19)\r\n# The 95% confidence interval for standard deviation\r\nright_i=sqrt((n-1)*(s^2)/(XL))\r\nleft_i=sqrt((n-1)*(s^2)/(XU))\r\nprint(left_i)\r\nprint(right_i)\r\n\r\n\r\n ", "meta": {"hexsha": "044243ac9e0f14aa61d357bf1e8ed01dba91dc6a", "size": 828, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH7/EX7.2/Ex7_2.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH7/EX7.2/Ex7_2.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH7/EX7.2/Ex7_2.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 29.5714285714, "max_line_length": 84, "alphanum_fraction": 0.6594202899, "num_tokens": 320, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9653811571768048, "lm_q2_score": 0.8198933271118221, "lm_q1q2_score": 0.7915095688887513}} {"text": "library(ISLR)\nset.seed(1)\ntrain=sample (392,196)\n\nlm.fit=lm(mpg~horsepower ,data=Auto,subset=train)\n\nmean((Auto$mpg - predict(lm.fit, Auto))[-train]^2)\n\nlibrary(boot)\nglm.fit=glm(mpg∼horsepower ,data=Auto)\ncv.err=cv.glm(Auto ,glm.fit)\ncv.err$delta\n\n#LOOCV test\ncv.error=rep(0,5)\nfor (i in 1:5){\n glm.fit=glm(mpg∼poly(horsepower ,i),data=Auto)\n cv.error[i]=cv.glm(Auto,glm.fit)$delta[1]\n}\ncv.error\n\n#10-fold CV test\nset.seed(17)\ncv.error.10=rep(0,10)\nfor (i in 1:10){\n glm.fit=glm(mpg ~ poly(horsepower ,i),data=Auto)\n cv.error.10[i]=cv.glm(Auto,glm.fit,K=10)$delta[1]\n}\ncv.error.10\n\n#bootstrap\nalpha.fn=function (data,index){\n X=data$X[index]\n Y=data$Y[index]\n return((var(Y)-cov(X,Y))/(var(X)+var(Y)-2*cov(X,Y)))\n}\n\nalpha.fn(Portfolio ,1:100)\nset.seed(1)\nalpha.fn(Portfolio ,sample (100,100, replace=T))\n\nboot(Portfolio, alpha.fn, R=1000)\n\n\n#bootstrap for linear regression coefficients\nboot.fn=function (data ,index) return(coef(lm(mpg ~ horsepower ,data=data,subset=index)))\nboot.fn(Auto ,1:392)\n\nset.seed(1)\nboot.fn(Auto ,sample (392,392, replace=T))\nboot(Auto ,boot.fn, 1000)\n\nboot.fn=function (data ,index) coefficients(lm(mpg~horsepower +I(horsepower ^2),data=data , subset=index))\nset.seed(1)\nboot(Auto ,boot.fn,1000)\n", "meta": {"hexsha": "bdf88746df78c8fd33bf074e7a3483baeec10037", "size": 1251, "ext": "r", "lang": "R", "max_stars_repo_path": "books/AnIntroductiontoStatisticalLearning/chapter05.lab.r", "max_stars_repo_name": "xunilrj/sandbox", "max_stars_repo_head_hexsha": "f92c12f83433cac01a885585e41c02bb5826a01f", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 7, "max_stars_repo_stars_event_min_datetime": "2017-04-01T17:18:35.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-12T05:23:23.000Z", "max_issues_repo_path": "books/AnIntroductiontoStatisticalLearning/chapter05.lab.r", "max_issues_repo_name": "xunilrj/sandbox", "max_issues_repo_head_hexsha": "f92c12f83433cac01a885585e41c02bb5826a01f", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 6, "max_issues_repo_issues_event_min_datetime": "2020-05-24T13:36:50.000Z", "max_issues_repo_issues_event_max_datetime": "2022-02-15T06:44:20.000Z", "max_forks_repo_path": "books/AnIntroductiontoStatisticalLearning/chapter05.lab.r", "max_forks_repo_name": "xunilrj/sandbox", "max_forks_repo_head_hexsha": "f92c12f83433cac01a885585e41c02bb5826a01f", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2018-09-20T01:07:39.000Z", "max_forks_repo_forks_event_max_datetime": "2019-02-22T14:55:38.000Z", "avg_line_length": 22.3392857143, "max_line_length": 124, "alphanum_fraction": 0.6866506795, "num_tokens": 439, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9124361557147439, "lm_q2_score": 0.8670357529306639, "lm_q1q2_score": 0.7911147692712935}} {"text": "#' rsvd\n#' \n#' Randomized singular value decomposition.\n#' \n#' @details\n#' A randomized SVD is an approximate method for computing using random\n#' projections to estimate singular values/vectors. It is usually faster than\n#' a full SVD (say via \\code{svd()}) when only the first few singular\n#' values/vectors are needed.\n#' \n#' @section Communication:\n#' The operation is completely local except for forming the crossproduct, which\n#' is an \\code{allreduce()} call, quadratic on the number of columns.\n#' \n#' @param x\n#' The input data matrix.\n#' @param k\n#' The number of singular values and/or left/right singular vectors\n#' to estimate.\n#' @param q\n#' An integer exponent, say 1, 2, or 3. See the paper for details.\n#' @param retu\n#' Logical; should the left singular vectors (\"U\") be returned?\n#' @param retv\n#' Logical; should the right singular vectors (\"V\") be returned?\n#' \n#' @return \n#' A list of elements \\code{d}, \\code{u}, and \\code{v}, as with R's own\n#' \\code{svd()}. The elements are, respectively, a regular vector, a shaq, and\n#' a regular matrix.\n#' \n#' @examples\n#' \\dontrun{\n#' library(kazaam)\n#' x = ranshaq(runif, 10, 3)\n#' \n#' svd = rsvd(x)\n#' comm.print(svd$d) # a globally owned vector\n#' svd$u # a shaq\n#' comm.print(svd$v) # a globally owned matrix\n#' \n#' finalize()\n#' }\n#' \n#' @references\n#' Halko, Martinsson, and Tropp. 2011. Finding structure with randomness:\n#' probabilistic algorithms for constructing approximate matrix decompositions.\n#' SIAM Review 53 217-288.\n#' \n#' @export\nrsvd <- function(x, k=1, q=2, retu=TRUE, retv=TRUE)\n{\n if (!is.shaq(x))\n comm.stop(\"input 'x' must be a shaq\")\n \n ### Stage A from the paper\n n = ncol(x)\n Omega = runif(n * 2*k) # nx(2k)\n dim(Omega) = c(n, 2*k)\n \n Y = x %*% Omega # mx(2k)\n Q = qr_Q(Y) # mx(2k)\n \n for (i in 1:q)\n {\n Y = crossprod(x, Q) # nx(2k)\n Q = qr.Q(qr(Y)) # nx(2k)\n Y = x %*% Q # mx(2k)\n Q = qr_Q(Y) # mx(2k)\n }\n \n ### Stage B\n B = crossprod(Q, x) # (2k)xn\n \n if (!retu)\n nu = 0\n else\n nu = min(dim(B))\n \n if (!retv)\n nv = 0\n else\n nv = min(dim(B))\n \n svd.B = svd(B, nu, nv)\n \n ind = 1L:k\n d = (svd.B$d)[ind]\n \n \n # Produce u/v as desired\n if (retu)\n {\n u = Q %*% svd.B$u\n u = u[, ind]\n }\n \n if (retv)\n v = svd.B$v[, ind, drop=FALSE]\n \n \n # wrangle return\n if (retu)\n {\n if (retv)\n svd <- list(d=d, u=u, v=v)\n else\n svd <- list(d=d, u=u)\n }\n else\n {\n if (retv)\n svd <- list(d=d, v=v)\n else\n svd <- list(d=d)\n }\n \n svd\n}\n", "meta": {"hexsha": "93b2c966550f47a1f1deec167b7a7f75d0d407e6", "size": 2525, "ext": "r", "lang": "R", "max_stars_repo_path": "R/rsvd.r", "max_stars_repo_name": "snoweye/kazaam", "max_stars_repo_head_hexsha": "0b6f290516f1a6e505ced665b6f2730ba9bc45d4", "max_stars_repo_licenses": ["BSD-2-Clause"], "max_stars_count": 4, "max_stars_repo_stars_event_min_datetime": "2017-07-16T19:21:57.000Z", "max_stars_repo_stars_event_max_datetime": "2020-06-24T13:07:08.000Z", "max_issues_repo_path": "R/rsvd.r", "max_issues_repo_name": "snoweye/kazaam", "max_issues_repo_head_hexsha": "0b6f290516f1a6e505ced665b6f2730ba9bc45d4", "max_issues_repo_licenses": ["BSD-2-Clause"], "max_issues_count": 2, "max_issues_repo_issues_event_min_datetime": "2017-06-24T21:33:17.000Z", "max_issues_repo_issues_event_max_datetime": "2018-08-07T03:33:48.000Z", "max_forks_repo_path": "R/rsvd.r", "max_forks_repo_name": "snoweye/kazaam", "max_forks_repo_head_hexsha": "0b6f290516f1a6e505ced665b6f2730ba9bc45d4", "max_forks_repo_licenses": ["BSD-2-Clause"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2017-06-24T21:22:10.000Z", "max_forks_repo_forks_event_max_datetime": "2017-06-24T21:22:10.000Z", "avg_line_length": 21.0416666667, "max_line_length": 79, "alphanum_fraction": 0.5861386139, "num_tokens": 874, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9263037282594921, "lm_q2_score": 0.8539127510928476, "lm_q1q2_score": 0.7909825649456245}} {"text": "# Example : 2 Chapter : 6.1 Page No: 285\r\n# Eigen values and eigen vectors of Projection matrix\r\nA<-matrix(c(0.5,0.5,0.5,0.5),ncol=2)\r\nsol<-eigen(A)\r\nlambda<-sol$values\r\nx<-sol$vectors #These are normalised eigen vectors \r\n#to get eigen vectors in text book multiply them with scalars\r\nx[,1]<-x[,1]*(1/x[1,1])\r\nx[,2]<-x[,2]*(1/x[1,2])\r\nprint(\"The eigen values of the matrix are\")\r\nprint(lambda)\r\nprint(\"The eigen vectors of the matrix are\")\r\nprint(x)", "meta": {"hexsha": "369a5e4729e8c7bfad24be05cef3c2447cd17bd6", "size": 456, "ext": "r", "lang": "R", "max_stars_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH6/EX6.1.2/Ex6.1_2.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH6/EX6.1.2/Ex6.1_2.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH6/EX6.1.2/Ex6.1_2.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 35.0769230769, "max_line_length": 62, "alphanum_fraction": 0.6710526316, "num_tokens": 151, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9263037262250325, "lm_q2_score": 0.8539127492339909, "lm_q1q2_score": 0.7909825614865076}} {"text": "# Packages used : pracma\n# To install pracma,type following in command line while connected to internet\n# install.packages(\"pracma\") \n# package can be included by command \" library(pracma) \"\n# for more information about pracma visit https://cran.r-project.org/web/packages/pracma/index.html\n\n# Example : 3.3A Chapter : 3.3 Page No: 149\n# Find the row reduced echelon form, rank and special solution for given matrix\n\nlibrary(pracma)\nsolution <- function(A){\n R<-rref(A)\n m<-nrow(A)\n n<-ncol(A)\n pivotcol<-c() #vector to store the column numbers of pivot columns\n freecol<-c() #vector to store the column numbers of free columns\n i<-1\n j<-1\n \n # to find which columns are pivot and which are free\n while(i<=m & j<=n){\n if(R[i,j]==1){\n pivotcol<-c(pivotcol,j)\n i<-i+1\n j<-j+1\n }\n else{\n j<-j+1\n }\n }\n y<-length(pivotcol)\n freecol<-c(1:n)\n freecol<-freecol[!freecol%in%pivotcol]\n x<-length(freecol)\n N<-c()\n #find the basis for null space based on Row reduced echelon form of given matrix\n if(y==n){\n N<-c()\n }\n else{\n for(i in 1:x){\n temp<-c(1:n)\n for(j in 1:x){\n temp[freecol[j]]<-0\n }\n temp[freecol[i]]<-1\n temp[freecol[i]]\n for(j in 1:y){\n temp[pivotcol[j]]<-R[j,freecol[i]]*-1\n }\n N<-c(N,temp)\n }\n N<-matrix(N,nrow=n,ncol=x)\n }\n print(\"Row reduced echelon form is\")\n print(R)\n print(\"Rank of the Matrix is\")\n print(y)\n print(\"Special solutions for given matrix are given by\")\n print(N)\n}\n\nA<-matrix(c(1,-1,0,0,-1,2,-1,0,0,-1,2,-1,0,0,-1,1),nrow=4)\nsolution(A)\n", "meta": {"hexsha": "5dbfb740572f33c11fd6fbc0a50b045dcca2de2a", "size": 1569, "ext": "r", "lang": "R", "max_stars_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH3/EX3.3.a/Ex3_3.3A.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH3/EX3.3.a/Ex3_3.3A.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH3/EX3.3.a/Ex3_3.3A.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 24.1384615385, "max_line_length": 99, "alphanum_fraction": 0.621414914, "num_tokens": 540, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9219218327098192, "lm_q2_score": 0.8577680995361899, "lm_q1q2_score": 0.7907951383644228}} {"text": "catch=c(3.6,.8,2.5,2.9,1.4,.9,3.2,2.7,2.2,5.9,3.3,2.9,3.6,2.4,.9,2.0,1.9,3.1,2.6,3.4)\r\nresidence=c(92.2,86.7,80.2,87.2,64.9,90.1,60.7,50.9,86.1,90.0,80.4,75.0,70.0,64.6,50.0,50.0,51.2,40.1,45.0,50.0)\r\nsize=c(.21,.30,.31,.40,.44,.56,.78,1.21,.34,.40,.52,.66,.78,.91,1.10,1.24,1.47,2.21,2.46,2.80)\r\naccess=c(0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1)\r\nstructures=c(81,26,52,64,40,22,80,60,30,90,74,50,61,40,22,50,37,61,39,53)\r\nrelation = lm(catch~residence+size+access+structures)\r\nprint(summary(relation))\r\nanova(relation)\r\n\r\n# for reduced model\r\nprint(\" for reduced model\")\r\nrelation = lm(catch~residence+size)\r\nprint(summary(relation))\r\nanova(relation)\r\n# complete linear regression model : -2.78 + .0268x1 + .504x2 + .743x3 + .0511x4\r\n# reduced model : -.87 + .0394x1 + .828x2\r\n# test statistic\r\nSSregression_complete=24.0624\r\nSSregression_reduced=2.913\r\nSsresidual_complete=2.2756\r\nn=20\r\na=(SSregression_complete-SSregression_reduced)/2\r\nb=(Ssresidual_complete)/(n-5)\r\nF=a/b\r\nprint(F)\r\nfvalue=qf(1-.01,2,15)\r\nprint(fvalue)\r\n# The value of the test statistic is much larger than the tabled value, so we have conclusive evidence that the access and structure variables add predictive value", "meta": {"hexsha": "1c06c1e058b31fd171064a327295f1b1ddcbcf82", "size": 1190, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH12/EX12.17/Ex12_17.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH12/EX12.17/Ex12_17.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH12/EX12.17/Ex12_17.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 42.5, "max_line_length": 164, "alphanum_fraction": 0.6882352941, "num_tokens": 532, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9416541577509315, "lm_q2_score": 0.8397339656668286, "lm_q1q2_score": 0.7907389801748471}} {"text": "##Correlation tests of local instability, island size and degree of NNI graph\n\n##number of areas vs island size\nareas <- c(4, 6, 6, 8, 9)\nislandSize <- c(18, 72, 90, 216, 486)\nareaBySize <- as.data.frame(cbind(areas,islandSize))\ncor.test(areaBySize$areas, areaBySize$islandSize, method = \"pearson\")\n#r=0.9053, pval=0.0345\n\n##number of possible topologies vs island size\ntopol <- c(3^4, 3^6, 3^6, 3^8, 3^9)\nislandSize <- c(18, 72, 90, 216, 486)\ntopolBySize <- as.data.frame(cbind(topol,islandSize))\ncor.test(topolBySize$topol, topolBySize$islandSize, method = \"pearson\")\n#r=0.9925, pval=0.0008\n\n##number of areas of instability vs degree\nareas <- c(4, 6, 6, 8, 9)\ndegree <- c(4.33,6.33,6.33,7.67,9.00)\nareaByDegree <- as.data.frame(cbind(areas,degree))\ncor.test(areaByDegree$areas, areaByDegree$degree, method = \"pearson\")\n#r=0.9936, pval=0.000615\n\n##island size vs degree\nislandSize <- c(18, 72, 90, 216, 486)\ndegree <- c(4.33,6.33,6.33,7.67,9.00)\nislandByDegree <- as.data.frame(cbind(islandSize,degree))\ncor.test(islandByDegree$islandSize, islandByDegree$degree, method = \"pearson\")\n#r=0.9158, pval=0.02895\n", "meta": {"hexsha": "9f3e76f981e89e904ddf297982897330c0addb5b", "size": 1109, "ext": "r", "lang": "R", "max_stars_repo_path": "correlationTests.r", "max_stars_repo_name": "anaserrasilva/MajorityRuleAndTreeIslands", "max_stars_repo_head_hexsha": "ddd11fa643562ea907221e01aabe2071b4d19a5c", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "correlationTests.r", "max_issues_repo_name": "anaserrasilva/MajorityRuleAndTreeIslands", "max_issues_repo_head_hexsha": "ddd11fa643562ea907221e01aabe2071b4d19a5c", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "correlationTests.r", "max_forks_repo_name": "anaserrasilva/MajorityRuleAndTreeIslands", "max_forks_repo_head_hexsha": "ddd11fa643562ea907221e01aabe2071b4d19a5c", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 36.9666666667, "max_line_length": 78, "alphanum_fraction": 0.7132551849, "num_tokens": 436, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9697854103128328, "lm_q2_score": 0.8152324848629215, "lm_q1q2_score": 0.7906005698331386}} {"text": "# Q.1 -> Q1. The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number?\r\n\r\neuler <- function(n) {\r\n if (n==1) return(NULL)\r\n if (n==2) return(n)\r\n l <- 2:n\r\n i <- 1\r\n p <- 2\r\n while (p^2<=n) {\r\n l <- l[l==p | l%%p!=0]\r\n i <- i+1 \r\n p <- l[i]\r\n }\r\n return(l)\r\n}\r\n\r\nprime.factors <- function (n) {\r\n factors <- c() \r\n primes <- esieve(floor(sqrt(n))) \r\n d <- which(n%%primes == 0) \r\n if (length(d) == 0) \r\n return(n)\r\n for (q in primes[d]) { \r\n while (n%%q == 0) { \r\n factors <- c(factors, q)\r\n n <- n/q } } \r\n if (n > 1) factors <- c(factors, n)\r\n return(factors)\r\n}\r\n\r\nprint(max(prime.factors(13195)))", "meta": {"hexsha": "6e116b12044093d2413c5ac2ccb05ed805400b80", "size": 678, "ext": "r", "lang": "R", "max_stars_repo_path": "Q.1.r", "max_stars_repo_name": "Subr1ata/D.A.-Lab-Assignments", "max_stars_repo_head_hexsha": "75e9eab3483e8650bd0396b0e102c89d0533b1eb", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Q.1.r", "max_issues_repo_name": "Subr1ata/D.A.-Lab-Assignments", "max_issues_repo_head_hexsha": "75e9eab3483e8650bd0396b0e102c89d0533b1eb", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Q.1.r", "max_forks_repo_name": "Subr1ata/D.A.-Lab-Assignments", "max_forks_repo_head_hexsha": "75e9eab3483e8650bd0396b0e102c89d0533b1eb", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 21.8709677419, "max_line_length": 109, "alphanum_fraction": 0.4867256637, "num_tokens": 253, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9433475746920262, "lm_q2_score": 0.8376199653600372, "lm_q1q2_score": 0.7901667628360102}} {"text": "# ......................................................................................\n# ...............................Exercise 2 - Probability...............................\n# code presented in this excercise is not required on homeworks or exams, its only to show what is possible in R an to complement the excercise with nice graphs.** \n# ......................................................................................\n\n# If text does not display correctly, set File \\Reopen with Encoding ... to UTF-8 \n# Use CTRL + SHIFT + O to display the contents of the script \n# Use CTRL + ENTER to run commands on a single line \n\n# In this exercise, we will go through an introduction to probability. We assume you are\n# familiar with the terms: **definition of probability, conditional probability, total\n# probability theorem, Bayes' theorem**.\n# \n# Auxiliary functions ####\n# \n# * Total probability ####\n# \n# $P(A)=\\sum_{i=1}^{n}P(B_i)P(A|B_i)$\n# \n\n\n# probability calculation P(A) - total probability theorem\ntotal_probability = function(P_B, P_AB)\n{ # we consider P_B as a vector of values P(B_i) and P_AB as a vector of values P(A|B_i)\n P_A = 0\n for (i in 1:length(P_B))\n {\n P_A = P_A + P_B[i]*P_AB[i]\n }\n return(P_A)\n}\n\n# * Bayes' theorem ####\n# \n# $P(B_k|A)=\\frac{P(B_k)P(A|B_k)}{\\sum_{i=1}^{n}P(B_i)P(A|B_i)}$\n# \n\n\n# calculation of conditional probability P(B_k|A) - Bayes' theorem\nbayes = function(P_B, P_AB, k)\n{ # we consider P_B as a vector of values P(B_i), P_AB as a vector of values P(A|B_i) and k as and index in P(B_k|A)\n P_A = total_probability(P_B, P_AB)\n P_BkA = P_B[k]*P_AB[k]/P_A\n return(P_BkA)\n} \n\n# **We will add functions from the last exercise for computing combinatorial selections,\n# they are in the combinatorics script.R**\n# \n\n\nsource('combinatorics.R')\n\n# Examples ####\n# \n# * Example 1. ####\n# \n# Determine the probability that a number greater than 14 will fall on a 20-wall fair\n# dice roll.\n# \n\n\nomega = 1:20\nA = c(15,16,17,18,19,20)\n# probability as a proportion favorable to all\nlength(A)/length(omega)\n\n# * Example 2. ####\n# \n# Determine the probability that a number greater than 14 will fall on a 20-wall dice\n# roll, if you know that even numbers fall twice as often as odd numbers.\n# \n\n\np_odd = 1/(20+10)\np_even = 2*p_odd\nprobability = c(p_odd, p_even, p_odd, p_even, p_odd, p_even, p_odd, p_even, p_odd, p_even, \n p_odd, p_even, p_odd, p_even, p_odd, p_even, p_odd, p_even, p_odd, p_even)\nprobability\n# probability is\nsum(probability[15:20])\n\n# * Example 3. ####\n# \n# Determine the probability that you will guess exactly 4 numbers in the lottery.(6\n# numbers out of 49 are drawn)\n# \n\n\n(combinations(6,4)*combinations(43,2))/combinations(49,6)\n\n# * Example 4. ####\n# \n# From the alphabetical list of students enrolled in the exercise, the teacher selects\n# the first 12 and offers them a bet: “If each of you was born in a different zodiac\n# sign, I will give each of you CZK 100. However, if there are at least two students\n# among you who were born in the same sign, each of you will give me 100 CZK. ”Is it\n# worthwhile for students to accept a bet? How likely are students to win?\n# \n\n\npermutation(12)/r_permutation_repetition(12,12)\n\n# * Example 5. ####\n# \n# Calculate the probability that an electric current will flow from point 1 to point 2\n# if part of the el. circuit, including the probability of failure of individual\n# components is indicated in the following figure.(The failures of the individual\n# components are independent of each other.)
\n# ![Image.png](attachment:image.png)\n# \n\n\n# divided into blocks I=(A, B) and II=(C, D, E)\nPI = 1 - (1 - 0.1)*(1 - 0.3)\nPI\nPII = 0.2*0.3*0.2\nPII\n# result\n(1 - PI)*(1-PII)\n\n# * Example 6. ####\n# \n# The patient is suspected of having one of four mutually exclusive diseases - N1, N2,\n# N3, N4 with a probability of occurrence of P(N1)=0.1; P(N2)=0.2; P(N3)=0.4; P(N4)=0.3.\n# Laboratory test A is positive in the case of the first disease in 50% of cases, in the\n# second disease in 75% of cases, in the third disease in 15% of cases and in the fourth\n# in 20% of cases. What is the probability that the result of the laboratory test will\n# be positive?\n# \n\n\n# total probability theorem\nP_N = c(0.1,0.2,0.4,0.3) # P(N1), P(N2),...\nP_PN = c(0.5,0.75,0.15,0.2) # P(P|N1), P(P|N2),...\nP_P = total_probability(P_B = P_N, P_AB = P_PN) # P(P)\nP_P\n\n# * Example 7. ####\n# \n# Telegraphic characters consist of \"dot\" and \"comma\" signals. It is statistically found\n# that 25% of \"dot\" messages and 20% of \"comma\" signals are distorted. It is also known\n# that signals are used in a 3: 2 ratio. Determine the probability that the signal was\n# received correctly if a \"dot\" signal was received.\n# \n\n\n# Bayes' theorem\nP_O = c(0.6, 0.4) # P(O.), P(O-)\nP_PO = c(0.75, 0.2) # P(P.|O.), P(P.|O-)\nbayes(P_B = P_O, P_AB = P_PO, k = 1) # k=1 because correctly=O.\n\n\n# * Example 8. ####\n# \n# 85% of green taxis and 15% of blue taxis run in one city. The witness of the traffic\n# accident testified that the accident was caused by the driver of the blue taxi, who\n# then left. Tests carried out under similar lighting conditions showed that the witness\n# identified the color of the taxi well in 80% of cases and was wrong in 20% of cases.\n# \n# - What is the probability that the culprit of the accident actually drove a blue taxi?\n# \n# - Subsequently, another independent witness was found who also claims that the taxi\n# was blue. What is the probability that the culprit of the accident actually drove a\n# blue taxi now?\n# \n# - Does the probability that the perpetrator of the accident actually drove a blue taxi\n# affect whether the two witnesses mentioned above testified gradually or\n# simultaneously?\n# \n\n\n# a) again Bayes' theorem\nP_B = c(0.85, 0.15) # P(Z), P(M)\nP_SB = c(0.20, 0.80) # P(SM|Z), P(SM|M)\nbayes(P_B = P_B, P_AB = P_SB, k = 2) # blue is second\n\n\n# b) first option - second pass through Bayes\nP_M = bayes(P_B = P_B, P_AB = P_SB, k = 2)\nP_B = c(1 - P_M, P_M) # P(Z), P(M)\nP_SB = c(0.20, 0.80) # P(S2M|Z), P(S2M|M)\nbayes(P_B = P_B, P_AB = P_SB, k = 2)\n\n# c) or answered at once\nP_B = c(0.85, 0.15) # P(Z), P(M)\nP_SB = c(0.20^2, 0.80^2) # P(S1M & S2M|Z), P(S1M & S2M|M)\nbayes(P_B = P_B, P_AB = P_SB, k = 2)\n\n# * Example 9. ####\n# \n# We need to find out the answer to a sensitive question. How to estimate what\n# percentage of respondents will answer YES to the question and at the same time\n# guarantee complete anonymity to all respondents? One of the solutions is the so-called\n# double-anonymous survey:\n# \n# We will let the respondents throw the coin A and the coin B. \n# - Those who got head on coin A will write the answer(YES/NO) to the sensitive question\n# on teir card. \n# - Those who got tail on coin A will write YES = if coin B landed on head or NO = if\n# coin B landed on tail. \n# \n# How do we determine the proportion of students who answered YES to a sensitive\n# question?\n# \n# Assume that respondents were asked if they were cheating on an exam. From the\n# questionnaires, it was found that 120 respondents answered \"YES\" and 200 respondents\n# answered \"NO\". What percentage of students cheated at the exam?\n# \n\n\n# total probability theorem\n# P(YES)=P(A_YES) * P(YES|A_YES) + P(A_NO) * P(B_YES|A_NO)\n# equation 120/320=0.5 * x + 0.5 * 0.5\n(120/320-0.5^2)/0.5\n\n# * Bonus - Monty Hall Problem ####\n# \n# You are winner of the TV competition. You are presented with three doors. Behind one\n# is the crown prize and behind twe there is nothing. You have to pick one door. Then\n# the moderator opens one of the two doors left (the ones you did not pick) and the\n# doors without a prize (as the moderator knows where the prize is, he will always pick\n# empty doors). \n# \n# Now the Question, will you stick with your original choice of the door, or you will\n# switch to the other one still not opened?\n\n\n", "meta": {"hexsha": "3564998e0994a0a1ac7ee4614084bb03e07e8c5a", "size": 7906, "ext": "r", "lang": "R", "max_stars_repo_path": "Exercise 2/T3_probability.r", "max_stars_repo_name": "Beremi/PS_eng_2022", "max_stars_repo_head_hexsha": "178bc329f3d67aa3bf6d8d16356692525502a87d", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Exercise 2/T3_probability.r", "max_issues_repo_name": "Beremi/PS_eng_2022", "max_issues_repo_head_hexsha": "178bc329f3d67aa3bf6d8d16356692525502a87d", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Exercise 2/T3_probability.r", "max_forks_repo_name": "Beremi/PS_eng_2022", "max_forks_repo_head_hexsha": "178bc329f3d67aa3bf6d8d16356692525502a87d", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2022-03-07T13:35:24.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-07T13:35:24.000Z", "avg_line_length": 34.5240174672, "max_line_length": 165, "alphanum_fraction": 0.6659499115, "num_tokens": 2384, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9252299570920387, "lm_q2_score": 0.8539127585282744, "lm_q1q2_score": 0.7900656649334598}} {"text": "MiniBatchGradientDescent <- function(X, Y, alpha=0.1, max.iter=1000, precision=0.0001, batchRate=0.5, seed=1){\r\n if (is.null(n <- nrow(X))) stop(\"'X' must be a matrix\")\r\n \r\n if(n == 0L) stop(\"0 (non-NA) cases\")\r\n \r\n p <- ncol(X)\r\n \r\n if(p == 0L) {\r\n return(list(\r\n x = X,\r\n y = Y,\r\n coefficients = numeric(),\r\n residuals = Y,\r\n fitted.values = 0 * Y\r\n ))\r\n }\r\n \r\n if(NROW(Y) != n) {\r\n stop(\"incompatible dimensions\")\r\n }\r\n\r\n # Initial value of coefficients\r\n B <- rep(0, ncol(X))\r\n # batch size\r\n batchSize <- ceiling(n * batchRate)\r\n # Recorded for loss vs iteration\r\n loss_iter <- data.frame(\r\n loss = numeric(),\r\n iter = integer()\r\n )\r\n for(iter in 1:max.iter){\r\n B.prev <- B\r\n\r\n for(i in seq(1, n, batchSize)){\r\n indexes <- i:min((i+batchSize), n)\r\n Xtemp <- X[indexes,,drop=FALSE]\r\n Ytemp <- Y[indexes,drop=FALSE]\r\n \r\n yhat <- Xtemp %*% B\r\n B <- B + (alpha / length(indexes)) * t(Xtemp) %*% (Ytemp - yhat)\r\n }\r\n \r\n loss <- Y - X %*% B\r\n loss_iter <- rbind(loss_iter, c(sqrt(mean(loss^2)), iter))\r\n \r\n if(any(is.na(B)) ||\r\n !any(abs(B.prev - B) > precision * B)){\r\n break\r\n }\r\n }\r\n \r\n names(B) <- colnames(X)\r\n fv <- X %*% B\r\n rs <- Y - fv\r\n coef <- as.vector(B)\r\n names(coef) <- rownames(B)\r\n colnames(loss_iter) <- c('loss', 'iter')\r\n \r\n z <- structure(list(\r\n x=X,\r\n y=Y,\r\n coefficients = coef,\r\n fitted.values = fv,\r\n residuals = rs,\r\n loss_iter = loss_iter\r\n ),\r\n class = c(\"rlm\", \"rlmmodel\"))\r\n \r\n z\r\n}\r\n", "meta": {"hexsha": "2653b082ee0156098825ca5cdcae5d36e3892a02", "size": 1573, "ext": "r", "lang": "R", "max_stars_repo_path": "R/mbgd.r", "max_stars_repo_name": "SiddheshAcharekar/rcane", "max_stars_repo_head_hexsha": "c385060cc7a2338c4ba19887abecbd6899d2f54e", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/mbgd.r", "max_issues_repo_name": "SiddheshAcharekar/rcane", "max_issues_repo_head_hexsha": "c385060cc7a2338c4ba19887abecbd6899d2f54e", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/mbgd.r", "max_forks_repo_name": "SiddheshAcharekar/rcane", "max_forks_repo_head_hexsha": "c385060cc7a2338c4ba19887abecbd6899d2f54e", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.1549295775, "max_line_length": 111, "alphanum_fraction": 0.5009535919, "num_tokens": 496, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9294404077216356, "lm_q2_score": 0.849971181358171, "lm_q1q2_score": 0.7899975613531787}} {"text": "## Zernike coefficients for a conic\n\nzconic <- function(D, rc, b = -1, lambda = 632.8, nmax = 6) {\n if ((nmax %%2) != 0) stop(\"nmax must be even\")\n nterms <- nmax/2+1\n sa <- zc <- zs <- numeric(0)\n cz <- matrix(0, nterms, nterms)\n\n sd <- D/2\n na <- (sd/rc)^2\n sa[1] <- sa[2] <- 0\n## 4th order conic term\n zs[3] <- (sd/rc)^3*sd*1e6/8/lambda\n zc[3] <- (1+b)*zs[3]\n sa[3] <- zc[3]-zs[3]\n## binomial expansion of conic\n if (nterms >= 4) {\n for (k in 4:nterms) {\n mult <- (1-3/(2*(k-1)))*na\n zc[k] <- mult*(1+b)*zc[k-1]\n zs[k] <- mult*zs[k-1]\n sa[k] <- zc[k]-zs[k]\n }\n }\t\n## recurrence relation for coefficients of radial zernikes\n cz[1,] <- (-1)^(0:(nterms-1))\n cz[2,2] <- 2\n for (j in 3:nterms) {\n for (i in 2:j) {\n n <- 2*(j-1)\n cz[i, j] <- (4*(n-1)*cz[i-1, j-1]-2*(n-1)*cz[i,j-1]-(n-2)*cz[i,j-2])/n\n }\n }\n for (j in 1:nterms) {\n n <- 2*(j-1)\n cz[,j] <- cz[,j]*sqrt(n+1)\n }\n solve(cz,sa)[-(1:2)]\n}\n\n## Zernike coefficients of Wavefront error due to testing a conic at center of curvature\n## this should be more accurate for numerical nulling than twice the height difference as in zconic\n\nsconic <- function(D, rc, b = -1, eps = 0., lambda = 632.8, nmax = 6) {\n \n if ((nmax %%2) != 0) stop(\"nmax must be even\")\n nz <- (nmax-2)/2\n zc <- numeric(nz)\n\n na <- D/2/rc\n p <- function(rho, na, b) {\n (rho*na)^2*(1 - 2/(1 + sqrt(1 - (1+b)*(rho*na)^2)) +\n (rho*na)^2/(1 + sqrt(1 - (1+b)*(rho*na)^2))^2)\n }\n q <- function(rho, na, b) 1 - sqrt(1 + p(rho, na, b))\n f <- function(rho, na, b, n) q(rho, na, b)*rzernike(sqrt((rho^2-eps^2)/(1-eps^2)), n, 0)*rho\n for (i in 1:nz) {\n n <- 2 + 2*i\n int <- integrate(f, lower=eps, upper=1, na=na, b=b, n=n)\n zc[i] <- 4 * rc * sqrt(n+1) * int$value * 1.e6/lambda/(1-eps^2)\n if (int$message != \"OK\") warning(\"coefficient may be inaccurate\")\n }\n zc\n}\n\n\n\n## returns cosine and sine components of Bath astigmatism\n\n##\n# D = diameter\n# rc = radius of curvature\n# s = beam separation\n# lambda = source wavelength\n# phi = angle from horizontal (degrees)\n##\n\nastig.bath <- function(D, rc, s, lambda=632.8, phi=0) {\n astig.tot <- D^2 * s^2/(32 * sqrt(6) * lambda* 1.e-6 * rc^3)\n astig.tot*c(cos(pi*phi/90), sin(pi*phi/90))\n}\n\n\n", "meta": {"hexsha": "c13dce75b68b031164c7828c76bb9ee984e0f7fe", "size": 2394, "ext": "r", "lang": "R", "max_stars_repo_path": "R/sa_astig_null.r", "max_stars_repo_name": "mlpeck/zernike", "max_stars_repo_head_hexsha": "553a956417c34847b80a179a3f6922d71120061d", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 4, "max_stars_repo_stars_event_min_datetime": "2019-05-15T09:28:48.000Z", "max_stars_repo_stars_event_max_datetime": "2021-06-16T17:28:29.000Z", "max_issues_repo_path": "R/sa_astig_null.r", "max_issues_repo_name": "mlpeck/zernike", "max_issues_repo_head_hexsha": "553a956417c34847b80a179a3f6922d71120061d", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/sa_astig_null.r", "max_forks_repo_name": "mlpeck/zernike", "max_forks_repo_head_hexsha": "553a956417c34847b80a179a3f6922d71120061d", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2019-01-17T13:30:49.000Z", "max_forks_repo_forks_event_max_datetime": "2019-01-17T13:30:49.000Z", "avg_line_length": 28.5, "max_line_length": 99, "alphanum_fraction": 0.5033416876, "num_tokens": 949, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9553191259110587, "lm_q2_score": 0.8267118026095991, "lm_q1q2_score": 0.7897735966493579}} {"text": "# Imitate Poisson process built on the exponential random variables and plot its trajectories\n\nlibrary(ggplot2)\n\nPoisson <- function(seed_n, seed_rate)\n{\n # function to generate values of the Poisson process contructed on exponential random variables\n return(c(0,cumsum(rexp(n = seed_n, rate = seed_rate))))\n}\n\nDrawTrajectory <- function(numInst,\n timeline,\n N,\n inRate)\n{\n # function drawing trajectories of the Poisson process over \n # and used to generate Poisson process instances within function\n \n plot <- ggplot() + ggtitle(\"Trajectories of Poisson process\") + labs(x = 't', y = 'N(t)')\n for(i in 1:numInst)\n {\n plot <- plot + geom_path(aes(x = T, y = Poisson(N, inRate)))\n }\n plot\n}\n\n## input parameters\nlambda <- 1.0\ntMax <- 10 * lambda\nnum <- tMax\nT <- 0:10\n# call example\nDrawTrajectory(10, T, num, lambda)", "meta": {"hexsha": "d859654049dd1e8a597d82f41c2945f2f110ec85", "size": 941, "ext": "r", "lang": "R", "max_stars_repo_path": "lab1.r", "max_stars_repo_name": "alexgulyi/randimitation", "max_stars_repo_head_hexsha": "f2840fe8fec1ba7439b936c81851558864d1cba1", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lab1.r", "max_issues_repo_name": "alexgulyi/randimitation", "max_issues_repo_head_hexsha": "f2840fe8fec1ba7439b936c81851558864d1cba1", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lab1.r", "max_forks_repo_name": "alexgulyi/randimitation", "max_forks_repo_head_hexsha": "f2840fe8fec1ba7439b936c81851558864d1cba1", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 28.5151515152, "max_line_length": 97, "alphanum_fraction": 0.6418703507, "num_tokens": 249, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9579122696813394, "lm_q2_score": 0.8244619306896955, "lm_q1q2_score": 0.7897621992928253}} {"text": "### 5.2-1 \n\np <- 0.29\nnSamples <- 83\npHat <- 17\n\nz <- (pHat - p*nSamples) / (sqrt(nSamples * p * (1 - p)))\nprint(z)\n\n### 1 - alpha / 2 = 1 - 0.025 = 0.975\nzCrit <- qnorm(0.975, mean=0, sd=1, lower.tail = TRUE, log.p = FALSE)\nprint(zCrit)\n\n### z = -1.710221 -> H0 is accepted (mu = 29%)\n", "meta": {"hexsha": "c6acc94f62171a07e9b2aae17c90900880c46e5a", "size": 288, "ext": "r", "lang": "R", "max_stars_repo_path": "TASK3/sem3/hypTest1.r", "max_stars_repo_name": "mortarsynth/StatisticalModelling", "max_stars_repo_head_hexsha": "ebb6c76cd8defa7dcb2a4d16515328b55989dedd", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "TASK3/sem3/hypTest1.r", "max_issues_repo_name": "mortarsynth/StatisticalModelling", "max_issues_repo_head_hexsha": "ebb6c76cd8defa7dcb2a4d16515328b55989dedd", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "TASK3/sem3/hypTest1.r", "max_forks_repo_name": "mortarsynth/StatisticalModelling", "max_forks_repo_head_hexsha": "ebb6c76cd8defa7dcb2a4d16515328b55989dedd", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 19.2, "max_line_length": 69, "alphanum_fraction": 0.5277777778, "num_tokens": 129, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9632305349799241, "lm_q2_score": 0.8198933425148214, "lm_q1q2_score": 0.7897463029370295}} {"text": "# N Queens Problem : Place N Queens on an N * N board so that no two queens attack each other.\n# The board is represented by a nested list. An empty square is represented by 0, a queen is represented by 1. \nnqueens {\n *board = list(\n list(0,0,0,0,0,0,0,0),\n list(0,0,0,0,0,0,0,0),\n list(0,0,0,0,0,0,0,0),\n list(0,0,0,0,0,0,0,0),\n list(0,0,0,0,0,0,0,0),\n list(0,0,0,0,0,0,0,0),\n list(0,0,0,0,0,0,0,0),\n list(0,0,0,0,0,0,0,0)\n );\n tryRow(*board, 0);\n}\n\n# Try to place a queen on row *a\ntryRow(*board, *a) {\n on(*a == size(*board)) {\n printBoard(*board);\n }\n or {\n trySquare(*board, *a, 0);\n }\n}\n\n# Try to place a queen at square (*a, *b)\ntrySquare(*board, *a, *b) {\n or {\n \taccept(*board,*a,*b);\n \ttryRow(updateBoard(*board, *a, *b, 1), *a+1);\n }\n on(*b+1 < size(elem(*board, *a))) {\n\t trySquare(*board, *a, *b+1);\n }\n}\n\n# Test if placing a queen at square (*a, *b) is acceptable.\n# Placing a queens at square (*a, *b) is acceptable if it does not attack any queen on the board.\naccept(*board, *a, *b) {\n for(*i=0;*i 0) * rank(abs(s))))\n# 111\n\n(V.mean <- n * (n + 1) / 4)\n# 95\n\n(V.var <- n * (n + 1) * (2 * n + 1) / 24)\n# 617.5\n\n### H0: X symmetric\n### H1: X not symmetric\n\n## Aymptotic pvalue (with continuity correction)\n2 * (1 - pnorm(abs(V + 0.5 * sign(V.mean - V) - V.mean) / sqrt(V.var)))\n# 0.532789272835132\n\n## Exact pvalue\n2 * (1 - psignrank(V - (V.mean < V), n, lower.tail = V.mean < V))\n# 0.541217803955078\n\nwilcox.test(s, alternative = \"two.sided\")\n# Wilcoxon signed rank test\n#\n# data: s\n# V = 111, p-value = 0.5412\n# alternative hypothesis: true location is not equal to 0", "meta": {"hexsha": "c992d52c4ce0592a375e956012d44423d1a896f0", "size": 883, "ext": "r", "lang": "R", "max_stars_repo_path": "statistical-inference/non-parametric/exercise-12.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "statistical-inference/non-parametric/exercise-12.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "statistical-inference/non-parametric/exercise-12.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 23.8648648649, "max_line_length": 80, "alphanum_fraction": 0.5809739524, "num_tokens": 366, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9372107931567177, "lm_q2_score": 0.8418256452674008, "lm_q1q2_score": 0.7889680807007264}} {"text": "### 主成分分析の例\n### - Lawyers' Ratings of State Judges in the US Superior Court\n\n## パッケージの読み込み\nrequire(tidyverse) \nrequire(reshape2) \nrequire(ggfortify)\nrequire(GGally)\n\n## データの読み込み (\"datasets::USJudgeRatings\"を用いる)\ndata(USJudgeRatings) # データの読み込み\n\n## データの内容を確認\nhelp(USJudgeRatings) # 内容の詳細を表示\n## print(USJudgeRatings) # 全データの表示\nhead(USJudgeRatings) # 最初の6個を表示\ntail(USJudgeRatings) # 最後の6個を表示\n\n## データの散布図 (一部項目のみ): 図(a)\nggpairs(USJudgeRatings, columns=1:6) +\n ggtitle(\"Ratings of US Judges\")\n\n## 各データの視覚化 (radar chart)\njdgs <- sapply(rownames(USJudgeRatings), # 姓だけ取り出す\n function(x){unlist(strsplit(x,\",\"))[1]})\nmydata <- mutate(USJudgeRatings, jdgs) %>% \n head(12) %>% melt(id.vars=\"jdgs\") # 最初の12名のみ表示\n## 各データの表示 (一部データのみ): 図(b)\nggplot(mydata, aes(x=variable, y=value, group=jdgs)) + \n geom_polygon(fill=\"lightgreen\") + coord_polar() +\n facet_wrap(~jdgs)\n\n## 主成分分析\nmodel <- prcomp(~ ., data=USJudgeRatings)\n\n## 結果の評価\nsummary(model) # 寄与率の表示\nround(model$rotation,3) # 主成分方向の表示(3桁)\n\n## 寄与率: 図(c)\nplot(model, col=\"lightblue\",\n main=\"Proportion of Variance\") # 寄与率\n## biplotによる表示\n## 主成分得点 (第1,2主成分): 図(d)\nautoplot(model, data=USJudgeRatings, colour=\"gray\", \n label=TRUE, label.size=3, label.colour=\"darkgreen\", \n loadings=TRUE, loadings.colour=\"blue\",\n loadings.label=TRUE, loadings.label.size=5,\n loadings.label.colour=\"blue\",\n main=\"PCA of US Judge Ratings\")\n## 主成分得点 (第2,3主成分): 図(e)\nautoplot(model, x=2, y=3, data=USJudgeRatings, colour=\"gray\", \n label=TRUE, label.size=3, label.colour=\"darkgreen\", \n loadings=TRUE, loadings.colour=\"blue\",\n loadings.label=TRUE, loadings.label.size=5,\n loadings.label.colour=\"blue\",\n main=\"PCA of US Judge Ratings\")\n\n## 主成分得点の散布図: 図(f)\nggpairs(model$x, columns=1:6) +\n ggtitle(\"Scatterplot of PCA result\")\n## (無相関になっていることを確認)\n", "meta": {"hexsha": "f4789172637665f9280555a3b5feaf409f939c15", "size": 1889, "ext": "r", "lang": "R", "max_stars_repo_path": "docs/code/p-usjudge.r", "max_stars_repo_name": "noboru-murata/multivariate-analysis", "max_stars_repo_head_hexsha": "645bff23d3868e5d7c245ef4af7d0ff9fe98e017", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "docs/code/p-usjudge.r", "max_issues_repo_name": "noboru-murata/multivariate-analysis", "max_issues_repo_head_hexsha": "645bff23d3868e5d7c245ef4af7d0ff9fe98e017", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "docs/code/p-usjudge.r", "max_forks_repo_name": "noboru-murata/multivariate-analysis", "max_forks_repo_head_hexsha": "645bff23d3868e5d7c245ef4af7d0ff9fe98e017", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 29.9841269841, "max_line_length": 70, "alphanum_fraction": 0.6627845421, "num_tokens": 761, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9324533107374444, "lm_q2_score": 0.8459424411924673, "lm_q1q2_score": 0.788801829983232}} {"text": "# a script to estimate the value of pi using the Monte Carlo calculation\n\nset.seed(0.537916728589)\n\n# random vectors of length 100k\nx=runif(100000)\ny=runif(100000)\n\n# radius\nz=sqrt(x^2+y^2)\n\n# count the number of points inside the quarter-circle\nwhich(z<1)\nlength(which(z<=1))*4/length(z)\n\n# make some plots\nplot(x[which(z<=1)],y[which(z<=1)],xlab=\"X\",ylab=\"Y\",main=\"Monte Carlo sim\")\npoints(x[which(z>1)],y[which(z>1)],col='yellow')\n", "meta": {"hexsha": "d5600ab4c757d6b06b0a427a61a4cbc45da95dbd", "size": 434, "ext": "r", "lang": "R", "max_stars_repo_path": "src/r.r", "max_stars_repo_name": "millecodex/decarepo", "max_stars_repo_head_hexsha": "66c4be085d434e3a236fa6754ec9d1463663b8f5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "src/r.r", "max_issues_repo_name": "millecodex/decarepo", "max_issues_repo_head_hexsha": "66c4be085d434e3a236fa6754ec9d1463663b8f5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "src/r.r", "max_forks_repo_name": "millecodex/decarepo", "max_forks_repo_head_hexsha": "66c4be085d434e3a236fa6754ec9d1463663b8f5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.8421052632, "max_line_length": 76, "alphanum_fraction": 0.702764977, "num_tokens": 146, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9591542875927781, "lm_q2_score": 0.8221891348788759, "lm_q1q2_score": 0.7886062339312707}} {"text": "# reminder on descriptive statistics\n{r}\ndata(iris)\nX = iris$Sepal.Length \n# we use famous iris dataset that is built in R\nhist(X)\n# lets see how histogram changes based on breaks specified\nhist(X, breaks=100)\n#it's also interesting to combine hist with an estimation of the \n#pdf function made by density\nhist(X, freq=FALSE)\nlines(density(X),col=2, lwd=2)\n\nboxplot(X) #let's now use boxplots\n#to relate boxplot with hist:\npar(mfrow=c(2,1))\nhist(X, freq=FALSE)\nlines(density(X),col=2, lwd=2)\nboxplot(X, horizontal = TRUE)\n\n#regarding multivariate data it's possible to perform boxplot\nboxplot(iris[,-5])\n#it's possible for iris data to plot several boxplots side by side\n#because 4 variables are all expressed in the same units (cm)\n\n#the alternative will be a for loop\npar(mfrow=c(2,2))\nfor (j in 1:4) boxplot(iris[,j], main=paste('variable',j))\n\n#about scatterplots:\nplot(iris[,-5])\n\ncor(iris[,-5]) #correlation matrix \n\n#it is possible to add to this plot an additional category\n#called variable(here the species)\nplot(iris[,-5], col=as.numeric(iris$Species))\n\n# of course, it is possible to have a classical scatter plot \n#when looking only at 2 variables\nplot(iris$Sepal.Length, iris$Petal.Length, col=as.numeric(iris$Species))\n\n# Multivariate numerical indicators\n\nmu = colMeans(iris[,-5]) #colMeans computes mean of each column of the dataset\nmu\n\n#mean() function computes mean of all data, NA for multiviriable\n\n#Covariance and correlation metrices:\n\nS = cov(iris[,-5])\nS\n\nC = cor(iris[,-5])\nC\n\n#it's easier to read correlation matrix where -1 -> inverse-relation\n# 0 -> no relation and 1 -> strong relation\n\n\n#LDA and logistic regression\n#lets start again with iris data (as Fisher used it himself)\ndata(iris)\nlibrary(MASS)\n\nX = iris[,-5]\nY = as.numeric(iris$Species)\n\n\nlibrary(MASS)\nsystem.time(f <- lda(X,Y))\n\n#after learning it's possible to examine the output \n#Call:\nlda(X,Y)\n\n#afterwards, if we would like to classify a new observation,\n#we have to call the 'predict' function:\n\nxstar = c(6, 2.9, 5, 3) #new observtion \n\nystar = predict(f, xstar)\nystar #it belongs to class 1 virginica \n\n#let's compute error rate of this model\n#first a single split\n\nn = nrow(X)\nlearn = sample(1:n, 2/3*n)\nf <- lda(X[learn,], Y[learn])\nystar = predict(f,X[-learn,])\n\n#compiute the classification error\nerr = sum(Y[-learn] != ystar$class) / length(ystar$class)\nerr\n\n# a better version with resampling (boostraping):\n\nn = nrow(X)\nerr = c()\nfor (i in 1:10){\n learn = sample(1:n, 2/3*n)\n f <- lda(X[learn,], Y[learn])\n ystar = predict(f,X[-learn,])\n #compute the classification error\n err[i] = sum(Y[-learn] != ystar$class) / length(ystar$class)\n}\nboxplot(err)\n\n\n\n", "meta": {"hexsha": "1a391007cd9ed32bb40b2bd900ce03f06008d8a7", "size": 2665, "ext": "r", "lang": "R", "max_stars_repo_path": "LDA on iris data R.r", "max_stars_repo_name": "milxss/R_and_stats", "max_stars_repo_head_hexsha": "67e6f7842e6a22adef636a0891f8681fc646b816", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "LDA on iris data R.r", "max_issues_repo_name": "milxss/R_and_stats", "max_issues_repo_head_hexsha": "67e6f7842e6a22adef636a0891f8681fc646b816", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "LDA on iris data R.r", "max_forks_repo_name": "milxss/R_and_stats", "max_forks_repo_head_hexsha": "67e6f7842e6a22adef636a0891f8681fc646b816", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 23.5840707965, "max_line_length": 79, "alphanum_fraction": 0.7144465291, "num_tokens": 802, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9173026505426831, "lm_q2_score": 0.8596637541053281, "lm_q1q2_score": 0.7885718402162909}} {"text": "\nlinear.model<-function(beta,covariate){\n # beta: a 2-vector, where the first entry is the intercept\n yout=covariate*beta[2]+beta[1]\n return(yout);\n # Note: this function only works with simple linear regression model\n # How would you generalize it?\n}\n\nfit.linear.model<-function(covariate,outcome){\n # I will write down the function for (multiple) linear regression here\n X=cbind(1,covariate);\n beta.fit=solve( t(X)%*%X )%*%t(X)%*%outcome;\n return(beta.fit)\n}\n\nsum.of.squares<-function(beta,covariate,outcome){\n yout=linear.model(beta=beta,covariate=covariate);\n res=outcome-yout;\n sos= sum(res^2);\n return(sos)\n}\n\nestimate.sigma.sq<-function(beta,covariate,outcome){\n residual.sum.of.squares=sum.of.squares(beta=beta,covariate=covariate,outcome=outcome)\n n=length(outcome)\n sigma.sq.hat=residual.sum.of.squares/(n-2)\n return(sigma.sq.hat)\n}\n\nestimate.coef.var<-function(beta,covariate,outcome){\n sigma.sq.hat=estimate.sigma.sq(beta,covariate,outcome)\n var.hat.beta=beta;\n var.hat.beta[2]=sigma.sq.hat/sum( (covariate-mean(covariate))^2 )\n n=length(outcome)\n var.hat.beta[1]=sigma.sq.hat*sum(covariate^2)/sum((covariate-mean(covariate))^2 )/n\n return( var.hat.beta)\n}\n\nestimate.coef.sd<-function(beta,covariate,outcome){\n var.hat.beta=estimate.coef.var(beta,covariate,outcome)\n sd.hat.beta=sqrt(var.hat.beta);\n return(sd.hat.beta)\n}\n\nconf.int.quantile<-function(alpha,type,...){\n if(type==\"t\"){\n out=qt(c(1-alpha/2,alpha/2), ... )\n }else if (type==\"normal\"){\n out=qnorm(c(1-alpha/2,alpha/2), ... )\n }\n return(out)\n}\n\nboot.fit<-function(covariate,outcome){\n n=length(outcome);\n sample_indices = sample(1:n,n,replace=TRUE) # sampling with replacement\n covariate.boot= covariate[sample_indices]; outcome.boot= outcome[sample_indices];\n\n beta.hat=fit.linear.model(covariate=covariate.boot,outcome=outcome.boot);\n return(t(beta.hat ))\n}\n\nconf.int<-function(alpha,type,covariate,outcome,B=1e5){\n\n beta.hat=fit.linear.model(covariate,outcome);\n beta.sd=estimate.coef.sd(beta=beta.hat,covariate,outcome);\n if(type=='bootstrap'){\n beta.hat.boot=replicate(B,boot.fit(covariate,outcome));\n out=t(apply(beta.hat.boot[1,,],1,quantile,probs=c(alpha/2,1-alpha/2)));\n }else if(type=='t'){\n quants<-conf.int.quantile(alpha,type='t',df=n-2)\n out=beta.hat%*%c(1,1)-beta.sd%*%quants;\n }else{\n quants<-conf.int.quantile(alpha,type='normal')\n out=beta.hat%*%c(1,1)-beta.sd%*%quants;\n }\n colnames(out)=c( paste(round(alpha*50,digits=3),'%'), paste(100-round(alpha*50,digits=3),'%') )\n return(out)\n}\n\ncalculate.t<-function(covariate,outcome){\n beta.hat=fit.linear.model(covariate=covariate,outcome=outcome)\n beta.hat.sd=estimate.coef.sd(beta=beta.hat,covariate=covariate,outcome=outcome)\n beta.hat.t = (beta.hat-0)/beta.hat.sd;\n return(beta.hat.t)\n}\n\n## Wrap up the above code into one function\ncalculate.pvalue<-function(covariate,outcome,type){\n beta.hat.t=calculate.t(covariate,outcome);\n if (type=='t'){\n n=length(outcome);\n pval=2*apply(cbind(pt(beta.hat.t,df=n-2),(1-pt(beta.hat.t,df=n-2))),1,min);\n\n }else if (type=='z'){\n pval=2*apply(cbind(pnorm(-abs(beta.hat.t)),(1-pnorm(abs(beta.hat.t)))),1,min);\n\n }else if (type == 'bootstrap'){\n\n beta.hat=fit.linear.model(covariate=covariate,outcome=outcome)\n beta.hat.boot=replicate(1e5,boot.fit(covariate=covariate,outcome=outcome));\n pval=numeric(length(beta.hat));\n for(i in 1:length(beta.hat)){\n boot.est=beta.hat.boot[1,i,]\n pval[i]=2*min( mean(0boot.est) )\n }\n }\n return(pval)\n}\n\npermutation.test<-function(covariate,outcome){\n n=length(outcome);\n sample_indices = sample(1:n,n,replace=FALSE) # sampling without replacement\n covariate.perm= covariate[sample_indices]; outcome.perm= outcome;\n\n beta.hat.t=calculate.t(covariate.perm,outcome.perm)\n\n return(beta.hat.t[2])\n}\n\n", "meta": {"hexsha": "f89f39730eaffa6b633ee0972ee82d97169b519d", "size": 3844, "ext": "r", "lang": "R", "max_stars_repo_path": "sources.r", "max_stars_repo_name": "ChenShizhe/STA108_UCD", "max_stars_repo_head_hexsha": "3ee97392086f17efc9eee572d0ad686efe203166", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-12-05T22:59:39.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-05T22:59:39.000Z", "max_issues_repo_path": "sources.r", "max_issues_repo_name": "ChenShizhe/STA108_UCD", "max_issues_repo_head_hexsha": "3ee97392086f17efc9eee572d0ad686efe203166", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "sources.r", "max_forks_repo_name": "ChenShizhe/STA108_UCD", "max_forks_repo_head_hexsha": "3ee97392086f17efc9eee572d0ad686efe203166", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": 13, "max_forks_repo_forks_event_min_datetime": "2020-04-13T19:11:32.000Z", "max_forks_repo_forks_event_max_datetime": "2020-09-20T15:40:22.000Z", "avg_line_length": 31.5081967213, "max_line_length": 98, "alphanum_fraction": 0.698491155, "num_tokens": 1213, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9390248242542283, "lm_q2_score": 0.8397339736884711, "lm_q1q2_score": 0.7885310470631214}} {"text": "## R code 0.1\r\nprint( \"All models are wrong, but some are useful.\" )\r\n\r\n## R code 0.2\r\nx <- 1:2\r\nx <- x*10\r\nx <- log(x)\r\nx <- sum(x)\r\nx <- exp(x)\r\nx\r\n\r\n## R code 0.3\r\n( log( 0.01^200 ) )\r\n( 200 * log(0.01) )\r\n\r\n## R code 0.4\r\n# Load the data:\r\n# car braking distances in feet paired with speeds in km/h\r\n# see ?cars for details\r\ndata(cars)\r\n\r\n# fit a linear regression of distance on speed\r\nm <- lm( dist ~ speed , data=cars )\r\n\r\n# estimated coefficients from the model\r\ncoef(m)\r\n\r\n# plot residuals against speed\r\nplot( resid(m) ~ speed , data=cars )\r\n\r\n## R code 0.5\r\ninstall.packages(c(\"coda\",\"mvtnorm\",\"devtools\",\"dagitty\"))\r\nlibrary(devtools)\r\ndevtools::install_github(\"rmcelreath/rethinking\")\r\n\r\n## R code 2.1\r\nways <- c( 0 , 3 , 8 , 9 , 0 )\r\nways/sum(ways)\r\n\r\n## R code 2.2\r\ndbinom( 6 , size=9 , prob=0.5 )\r\n\r\n## R code 2.3\r\n# define grid\r\np_grid <- seq( from=0 , to=1 , length.out=20 )\r\n\r\n# define prior\r\nprior <- rep( 1 , 20 )\r\n\r\n# compute likelihood at each value in grid\r\nlikelihood <- dbinom( 6 , size=9 , prob=p_grid )\r\n\r\n# compute product of likelihood and prior\r\nunstd.posterior <- likelihood * prior\r\n\r\n# standardize the posterior, so it sums to 1\r\nposterior <- unstd.posterior / sum(unstd.posterior)\r\n\r\n## R code 2.4\r\nplot( p_grid , posterior , type=\"b\" ,\r\n xlab=\"probability of water\" , ylab=\"posterior probability\" )\r\nmtext( \"20 points\" )\r\n\r\n## R code 2.5\r\nprior <- ifelse( p_grid < 0.5 , 0 , 1 )\r\nprior <- exp( -5*abs( p_grid - 0.5 ) )\r\n\r\n## R code 2.6\r\nlibrary(rethinking)\r\nglobe.qa <- quap(\r\n alist(\r\n W ~ dbinom( W+L ,p) , # binomial likelihood\r\n p ~ dunif(0,1) # uniform prior\r\n ) ,\r\n data=list(W=6,L=3) )\r\n\r\n# display summary of quadratic approximation\r\nprecis( globe.qa )\r\n\r\n## R code 2.7\r\n# analytical calculation\r\nW <- 6\r\nL <- 3\r\ncurve( dbeta( x , W+1 , L+1 ) , from=0 , to=1 )\r\n# quadratic approximation\r\ncurve( dnorm( x , 0.67 , 0.16 ) , lty=2 , add=TRUE )\r\n\r\n## R code 2.8\r\nn_samples <- 1000\r\np <- rep( NA , n_samples )\r\np[1] <- 0.5\r\nW <- 6\r\nL <- 3\r\nfor ( i in 2:n_samples ) {\r\n p_new <- rnorm( 1 , p[i-1] , 0.1 )\r\n if ( p_new < 0 ) p_new <- abs( p_new )\r\n if ( p_new > 1 ) p_new <- 2 - p_new\r\n q0 <- dbinom( W , W+L , p[i-1] )\r\n q1 <- dbinom( W , W+L , p_new )\r\n p[i] <- ifelse( runif(1) < q1/q0 , p_new , p[i-1] )\r\n}\r\n\r\n## R code 2.9\r\ndens( p , xlim=c(0,1) )\r\ncurve( dbeta( x , W+1 , L+1 ) , lty=2 , add=TRUE )\r\n\r\n## R code 3.1\r\nPr_Positive_Vampire <- 0.95\r\nPr_Positive_Mortal <- 0.01\r\nPr_Vampire <- 0.001\r\nPr_Positive <- Pr_Positive_Vampire * Pr_Vampire +\r\n Pr_Positive_Mortal * ( 1 - Pr_Vampire )\r\n( Pr_Vampire_Positive <- Pr_Positive_Vampire*Pr_Vampire / Pr_Positive )\r\n\r\n## R code 3.2\r\np_grid <- seq( from=0 , to=1 , length.out=1000 )\r\nprob_p <- rep( 1 , 1000 )\r\nprob_data <- dbinom( 6 , size=9 , prob=p_grid )\r\nposterior <- prob_data * prob_p\r\nposterior <- posterior / sum(posterior)\r\n\r\n## R code 3.3\r\nsamples <- sample( p_grid , prob=posterior , size=1e4 , replace=TRUE )\r\n\r\n## R code 3.4\r\nplot( samples )\r\n\r\n## R code 3.5\r\nlibrary(rethinking)\r\ndens( samples )\r\n\r\n## R code 3.6\r\n# add up posterior probability where p < 0.5\r\nsum( posterior[ p_grid < 0.5 ] )\r\n\r\n## R code 3.7\r\nsum( samples < 0.5 ) / 1e4\r\n\r\n## R code 3.8\r\nsum( samples > 0.5 & samples < 0.75 ) / 1e4\r\n\r\n## R code 3.9\r\nquantile( samples , 0.8 )\r\n\r\n## R code 3.10\r\nquantile( samples , c( 0.1 , 0.9 ) )\r\n\r\n## R code 3.11\r\np_grid <- seq( from=0 , to=1 , length.out=1000 )\r\nprior <- rep(1,1000)\r\nlikelihood <- dbinom( 3 , size=3 , prob=p_grid )\r\nposterior <- likelihood * prior\r\nposterior <- posterior / sum(posterior)\r\nsamples <- sample( p_grid , size=1e4 , replace=TRUE , prob=posterior )\r\n\r\n## R code 3.12\r\nPI( samples , prob=0.5 )\r\n\r\n## R code 3.13\r\nHPDI( samples , prob=0.5 )\r\n\r\n## R code 3.14\r\np_grid[ which.max(posterior) ]\r\n\r\n## R code 3.15\r\nchainmode( samples , adj=0.01 )\r\n\r\n## R code 3.16\r\nmean( samples )\r\nmedian( samples )\r\n\r\n## R code 3.17\r\nsum( posterior*abs( 0.5 - p_grid ) )\r\n\r\n## R code 3.18\r\nloss <- sapply( p_grid , function(d) sum( posterior*abs( d - p_grid ) ) )\r\n\r\n## R code 3.19\r\np_grid[ which.min(loss) ]\r\n\r\n## R code 3.20\r\ndbinom( 0:2 , size=2 , prob=0.7 )\r\n\r\n## R code 3.21\r\nrbinom( 1 , size=2 , prob=0.7 )\r\n\r\n## R code 3.22\r\nrbinom( 10 , size=2 , prob=0.7 )\r\n\r\n## R code 3.23\r\ndummy_w <- rbinom( 1e5 , size=2 , prob=0.7 )\r\ntable(dummy_w)/1e5\r\n\r\n## R code 3.24\r\ndummy_w <- rbinom( 1e5 , size=9 , prob=0.7 )\r\nsimplehist( dummy_w , xlab=\"dummy water count\" )\r\n\r\n## R code 3.25\r\nw <- rbinom( 1e4 , size=9 , prob=0.6 )\r\n\r\n## R code 3.26\r\nw <- rbinom( 1e4 , size=9 , prob=samples )\r\n\r\n## R code 3.27\r\np_grid <- seq( from=0 , to=1 , length.out=1000 )\r\nprior <- rep( 1 , 1000 )\r\nlikelihood <- dbinom( 6 , size=9 , prob=p_grid )\r\nposterior <- likelihood * prior\r\nposterior <- posterior / sum(posterior)\r\nset.seed(100)\r\nsamples <- sample( p_grid , prob=posterior , size=1e4 , replace=TRUE )\r\n\r\n## R code 3.28\r\nbirth1 <- c(1,0,0,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0,1,0,\r\n0,0,0,1,1,1,0,1,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,0,0,\r\n1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,1,1,0,1,0,1,1,1,1,1,0,0,1,0,1,1,0,\r\n1,0,1,1,1,0,1,1,1,1)\r\nbirth2 <- c(0,1,0,1,0,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,0,0,1,1,1,0,\r\n1,1,1,0,1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,\r\n1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0,1,1,0,0,1,0,0,1,1,\r\n0,0,0,1,1,1,0,0,0,0)\r\n\r\n## R code 3.29\r\nlibrary(rethinking)\r\ndata(homeworkch3)\r\n\r\n## R code 3.30\r\nsum(birth1) + sum(birth2)\r\n\r\n## R code 4.1\r\npos <- replicate( 1000 , sum( runif(16,-1,1) ) )\r\n\r\n## R code 4.2\r\nprod( 1 + runif(12,0,0.1) )\r\n\r\n## R code 4.3\r\ngrowth <- replicate( 10000 , prod( 1 + runif(12,0,0.1) ) )\r\ndens( growth , norm.comp=TRUE )\r\n\r\n## R code 4.4\r\nbig <- replicate( 10000 , prod( 1 + runif(12,0,0.5) ) )\r\nsmall <- replicate( 10000 , prod( 1 + runif(12,0,0.01) ) )\r\n\r\n## R code 4.5\r\nlog.big <- replicate( 10000 , log(prod(1 + runif(12,0,0.5))) )\r\n\r\n## R code 4.6\r\nw <- 6; n <- 9;\r\np_grid <- seq(from=0,to=1,length.out=100)\r\nposterior <- dbinom(w,n,p_grid)*dunif(p_grid,0,1)\r\nposterior <- posterior/sum(posterior)\r\n\r\n## R code 4.7\r\nlibrary(rethinking)\r\ndata(Howell1)\r\nd <- Howell1\r\n\r\n## R code 4.8\r\nstr( d )\r\n\r\n## R code 4.9\r\nprecis( d )\r\n\r\n## R code 4.10\r\nd$height\r\n\r\n## R code 4.11\r\nd2 <- d[ d$age >= 18 , ]\r\n\r\n## R code 4.12\r\ncurve( dnorm( x , 178 , 20 ) , from=100 , to=250 )\r\n\r\n## R code 4.13\r\ncurve( dunif( x , 0 , 50 ) , from=-10 , to=60 )\r\n\r\n## R code 4.14\r\nsample_mu <- rnorm( 1e4 , 178 , 20 )\r\nsample_sigma <- runif( 1e4 , 0 , 50 )\r\nprior_h <- rnorm( 1e4 , sample_mu , sample_sigma )\r\ndens( prior_h )\r\n\r\n## R code 4.15\r\nsample_mu <- rnorm( 1e4 , 178 , 100 )\r\nprior_h <- rnorm( 1e4 , sample_mu , sample_sigma )\r\ndens( prior_h )\r\n\r\n## R code 4.16\r\nmu.list <- seq( from=150, to=160 , length.out=100 )\r\nsigma.list <- seq( from=7 , to=9 , length.out=100 )\r\npost <- expand.grid( mu=mu.list , sigma=sigma.list )\r\npost$LL <- sapply( 1:nrow(post) , function(i) sum(\r\n dnorm( d2$height , post$mu[i] , post$sigma[i] , log=TRUE ) ) )\r\npost$prod <- post$LL + dnorm( post$mu , 178 , 20 , TRUE ) +\r\n dunif( post$sigma , 0 , 50 , TRUE )\r\npost$prob <- exp( post$prod - max(post$prod) )\r\n\r\n## R code 4.17\r\ncontour_xyz( post$mu , post$sigma , post$prob )\r\n\r\n## R code 4.18\r\nimage_xyz( post$mu , post$sigma , post$prob )\r\n\r\n## R code 4.19\r\nsample.rows <- sample( 1:nrow(post) , size=1e4 , replace=TRUE ,\r\n prob=post$prob )\r\nsample.mu <- post$mu[ sample.rows ]\r\nsample.sigma <- post$sigma[ sample.rows ]\r\n\r\n## R code 4.20\r\nplot( sample.mu , sample.sigma , cex=0.5 , pch=16 , col=col.alpha(rangi2,0.1) )\r\n\r\n## R code 4.21\r\ndens( sample.mu )\r\ndens( sample.sigma )\r\n\r\n## R code 4.22\r\nPI( sample.mu )\r\nPI( sample.sigma )\r\n\r\n## R code 4.23\r\nd3 <- sample( d2$height , size=20 )\r\n\r\n## R code 4.24\r\nmu.list <- seq( from=150, to=170 , length.out=200 )\r\nsigma.list <- seq( from=4 , to=20 , length.out=200 )\r\npost2 <- expand.grid( mu=mu.list , sigma=sigma.list )\r\npost2$LL <- sapply( 1:nrow(post2) , function(i)\r\n sum( dnorm( d3 , mean=post2$mu[i] , sd=post2$sigma[i] ,\r\n log=TRUE ) ) )\r\npost2$prod <- post2$LL + dnorm( post2$mu , 178 , 20 , TRUE ) +\r\n dunif( post2$sigma , 0 , 50 , TRUE )\r\npost2$prob <- exp( post2$prod - max(post2$prod) )\r\nsample2.rows <- sample( 1:nrow(post2) , size=1e4 , replace=TRUE ,\r\n prob=post2$prob )\r\nsample2.mu <- post2$mu[ sample2.rows ]\r\nsample2.sigma <- post2$sigma[ sample2.rows ]\r\nplot( sample2.mu , sample2.sigma , cex=0.5 ,\r\n col=col.alpha(rangi2,0.1) ,\r\n xlab=\"mu\" , ylab=\"sigma\" , pch=16 )\r\n\r\n## R code 4.25\r\ndens( sample2.sigma , norm.comp=TRUE )\r\n\r\n## R code 4.26\r\nlibrary(rethinking)\r\ndata(Howell1)\r\nd <- Howell1\r\nd2 <- d[ d$age >= 18 , ]\r\n\r\n## R code 4.27\r\nflist <- alist(\r\n height ~ dnorm( mu , sigma ) ,\r\n mu ~ dnorm( 178 , 20 ) ,\r\n sigma ~ dunif( 0 , 50 )\r\n)\r\n\r\n## R code 4.28\r\nm4.1 <- quap( flist , data=d2 )\r\n\r\n## R code 4.29\r\nprecis( m4.1 )\r\n\r\n## R code 4.30\r\nstart <- list(\r\n mu=mean(d2$height),\r\n sigma=sd(d2$height)\r\n)\r\nm4.1 <- quap( flist , data=d2 , start=start )\r\n\r\n## R code 4.31\r\nm4.2 <- quap(\r\n alist(\r\n height ~ dnorm( mu , sigma ) ,\r\n mu ~ dnorm( 178 , 0.1 ) ,\r\n sigma ~ dunif( 0 , 50 )\r\n ) , data=d2 )\r\nprecis( m4.2 )\r\n\r\n## R code 4.32\r\nvcov( m4.1 )\r\n\r\n## R code 4.33\r\ndiag( vcov( m4.1 ) )\r\ncov2cor( vcov( m4.1 ) )\r\n\r\n## R code 4.34\r\nlibrary(rethinking)\r\npost <- extract.samples( m4.1 , n=1e4 )\r\nhead(post)\r\n\r\n## R code 4.35\r\nprecis(post)\r\n\r\n## R code 4.36\r\nlibrary(MASS)\r\npost <- mvrnorm( n=1e4 , mu=coef(m4.1) , Sigma=vcov(m4.1) )\r\n\r\n## R code 4.37\r\nlibrary(rethinking)\r\ndata(Howell1); d <- Howell1; d2 <- d[ d$age >= 18 , ]\r\nplot( d2$height ~ d2$weight )\r\n\r\n## R code 4.38\r\nset.seed(2971)\r\nN <- 100 # 100 lines\r\na <- rnorm( N , 178 , 20 )\r\nb <- rnorm( N , 0 , 10 )\r\n\r\n## R code 4.39\r\nplot( NULL , xlim=range(d2$weight) , ylim=c(-100,400) ,\r\n xlab=\"weight\" , ylab=\"height\" )\r\nabline( h=0 , lty=2 )\r\nabline( h=272 , lty=1 , lwd=0.5 )\r\nmtext( \"b ~ dnorm(0,10)\" )\r\nxbar <- mean(d2$weight)\r\nfor ( i in 1:N ) curve( a[i] + b[i]*(x - xbar) ,\r\n from=min(d2$weight) , to=max(d2$weight) , add=TRUE ,\r\n col=col.alpha(\"black\",0.2) )\r\n\r\n## R code 4.40\r\nb <- rlnorm( 1e4 , 0 , 1 )\r\ndens( b , xlim=c(0,5) , adj=0.1 )\r\n\r\n## R code 4.41\r\nset.seed(2971)\r\nN <- 100 # 100 lines\r\na <- rnorm( N , 178 , 20 )\r\nb <- rlnorm( N , 0 , 1 )\r\n\r\n## R code 4.42\r\n# load data again, since it's a long way back\r\nlibrary(rethinking)\r\ndata(Howell1); d <- Howell1; d2 <- d[ d$age >= 18 , ]\r\n\r\n# define the average weight, x-bar\r\nxbar <- mean(d2$weight)\r\n\r\n# fit model\r\nm4.3 <- quap(\r\n alist(\r\n height ~ dnorm( mu , sigma ) ,\r\n mu <- a + b*( weight - xbar ) ,\r\n a ~ dnorm( 178 , 20 ) ,\r\n b ~ dlnorm( 0 , 1 ) ,\r\n sigma ~ dunif( 0 , 50 )\r\n ) , data=d2 )\r\n\r\n## R code 4.43\r\nm4.3b <- quap(\r\n alist(\r\n height ~ dnorm( mu , sigma ) ,\r\n mu <- a + exp(log_b)*( weight - xbar ),\r\n a ~ dnorm( 178 , 20 ) ,\r\n log_b ~ dnorm( 0 , 1 ) ,\r\n sigma ~ dunif( 0 , 50 )\r\n ) , data=d2 )\r\n\r\n## R code 4.44\r\nprecis( m4.3 )\r\n\r\n## R code 4.45\r\nround( vcov( m4.3 ) , 3 )\r\n\r\n## R code 4.46\r\nplot( height ~ weight , data=d2 , col=rangi2 )\r\npost <- extract.samples( m4.3 )\r\na_map <- mean(post$a)\r\nb_map <- mean(post$b)\r\ncurve( a_map + b_map*(x - xbar) , add=TRUE )\r\n\r\n## R code 4.47\r\npost <- extract.samples( m4.3 )\r\npost[1:5,]\r\n\r\n## R code 4.48\r\nN <- 10\r\ndN <- d2[ 1:N , ]\r\nmN <- quap(\r\n alist(\r\n height ~ dnorm( mu , sigma ) ,\r\n mu <- a + b*( weight - mean(weight) ) ,\r\n a ~ dnorm( 178 , 20 ) ,\r\n b ~ dlnorm( 0 , 1 ) ,\r\n sigma ~ dunif( 0 , 50 )\r\n ) , data=dN )\r\n\r\n## R code 4.49\r\n# extract 20 samples from the posterior\r\npost <- extract.samples( mN , n=20 )\r\n\r\n# display raw data and sample size\r\nplot( dN$weight , dN$height ,\r\n xlim=range(d2$weight) , ylim=range(d2$height) ,\r\n col=rangi2 , xlab=\"weight\" , ylab=\"height\" )\r\nmtext(concat(\"N = \",N))\r\n\r\n# plot the lines, with transparency\r\nfor ( i in 1:20 )\r\n curve( post$a[i] + post$b[i]*(x-mean(dN$weight)) ,\r\n col=col.alpha(\"black\",0.3) , add=TRUE )\r\n\r\n## R code 4.50\r\npost <- extract.samples( m4.3 )\r\nmu_at_50 <- post$a + post$b * ( 50 - xbar )\r\n\r\n## R code 4.51\r\ndens( mu_at_50 , col=rangi2 , lwd=2 , xlab=\"mu|weight=50\" )\r\n\r\n## R code 4.52\r\nPI( mu_at_50 , prob=0.89 )\r\n\r\n## R code 4.53\r\nmu <- link( m4.3 )\r\nstr(mu)\r\n\r\n## R code 4.54\r\n# define sequence of weights to compute predictions for\r\n# these values will be on the horizontal axis\r\nweight.seq <- seq( from=25 , to=70 , by=1 )\r\n\r\n# use link to compute mu\r\n# for each sample from posterior\r\n# and for each weight in weight.seq\r\nmu <- link( m4.3 , data=data.frame(weight=weight.seq) )\r\nstr(mu)\r\n\r\n## R code 4.55\r\n# use type=\"n\" to hide raw data\r\nplot( height ~ weight , d2 , type=\"n\" )\r\n\r\n# loop over samples and plot each mu value\r\nfor ( i in 1:100 )\r\n points( weight.seq , mu[i,] , pch=16 , col=col.alpha(rangi2,0.1) )\r\n\r\n## R code 4.56\r\n# summarize the distribution of mu\r\nmu.mean <- apply( mu , 2 , mean )\r\nmu.PI <- apply( mu , 2 , PI , prob=0.89 )\r\n\r\n## R code 4.57\r\n# plot raw data\r\n# fading out points to make line and interval more visible\r\nplot( height ~ weight , data=d2 , col=col.alpha(rangi2,0.5) )\r\n\r\n# plot the MAP line, aka the mean mu for each weight\r\nlines( weight.seq , mu.mean )\r\n\r\n# plot a shaded region for 89% PI\r\nshade( mu.PI , weight.seq )\r\n\r\n## R code 4.58\r\npost <- extract.samples(m4.3)\r\nmu.link <- function(weight) post$a + post$b*( weight - xbar )\r\nweight.seq <- seq( from=25 , to=70 , by=1 )\r\nmu <- sapply( weight.seq , mu.link )\r\nmu.mean <- apply( mu , 2 , mean )\r\nmu.CI <- apply( mu , 2 , PI , prob=0.89 )\r\n\r\n## R code 4.59\r\nsim.height <- sim( m4.3 , data=list(weight=weight.seq) )\r\nstr(sim.height)\r\n\r\n## R code 4.60\r\nheight.PI <- apply( sim.height , 2 , PI , prob=0.89 )\r\n\r\n## R code 4.61\r\n# plot raw data\r\nplot( height ~ weight , d2 , col=col.alpha(rangi2,0.5) )\r\n\r\n# draw MAP line\r\nlines( weight.seq , mu.mean )\r\n\r\n# draw HPDI region for line\r\nshade( mu.HPDI , weight.seq )\r\n\r\n# draw PI region for simulated heights\r\nshade( height.PI , weight.seq )\r\n\r\n## R code 4.62\r\nsim.height <- sim( m4.3 , data=list(weight=weight.seq) , n=1e4 )\r\nheight.PI <- apply( sim.height , 2 , PI , prob=0.89 )\r\n\r\n## R code 4.63\r\npost <- extract.samples(m4.3)\r\nweight.seq <- 25:70\r\nsim.height <- sapply( weight.seq , function(weight)\r\n rnorm(\r\n n=nrow(post) ,\r\n mean=post$a + post$b*( weight - xbar ) ,\r\n sd=post$sigma ) )\r\nheight.PI <- apply( sim.height , 2 , PI , prob=0.89 )\r\n\r\n## R code 4.64\r\nlibrary(rethinking)\r\ndata(Howell1)\r\nd <- Howell1\r\n\r\n## R code 4.65\r\nd$weight_s <- ( d$weight - mean(d$weight) )/sd(d$weight)\r\nd$weight_s2 <- d$weight_s^2\r\nm4.5 <- quap(\r\n alist(\r\n height ~ dnorm( mu , sigma ) ,\r\n mu <- a + b1*weight_s + b2*weight_s2 ,\r\n a ~ dnorm( 178 , 20 ) ,\r\n b1 ~ dlnorm( 0 , 1 ) ,\r\n b2 ~ dnorm( 0 , 1 ) ,\r\n sigma ~ dunif( 0 , 50 )\r\n ) , data=d )\r\n\r\n## R code 4.66\r\nprecis( m4.5 )\r\n\r\n## R code 4.67\r\nweight.seq <- seq( from=-2.2 , to=2 , length.out=30 )\r\npred_dat <- list( weight_s=weight.seq , weight_s2=weight.seq^2 )\r\nmu <- link( m4.5 , data=pred_dat )\r\nmu.mean <- apply( mu , 2 , mean )\r\nmu.PI <- apply( mu , 2 , PI , prob=0.89 )\r\nsim.height <- sim( m4.5 , data=pred_dat )\r\nheight.PI <- apply( sim.height , 2 , PI , prob=0.89 )\r\n\r\n## R code 4.68\r\nplot( height ~ weight_s , d , col=col.alpha(rangi2,0.5) )\r\nlines( weight.seq , mu.mean )\r\nshade( mu.PI , weight.seq )\r\nshade( height.PI , weight.seq )\r\n\r\n## R code 4.69\r\nd$weight_s3 <- d$weight_s^3\r\nm4.6 <- quap(\r\n alist(\r\n height ~ dnorm( mu , sigma ) ,\r\n mu <- a + b1*weight_s + b2*weight_s2 + b3*weight_s3 ,\r\n a ~ dnorm( 178 , 20 ) ,\r\n b1 ~ dlnorm( 0 , 1 ) ,\r\n b2 ~ dnorm( 0 , 10 ) ,\r\n b3 ~ dnorm( 0 , 10 ) ,\r\n sigma ~ dunif( 0 , 50 )\r\n ) , data=d )\r\n\r\n## R code 4.70\r\nplot( height ~ weight_s , d , col=col.alpha(rangi2,0.5) , xaxt=\"n\" )\r\n\r\n## R code 4.71\r\nat <- c(-2,-1,0,1,2)\r\nlabels <- at*sd(d$weight) + mean(d$weight)\r\naxis( side=1 , at=at , labels=round(labels,1) )\r\n\r\n## R code 4.72\r\nlibrary(rethinking)\r\ndata(cherry_blossoms)\r\nd <- cherry_blossoms\r\nprecis(d)\r\n\r\n## R code 4.73\r\nd2 <- d[ complete.cases(d$doy) , ] # complete cases on doy\r\nnum_knots <- 15\r\nknot_list <- quantile( d2$year , probs=seq(0,1,length.out=num_knots) )\r\n\r\n## R code 4.74\r\nlibrary(splines)\r\nB <- bs(d2$year,\r\n knots=knot_list[-c(1,num_knots)] ,\r\n degree=3 , intercept=TRUE )\r\n\r\n## R code 4.75\r\nplot( NULL , xlim=range(d2$year) , ylim=c(0,1) , xlab=\"year\" , ylab=\"basis\" )\r\nfor ( i in 1:ncol(B) ) lines( d2$year , B[,i] )\r\n\r\n## R code 4.76\r\nm4.7 <- quap(\r\n alist(\r\n D ~ dnorm( mu , sigma ) ,\r\n mu <- a + B %*% w ,\r\n a ~ dnorm(100,10),\r\n w ~ dnorm(0,10),\r\n sigma ~ dexp(1)\r\n ), data=list( D=d2$doy , B=B ) ,\r\n start=list( w=rep( 0 , ncol(B) ) ) )\r\n\r\n## R code 4.77\r\npost <- extract.samples( m4.7 )\r\nw <- apply( post$w , 2 , mean )\r\nplot( NULL , xlim=range(d2$year) , ylim=c(-6,6) ,\r\n xlab=\"year\" , ylab=\"basis * weight\" )\r\nfor ( i in 1:ncol(B) ) lines( d2$year , w[i]*B[,i] )\r\n\r\n## R code 4.78\r\nmu <- link( m4.7 )\r\nmu_PI <- apply(mu,2,PI,0.97)\r\nplot( d2$year , d2$doy , col=col.alpha(rangi2,0.3) , pch=16 )\r\nshade( mu_PI , d2$year , col=col.alpha(\"black\",0.5) )\r\n\r\n## R code 4.79\r\nm4.7alt <- quap(\r\n alist(\r\n D ~ dnorm( mu , sigma ) ,\r\n mu <- a + sapply( 1:827 , function(i) sum( B[i,]*w ) ) ,\r\n a ~ dnorm(100,1),\r\n w ~ dnorm(0,10),\r\n sigma ~ dexp(1)\r\n ),\r\n data=list( D=d2$doy , B=B ) ,\r\n start=list( w=rep( 0 , ncol(B) ) ) )\r\n\r\n## R code 5.1\r\n# load data and copy\r\nlibrary(rethinking)\r\ndata(WaffleDivorce)\r\nd <- WaffleDivorce\r\n\r\n# standardize variables\r\nd$D <- standardize( d$Divorce )\r\nd$M <- standardize( d$Marriage )\r\nd$A <- standardize( d$MedianAgeMarriage )\r\n\r\n## R code 5.2\r\nsd( d$MedianAgeMarriage )\r\n\r\n## R code 5.3\r\nm5.1 <- quap(\r\n alist(\r\n D ~ dnorm( mu , sigma ) ,\r\n mu <- a + bA * A ,\r\n a ~ dnorm( 0 , 0.2 ) ,\r\n bA ~ dnorm( 0 , 0.5 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data = d )\r\n\r\n## R code 5.4\r\nset.seed(10)\r\nprior <- extract.prior( m5.1 )\r\nmu <- link( m5.1 , post=prior , data=list( A=c(-2,2) ) )\r\nplot( NULL , xlim=c(-2,2) , ylim=c(-2,2) )\r\nfor ( i in 1:50 ) lines( c(-2,2) , mu[i,] , col=col.alpha(\"black\",0.4) )\r\n\r\n## R code 5.5\r\n# compute percentile interval of mean\r\nA_seq <- seq( from=-3 , to=3.2 , length.out=30 )\r\nmu <- link( m5.1 , data=list(A=A_seq) )\r\nmu.mean <- apply( mu , 2, mean )\r\nmu.PI <- apply( mu , 2 , PI )\r\n\r\n# plot it all\r\nplot( D ~ A , data=d , col=rangi2 )\r\nlines( A_seq , mu.mean , lwd=2 )\r\nshade( mu.PI , A_seq )\r\n\r\n## R code 5.6\r\nm5.2 <- quap(\r\n alist(\r\n D ~ dnorm( mu , sigma ) ,\r\n mu <- a + bM * M ,\r\n a ~ dnorm( 0 , 0.2 ) ,\r\n bM ~ dnorm( 0 , 0.5 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data = d )\r\n\r\n## R code 5.7\r\nlibrary(dagitty)\r\ndag5.1 <- dagitty( \"dag{ A -> D; A -> M; M -> D }\" )\r\ncoordinates(dag5.1) <- list( x=c(A=0,D=1,M=2) , y=c(A=0,D=1,M=0) )\r\ndrawdag( dag5.1 )\r\n\r\n## R code 5.8\r\nDMA_dag2 <- dagitty('dag{ D <- A -> M }')\r\nimpliedConditionalIndependencies( DMA_dag2 )\r\n\r\n## R code 5.9\r\nDMA_dag1 <- dagitty('dag{ D <- A -> M -> D }')\r\nimpliedConditionalIndependencies( DMA_dag1 )\r\n\r\n## R code 5.10\r\nm5.3 <- quap(\r\n alist(\r\n D ~ dnorm( mu , sigma ) ,\r\n mu <- a + bM*M + bA*A ,\r\n a ~ dnorm( 0 , 0.2 ) ,\r\n bM ~ dnorm( 0 , 0.5 ) ,\r\n bA ~ dnorm( 0 , 0.5 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data = d )\r\nprecis( m5.3 )\r\n\r\n## R code 5.11\r\nplot( coeftab(m5.1,m5.2,m5.3), par=c(\"bA\",\"bM\") )\r\n\r\n## R code 5.12\r\nN <- 50 # number of simulated States\r\nage <- rnorm( N ) # sim A\r\nmar <- rnorm( N , -age ) # sim A -> M\r\ndiv <- rnorm( N , age ) # sim A -> D\r\n\r\n## R code 5.13\r\nm5.4 <- quap(\r\n alist(\r\n M ~ dnorm( mu , sigma ) ,\r\n mu <- a + bAM * A ,\r\n a ~ dnorm( 0 , 0.2 ) ,\r\n bAM ~ dnorm( 0 , 0.5 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data = d )\r\n\r\n## R code 5.14\r\nmu <- link(m5.4)\r\nmu_mean <- apply( mu , 2 , mean )\r\nmu_resid <- d$M - mu_mean\r\n\r\n## R code 5.15\r\n# call link without specifying new data\r\n# so it uses original data\r\nmu <- link( m5.3 )\r\n\r\n# summarize samples across cases\r\nmu_mean <- apply( mu , 2 , mean )\r\nmu_PI <- apply( mu , 2 , PI )\r\n\r\n# simulate observations\r\n# again no new data, so uses original data\r\nD_sim <- sim( m5.3 , n=1e4 )\r\nD_PI <- apply( D_sim , 2 , PI )\r\n\r\n## R code 5.16\r\nplot( mu_mean ~ d$D , col=rangi2 , ylim=range(mu_PI) ,\r\n xlab=\"Observed divorce\" , ylab=\"Predicted divorce\" )\r\nabline( a=0 , b=1 , lty=2 )\r\nfor ( i in 1:nrow(d) ) lines( rep(d$D[i],2) , mu_PI[,i] , col=rangi2 )\r\n\r\n## R code 5.17\r\nidentify( x=d$D , y=mu_mean , labels=d$Loc )\r\n\r\n## R code 5.18\r\nN <- 100 # number of cases\r\nx_real <- rnorm( N ) # x_real as Gaussian with mean 0 and stddev 1\r\nx_spur <- rnorm( N , x_real ) # x_spur as Gaussian with mean=x_real\r\ny <- rnorm( N , x_real ) # y as Gaussian with mean=x_real\r\nd <- data.frame(y,x_real,x_spur) # bind all together in data frame\r\n\r\n## R code 5.19\r\ndata(WaffleDivorce)\r\nd <- list()\r\nd$A <- standardize( WaffleDivorce$MedianAgeMarriage )\r\nd$D <- standardize( WaffleDivorce$Divorce )\r\nd$M <- standardize( WaffleDivorce$Marriage )\r\n\r\nm5.3_A <- quap(\r\n alist(\r\n ## A -> D <- M\r\n D ~ dnorm( mu , sigma ) ,\r\n mu <- a + bM*M + bA*A ,\r\n a ~ dnorm( 0 , 0.2 ) ,\r\n bM ~ dnorm( 0 , 0.5 ) ,\r\n bA ~ dnorm( 0 , 0.5 ) ,\r\n sigma ~ dexp( 1 ),\r\n ## A -> M\r\n M ~ dnorm( mu_M , sigma_M ),\r\n mu_M <- aM + bAM*A,\r\n aM ~ dnorm( 0 , 0.2 ),\r\n bAM ~ dnorm( 0 , 0.5 ),\r\n sigma_M ~ dexp( 1 )\r\n ) , data = d )\r\n\r\n## R code 5.20\r\nA_seq <- seq( from=-2 , to=2 , length.out=30 )\r\n\r\n## R code 5.21\r\n# prep data\r\nsim_dat <- data.frame( A=A_seq )\r\n\r\n# simulate M and then D, using A_seq\r\ns <- sim( m5.3_A , data=sim_dat , vars=c(\"M\",\"D\") )\r\n\r\n## R code 5.22\r\nplot( sim_dat$A , colMeans(s$D) , ylim=c(-2,2) , type=\"l\" ,\r\n xlab=\"manipulated A\" , ylab=\"counterfactual D\" )\r\nshade( apply(s$D,2,PI) , sim_dat$A )\r\nmtext( \"Total counterfactual effect of A on D\" )\r\n\r\n## R code 5.23\r\n# new data frame, standardized to mean 26.1 and std dev 1.24\r\nsim2_dat <- data.frame( A=(c(20,30)-26.1)/1.24 )\r\ns2 <- sim( m5.3_A , data=sim2_dat , vars=c(\"M\",\"D\") )\r\nmean( s2$D[,2] - s2$D[,1] )\r\n\r\n## R code 5.24\r\nsim_dat <- data.frame( M=seq(from=-2,to=2,length.out=30) , A=0 )\r\ns <- sim( m5.3_A , data=sim_dat , vars=\"D\" )\r\n\r\nplot( sim_dat$M , colMeans(s) , ylim=c(-2,2) , type=\"l\" ,\r\n xlab=\"manipulated M\" , ylab=\"counterfactual D\" )\r\nshade( apply(s,2,PI) , sim_dat$M )\r\nmtext( \"Total counterfactual effect of M on D\" )\r\n\r\n## R code 5.25\r\nA_seq <- seq( from=-2 , to=2 , length.out=30 )\r\n\r\n## R code 5.26\r\npost <- extract.samples( m5.3_A )\r\nM_sim <- with( post , sapply( 1:30 ,\r\n function(i) rnorm( 1e3 , aM + bAM*A_seq[i] , sigma_M ) ) )\r\n\r\n## R code 5.27\r\nD_sim <- with( post , sapply( 1:30 ,\r\n function(i) rnorm( 1e3 , a + bA*A_seq[i] + bM*M_sim[,i] , sigma ) ) )\r\n\r\n## R code 5.28\r\nlibrary(rethinking)\r\ndata(milk)\r\nd <- milk\r\nstr(d)\r\n\r\n## R code 5.29\r\nd$K <- standardize( d$kcal.per.g )\r\nd$N <- standardize( d$neocortex.perc )\r\nd$M <- standardize( log(d$mass) )\r\n\r\n## R code 5.30\r\nm5.5_draft <- quap(\r\n alist(\r\n K ~ dnorm( mu , sigma ) ,\r\n mu <- a + bN*N ,\r\n a ~ dnorm( 0 , 1 ) ,\r\n bN ~ dnorm( 0 , 1 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=d )\r\n\r\n## R code 5.31\r\nd$neocortex.perc\r\n\r\n## R code 5.32\r\ndcc <- d[ complete.cases(d$K,d$N,d$M) , ]\r\n\r\n## R code 5.33\r\nm5.5_draft <- quap(\r\n alist(\r\n K ~ dnorm( mu , sigma ) ,\r\n mu <- a + bN*N ,\r\n a ~ dnorm( 0 , 1 ) ,\r\n bN ~ dnorm( 0 , 1 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=dcc )\r\n\r\n## R code 5.34\r\nprior <- extract.prior( m5.5_draft )\r\nxseq <- c(-2,2)\r\nmu <- link( m5.5_draft , post=prior , data=list(N=xseq) )\r\nplot( NULL , xlim=xseq , ylim=xseq )\r\nfor ( i in 1:50 ) lines( xseq , mu[i,] , col=col.alpha(\"black\",0.3) )\r\n\r\n## R code 5.35\r\nm5.5 <- quap(\r\n alist(\r\n K ~ dnorm( mu , sigma ) ,\r\n mu <- a + bN*N ,\r\n a ~ dnorm( 0 , 0.2 ) ,\r\n bN ~ dnorm( 0 , 0.5 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=dcc )\r\n\r\n## R code 5.36\r\nprecis( m5.5 )\r\n\r\n## R code 5.37\r\nxseq <- seq( from=min(dcc$N)-0.15 , to=max(dcc$N)+0.15 , length.out=30 )\r\nmu <- link( m5.5 , data=list(N=xseq) )\r\nmu_mean <- apply(mu,2,mean)\r\nmu_PI <- apply(mu,2,PI)\r\nplot( K ~ N , data=dcc )\r\nlines( xseq , mu_mean , lwd=2 )\r\nshade( mu_PI , xseq )\r\n\r\n## R code 5.38\r\nm5.6 <- quap(\r\n alist(\r\n K ~ dnorm( mu , sigma ) ,\r\n mu <- a + bM*M ,\r\n a ~ dnorm( 0 , 0.2 ) ,\r\n bM ~ dnorm( 0 , 0.5 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=dcc )\r\nprecis(m5.6)\r\n\r\n## R code 5.39\r\nm5.7 <- quap(\r\n alist(\r\n K ~ dnorm( mu , sigma ) ,\r\n mu <- a + bN*N + bM*M ,\r\n a ~ dnorm( 0 , 0.2 ) ,\r\n bN ~ dnorm( 0 , 0.5 ) ,\r\n bM ~ dnorm( 0 , 0.5 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=dcc )\r\nprecis(m5.7)\r\n\r\n## R code 5.40\r\nplot( coeftab( m5.5 , m5.6 , m5.7 ) , pars=c(\"bM\",\"bN\") )\r\n\r\n## R code 5.41\r\nxseq <- seq( from=min(dcc$M)-0.15 , to=max(dcc$M)+0.15 , length.out=30 )\r\nmu <- link( m5.7 , data=data.frame( M=xseq , N=0 ) )\r\nmu_mean <- apply(mu,2,mean)\r\nmu_PI <- apply(mu,2,PI)\r\nplot( NULL , xlim=range(dcc$M) , ylim=range(dcc$K) )\r\nlines( xseq , mu_mean , lwd=2 )\r\nshade( mu_PI , xseq )\r\n\r\n## R code 5.42\r\n# M -> K <- N\r\n# M -> N\r\nn <- 100\r\nM <- rnorm( n )\r\nN <- rnorm( n , M )\r\nK <- rnorm( n , N - M )\r\nd_sim <- data.frame(K=K,N=N,M=M)\r\n\r\n## R code 5.43\r\n# M -> K <- N\r\n# N -> M\r\nn <- 100\r\nN <- rnorm( n )\r\nM <- rnorm( n , N )\r\nK <- rnorm( n , N - M )\r\nd_sim2 <- data.frame(K=K,N=N,M=M)\r\n\r\n# M -> K <- N\r\n# M <- U -> N\r\nn <- 100\r\nU <- rnorm( n )\r\nN <- rnorm( n , U )\r\nM <- rnorm( n , U )\r\nK <- rnorm( n , N - M )\r\nd_sim3 <- data.frame(K=K,N=N,M=M)\r\n\r\n## R code 5.44\r\ndag5.7 <- dagitty( \"dag{\r\n M -> K <- N\r\n M -> N }\" )\r\ncoordinates(dag5.7) <- list( x=c(M=0,K=1,N=2) , y=c(M=0.5,K=1,N=0.5) )\r\nMElist <- equivalentDAGs(dag5.7)\r\n\r\n## R code 5.45\r\ndata(Howell1)\r\nd <- Howell1\r\nstr(d)\r\n\r\n## R code 5.46\r\nmu_female <- rnorm(1e4,178,20)\r\nmu_male <- rnorm(1e4,178,20) + rnorm(1e4,0,10)\r\nprecis( data.frame( mu_female , mu_male ) )\r\n\r\n## R code 5.47\r\nd$sex <- ifelse( d$male==1 , 2 , 1 )\r\nstr( d$sex )\r\n\r\n## R code 5.48\r\nm5.8 <- quap(\r\n alist(\r\n height ~ dnorm( mu , sigma ) ,\r\n mu <- a[sex] ,\r\n a[sex] ~ dnorm( 178 , 20 ) ,\r\n sigma ~ dunif( 0 , 50 )\r\n ) , data=d )\r\nprecis( m5.8 , depth=2 )\r\n\r\n## R code 5.49\r\npost <- extract.samples(m5.8)\r\npost$diff_fm <- post$a[,1] - post$a[,2]\r\nprecis( post , depth=2 )\r\n\r\n## R code 5.50\r\ndata(milk)\r\nd <- milk\r\nlevels(d$clade)\r\n\r\n## R code 5.51\r\nd$clade_id <- as.integer( d$clade )\r\n\r\n## R code 5.52\r\nd$K <- standardize( d$kcal.per.g )\r\nm5.9 <- quap(\r\n alist(\r\n K ~ dnorm( mu , sigma ),\r\n mu <- a[clade_id],\r\n a[clade_id] ~ dnorm( 0 , 0.5 ),\r\n sigma ~ dexp( 1 )\r\n ) , data=d )\r\nlabels <- paste( \"a[\" , 1:4 , \"]:\" , levels(d$clade) , sep=\"\" )\r\nplot( precis( m5.9 , depth=2 , pars=\"a\" ) , labels=labels ,\r\n xlab=\"expected kcal (std)\" )\r\n\r\n## R code 5.53\r\nset.seed(63)\r\nd$house <- sample( rep(1:4,each=8) , size=nrow(d) )\r\n\r\n## R code 5.54\r\nm5.10 <- quap(\r\n alist(\r\n K ~ dnorm( mu , sigma ),\r\n mu <- a[clade_id] + h[house],\r\n a[clade_id] ~ dnorm( 0 , 0.5 ),\r\n h[house] ~ dnorm( 0 , 0.5 ),\r\n sigma ~ dexp( 1 )\r\n ) , data=d )\r\n\r\n## R code 6.1\r\nset.seed(1914)\r\nN <- 200 # num grant proposals\r\np <- 0.1 # proportion to select\r\n# uncorrelated newsworthiness and trustworthiness\r\nnw <- rnorm(N)\r\ntw <- rnorm(N)\r\n# select top 10% of combined scores\r\ns <- nw + tw # total score\r\nq <- quantile( s , 1-p ) # top 10% threshold\r\nselected <- ifelse( s >= q , TRUE , FALSE )\r\ncor( tw[selected] , nw[selected] )\r\n\r\n## R code 6.2\r\nN <- 100 # number of individuals\r\nset.seed(909)\r\nheight <- rnorm(N,10,2) # sim total height of each\r\nleg_prop <- runif(N,0.4,0.5) # leg as proportion of height\r\nleg_left <- leg_prop*height + # sim left leg as proportion + error\r\n rnorm( N , 0 , 0.02 )\r\nleg_right <- leg_prop*height + # sim right leg as proportion + error\r\n rnorm( N , 0 , 0.02 )\r\n # combine into data frame\r\nd <- data.frame(height,leg_left,leg_right)\r\n\r\n## R code 6.3\r\nm6.1 <- quap(\r\n alist(\r\n height ~ dnorm( mu , sigma ) ,\r\n mu <- a + bl*leg_left + br*leg_right ,\r\n a ~ dnorm( 10 , 100 ) ,\r\n bl ~ dnorm( 2 , 10 ) ,\r\n br ~ dnorm( 2 , 10 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=d )\r\nprecis(m6.1)\r\n\r\n## R code 6.4\r\nplot(precis(m6.1))\r\n\r\n## R code 6.5\r\npost <- extract.samples(m6.1)\r\nplot( bl ~ br , post , col=col.alpha(rangi2,0.1) , pch=16 )\r\n\r\n## R code 6.6\r\nsum_blbr <- post$bl + post$br\r\ndens( sum_blbr , col=rangi2 , lwd=2 , xlab=\"sum of bl and br\" )\r\n\r\n## R code 6.7\r\nm6.2 <- quap(\r\n alist(\r\n height ~ dnorm( mu , sigma ) ,\r\n mu <- a + bl*leg_left,\r\n a ~ dnorm( 10 , 100 ) ,\r\n bl ~ dnorm( 2 , 10 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=d )\r\nprecis(m6.2)\r\n\r\n## R code 6.8\r\nlibrary(rethinking)\r\ndata(milk)\r\nd <- milk\r\nd$K <- standardize( d$kcal.per.g )\r\nd$F <- standardize( d$perc.fat )\r\nd$L <- standardize( d$perc.lactose )\r\n\r\n## R code 6.9\r\n# kcal.per.g regressed on perc.fat\r\nm6.3 <- quap(\r\n alist(\r\n K ~ dnorm( mu , sigma ) ,\r\n mu <- a + bF*F ,\r\n a ~ dnorm( 0 , 0.2 ) ,\r\n bF ~ dnorm( 0 , 0.5 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=d )\r\n\r\n# kcal.per.g regressed on perc.lactose\r\nm6.4 <- quap(\r\n alist(\r\n K ~ dnorm( mu , sigma ) ,\r\n mu <- a + bL*L ,\r\n a ~ dnorm( 0 , 0.2 ) ,\r\n bL ~ dnorm( 0 , 0.5 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=d )\r\n\r\nprecis( m6.3 )\r\nprecis( m6.4 )\r\n\r\n## R code 6.10\r\nm6.5 <- quap(\r\n alist(\r\n K ~ dnorm( mu , sigma ) ,\r\n mu <- a + bF*F + bL*L ,\r\n a ~ dnorm( 0 , 0.2 ) ,\r\n bF ~ dnorm( 0 , 0.5 ) ,\r\n bL ~ dnorm( 0 , 0.5 ) ,\r\n sigma ~ dexp( 1 )\r\n ) ,\r\n data=d )\r\nprecis( m6.5 )\r\n\r\n## R code 6.11\r\npairs( ~ kcal.per.g + perc.fat + perc.lactose , data=d , col=rangi2 )\r\n\r\n## R code 6.12\r\nlibrary(rethinking)\r\ndata(milk)\r\nd <- milk\r\nsim.coll <- function( r=0.9 ) {\r\n d$x <- rnorm( nrow(d) , mean=r*d$perc.fat ,\r\n sd=sqrt( (1-r^2)*var(d$perc.fat) ) )\r\n m <- lm( kcal.per.g ~ perc.fat + x , data=d )\r\n sqrt( diag( vcov(m) ) )[2] # stddev of parameter\r\n}\r\nrep.sim.coll <- function( r=0.9 , n=100 ) {\r\n stddev <- replicate( n , sim.coll(r) )\r\n mean(stddev)\r\n}\r\nr.seq <- seq(from=0,to=0.99,by=0.01)\r\nstddev <- sapply( r.seq , function(z) rep.sim.coll(r=z,n=100) )\r\nplot( stddev ~ r.seq , type=\"l\" , col=rangi2, lwd=2 , xlab=\"correlation\" )\r\n\r\n## R code 6.13\r\nset.seed(71)\r\n# number of plants\r\nN <- 100\r\n\r\n# simulate initial heights\r\nh0 <- rnorm(N,10,2)\r\n\r\n# assign treatments and simulate fungus and growth\r\ntreatment <- rep( 0:1 , each=N/2 )\r\nfungus <- rbinom( N , size=1 , prob=0.5 - treatment*0.4 )\r\nh1 <- h0 + rnorm(N, 5 - 3*fungus)\r\n\r\n# compose a clean data frame\r\nd <- data.frame( h0=h0 , h1=h1 , treatment=treatment , fungus=fungus )\r\nprecis(d)\r\n\r\n## R code 6.14\r\nsim_p <- rlnorm( 1e4 , 0 , 0.25 )\r\nprecis( data.frame(sim_p) )\r\n\r\n## R code 6.15\r\nm6.6 <- quap(\r\n alist(\r\n h1 ~ dnorm( mu , sigma ),\r\n mu <- h0*p,\r\n p ~ dlnorm( 0 , 0.25 ),\r\n sigma ~ dexp( 1 )\r\n ), data=d )\r\nprecis(m6.6)\r\n\r\n## R code 6.16\r\nm6.7 <- quap(\r\n alist(\r\n h1 ~ dnorm( mu , sigma ),\r\n mu <- h0 * p,\r\n p <- a + bt*treatment + bf*fungus,\r\n a ~ dlnorm( 0 , 0.2 ) ,\r\n bt ~ dnorm( 0 , 0.5 ),\r\n bf ~ dnorm( 0 , 0.5 ),\r\n sigma ~ dexp( 1 )\r\n ), data=d )\r\nprecis(m6.7)\r\n\r\n## R code 6.17\r\nm6.8 <- quap(\r\n alist(\r\n h1 ~ dnorm( mu , sigma ),\r\n mu <- h0 * p,\r\n p <- a + bt*treatment,\r\n a ~ dlnorm( 0 , 0.2 ),\r\n bt ~ dnorm( 0 , 0.5 ),\r\n sigma ~ dexp( 1 )\r\n ), data=d )\r\nprecis(m6.8)\r\n\r\n## R code 6.18\r\nlibrary(dagitty)\r\nplant_dag <- dagitty( \"dag {\r\n H_0 -> H_1\r\n F -> H_1\r\n T -> F\r\n}\")\r\ncoordinates( plant_dag ) <- list( x=c(H_0=0,T=2,F=1.5,H_1=1) ,\r\n y=c(H_0=0,T=0,F=0,H_1=0) )\r\ndrawdag( plant_dag )\r\n\r\n## R code 6.19\r\nimpliedConditionalIndependencies(plant_dag)\r\n\r\n## R code 6.20\r\nset.seed(71)\r\nN <- 1000\r\nh0 <- rnorm(N,10,2)\r\ntreatment <- rep( 0:1 , each=N/2 )\r\nM <- rbern(N)\r\nfungus <- rbinom( N , size=1 , prob=0.5 - treatment*0.4 + 0.4*M )\r\nh1 <- h0 + rnorm( N , 5 + 3*M )\r\nd2 <- data.frame( h0=h0 , h1=h1 , treatment=treatment , fungus=fungus )\r\n\r\n## R code 6.21\r\nlibrary(rethinking)\r\nd <- sim_happiness( seed=1977 , N_years=1000 )\r\nprecis(d)\r\n\r\n## R code 6.22\r\nd2 <- d[ d$age>17 , ] # only adults\r\nd2$A <- ( d2$age - 18 ) / ( 65 - 18 )\r\n\r\n## R code 6.23\r\nd2$mid <- d2$married + 1\r\nm6.9 <- quap(\r\n alist(\r\n happiness ~ dnorm( mu , sigma ),\r\n mu <- a[mid] + bA*A,\r\n a[mid] ~ dnorm( 0 , 1 ),\r\n bA ~ dnorm( 0 , 2 ),\r\n sigma ~ dexp(1)\r\n ) , data=d2 )\r\nprecis(m6.9,depth=2)\r\n\r\n## R code 6.24\r\nm6.10 <- quap(\r\n alist(\r\n happiness ~ dnorm( mu , sigma ),\r\n mu <- a + bA*A,\r\n a ~ dnorm( 0 , 1 ),\r\n bA ~ dnorm( 0 , 2 ),\r\n sigma ~ dexp(1)\r\n ) , data=d2 )\r\nprecis(m6.10)\r\n\r\n## R code 6.25\r\nN <- 200 # number of grandparent-parent-child triads\r\nb_GP <- 1 # direct effect of G on P\r\nb_GC <- 0 # direct effect of G on C\r\nb_PC <- 1 # direct effect of P on C\r\nb_U <- 2 # direct effect of U on P and C\r\n\r\n## R code 6.26\r\nset.seed(1)\r\nU <- 2*rbern( N , 0.5 ) - 1\r\nG <- rnorm( N )\r\nP <- rnorm( N , b_GP*G + b_U*U )\r\nC <- rnorm( N , b_PC*P + b_GC*G + b_U*U )\r\nd <- data.frame( C=C , P=P , G=G , U=U )\r\n\r\n## R code 6.27\r\nm6.11 <- quap(\r\n alist(\r\n C ~ dnorm( mu , sigma ),\r\n mu <- a + b_PC*P + b_GC*G,\r\n a ~ dnorm( 0 , 1 ),\r\n c(b_PC,b_GC) ~ dnorm( 0 , 1 ),\r\n sigma ~ dexp( 1 )\r\n ), data=d )\r\nprecis(m6.11)\r\n\r\n## R code 6.28\r\nm6.12 <- quap(\r\n alist(\r\n C ~ dnorm( mu , sigma ),\r\n mu <- a + b_PC*P + b_GC*G + b_U*U,\r\n a ~ dnorm( 0 , 1 ),\r\n c(b_PC,b_GC,b_U) ~ dnorm( 0 , 1 ),\r\n sigma ~ dexp( 1 )\r\n ), data=d )\r\nprecis(m6.12)\r\n\r\n## R code 6.29\r\nlibrary(dagitty)\r\ndag_6.1 <- dagitty( \"dag {\r\n U [unobserved]\r\n X -> Y\r\n X <- U <- A -> C -> Y\r\n U -> B <- C\r\n}\")\r\nadjustmentSets( dag_6.1 , exposure=\"X\" , outcome=\"Y\" )\r\n\r\n## R code 6.30\r\nlibrary(dagitty)\r\ndag_6.2 <- dagitty( \"dag {\r\n A -> D\r\n A -> M -> D\r\n A <- S -> M\r\n S -> W -> D\r\n}\")\r\nadjustmentSets( dag_6.2 , exposure=\"W\" , outcome=\"D\" )\r\n\r\n## R code 6.31\r\nimpliedConditionalIndependencies( dag_6.2 )\r\n\r\n## R code 7.1\r\nsppnames <- c( \"afarensis\",\"africanus\",\"habilis\",\"boisei\",\r\n \"rudolfensis\",\"ergaster\",\"sapiens\")\r\nbrainvolcc <- c( 438 , 452 , 612, 521, 752, 871, 1350 )\r\nmasskg <- c( 37.0 , 35.5 , 34.5 , 41.5 , 55.5 , 61.0 , 53.5 )\r\nd <- data.frame( species=sppnames , brain=brainvolcc , mass=masskg )\r\n\r\n## R code 7.2\r\nd$mass_std <- (d$mass - mean(d$mass))/sd(d$mass)\r\nd$brain_std <- d$brain / max(d$brain)\r\n\r\n## R code 7.3\r\nm7.1 <- quap(\r\n alist(\r\n brain_std ~ dnorm( mu , exp(log_sigma) ),\r\n mu <- a + b*mass_std,\r\n a ~ dnorm( 0.5 , 1 ),\r\n b ~ dnorm( 0 , 10 ),\r\n log_sigma ~ dnorm( 0 , 1 )\r\n ), data=d )\r\n\r\n## R code 7.4\r\nm7.1_OLS <- lm( brain_std ~ mass_std , data=d )\r\npost <- extract.samples( m7.1_OLS )\r\n\r\n## R code 7.5\r\nset.seed(12)\r\ns <- sim( m7.1 )\r\nr <- apply(s,2,mean) - d$brain_std\r\nresid_var <- var2(r)\r\noutcome_var <- var2( d$brain_std )\r\n1 - resid_var/outcome_var\r\n\r\n## R code 7.6\r\nR2_is_bad <- function( quap_fit ) {\r\n s <- sim( quap_fit , refresh=0 )\r\n r <- apply(s,2,mean) - d$brain_std\r\n 1 - var2(r)/var2(d$brain_std)\r\n}\r\n\r\n## R code 7.7\r\nm7.2 <- quap(\r\n alist(\r\n brain_std ~ dnorm( mu , exp(log_sigma) ),\r\n mu <- a + b[1]*mass_std + b[2]*mass_std^2,\r\n a ~ dnorm( 0.5 , 1 ),\r\n b ~ dnorm( 0 , 10 ),\r\n log_sigma ~ dnorm( 0 , 1 )\r\n ), data=d , start=list(b=rep(0,2)) )\r\n\r\n## R code 7.8\r\nm7.3 <- quap(\r\n alist(\r\n brain_std ~ dnorm( mu , exp(log_sigma) ),\r\n mu <- a + b[1]*mass_std + b[2]*mass_std^2 +\r\n b[3]*mass_std^3,\r\n a ~ dnorm( 0.5 , 1 ),\r\n b ~ dnorm( 0 , 10 ),\r\n log_sigma ~ dnorm( 0 , 1 )\r\n ), data=d , start=list(b=rep(0,3)) )\r\n\r\nm7.4 <- quap(\r\n alist(\r\n brain_std ~ dnorm( mu , exp(log_sigma) ),\r\n mu <- a + b[1]*mass_std + b[2]*mass_std^2 +\r\n b[3]*mass_std^3 + b[4]*mass_std^4,\r\n a ~ dnorm( 0.5 , 1 ),\r\n b ~ dnorm( 0 , 10 ),\r\n log_sigma ~ dnorm( 0 , 1 )\r\n ), data=d , start=list(b=rep(0,4)) )\r\n\r\nm7.5 <- quap(\r\n alist(\r\n brain_std ~ dnorm( mu , exp(log_sigma) ),\r\n mu <- a + b[1]*mass_std + b[2]*mass_std^2 +\r\n b[3]*mass_std^3 + b[4]*mass_std^4 +\r\n b[5]*mass_std^5,\r\n a ~ dnorm( 0.5 , 1 ),\r\n b ~ dnorm( 0 , 10 ),\r\n log_sigma ~ dnorm( 0 , 1 )\r\n ), data=d , start=list(b=rep(0,5)) )\r\n\r\n## R code 7.9\r\nm7.6 <- quap(\r\n alist(\r\n brain_std ~ dnorm( mu , 0.001 ),\r\n mu <- a + b[1]*mass_std + b[2]*mass_std^2 +\r\n b[3]*mass_std^3 + b[4]*mass_std^4 +\r\n b[5]*mass_std^5 + b[6]*mass_std^6,\r\n a ~ dnorm( 0.5 , 1 ),\r\n b ~ dnorm( 0 , 10 )\r\n ), data=d , start=list(b=rep(0,6)) )\r\n\r\n## R code 7.10\r\npost <- extract.samples(m7.1)\r\nmass_seq <- seq( from=min(d$mass_std) , to=max(d$mass_std) , length.out=100 )\r\nl <- link( m7.1 , data=list( mass_std=mass_seq ) )\r\nmu <- apply( l , 2 , mean )\r\nci <- apply( l , 2 , PI )\r\nplot( brain_std ~ mass_std , data=d )\r\nlines( mass_seq , mu )\r\nshade( ci , mass_seq )\r\n\r\n## R code 7.11\r\nd_minus_i <- d[ -i , ]\r\n\r\n## R code 7.12\r\np <- c( 0.3 , 0.7 )\r\n-sum( p*log(p) )\r\n\r\n## R code 7.13\r\nset.seed(1)\r\nlppd( m7.1 , n=1e4 )\r\n\r\n## R code 7.14\r\nset.seed(1)\r\nlogprob <- sim( m7.1 , ll=TRUE , n=1e4 )\r\nn <- ncol(logprob)\r\nns <- nrow(logprob)\r\nf <- function( i ) log_sum_exp( logprob[,i] ) - log(ns)\r\n( lppd <- sapply( 1:n , f ) )\r\n\r\n## R code 7.15\r\nset.seed(1)\r\nsapply( list(m7.1,m7.2,m7.3,m7.4,m7.5,m7.6) , function(m) sum(lppd(m)) )\r\n\r\n## R code 7.16\r\nN <- 20\r\nkseq <- 1:5\r\ndev <- sapply( kseq , function(k) {\r\n print(k);\r\n r <- replicate( 1e4 , sim_train_test( N=N, k=k ) );\r\n c( mean(r[1,]) , mean(r[2,]) , sd(r[1,]) , sd(r[2,]) )\r\n } )\r\n\r\n## R code 7.17\r\n r <- mcreplicate( 1e4 , sim_train_test( N=N, k=k ) , mc.cores=4 )\r\n\r\n## R code 7.18\r\nplot( 1:5 , dev[1,] , ylim=c( min(dev[1:2,])-5 , max(dev[1:2,])+10 ) ,\r\n xlim=c(1,5.1) , xlab=\"number of parameters\" , ylab=\"deviance\" ,\r\n pch=16 , col=rangi2 )\r\nmtext( concat( \"N = \",N ) )\r\npoints( (1:5)+0.1 , dev[2,] )\r\nfor ( i in kseq ) {\r\n pts_in <- dev[1,i] + c(-1,+1)*dev[3,i]\r\n pts_out <- dev[2,i] + c(-1,+1)*dev[4,i]\r\n lines( c(i,i) , pts_in , col=rangi2 )\r\n lines( c(i,i)+0.1 , pts_out )\r\n}\r\n\r\n## R code 7.19\r\ndata(cars)\r\nm <- quap(\r\n alist(\r\n dist ~ dnorm(mu,sigma),\r\n mu <- a + b*speed,\r\n a ~ dnorm(0,100),\r\n b ~ dnorm(0,10),\r\n sigma ~ dexp(1)\r\n ) , data=cars )\r\nset.seed(94)\r\npost <- extract.samples(m,n=1000)\r\n\r\n## R code 7.20\r\nn_samples <- 1000\r\nlogprob <- sapply( 1:n_samples ,\r\n function(s) {\r\n mu <- post$a[s] + post$b[s]*cars$speed\r\n dnorm( cars$dist , mu , post$sigma[s] , log=TRUE )\r\n } )\r\n\r\n## R code 7.21\r\nn_cases <- nrow(cars)\r\nlppd <- sapply( 1:n_cases , function(i) log_sum_exp(logprob[i,]) - log(n_samples) )\r\n\r\n## R code 7.22\r\npWAIC <- sapply( 1:n_cases , function(i) var(logprob[i,]) )\r\n\r\n## R code 7.23\r\n-2*( sum(lppd) - sum(pWAIC) )\r\n\r\n## R code 7.24\r\nwaic_vec <- -2*( lppd - pWAIC )\r\nsqrt( n_cases*var(waic_vec) )\r\n\r\n## R code 7.25\r\nset.seed(11)\r\nWAIC( m6.7 )\r\n\r\n## R code 7.26\r\nset.seed(77)\r\ncompare( m6.6 , m6.7 , m6.8 , func=WAIC )\r\n\r\n## R code 7.27\r\nset.seed(91)\r\nwaic_m6.7 <- WAIC( m6.7 , pointwise=TRUE )$WAIC\r\nwaic_m6.8 <- WAIC( m6.8 , pointwise=TRUE )$WAIC\r\nn <- length(waic_m6.7)\r\ndiff_m6.7_m6.8 <- waic_m6.7 - waic_m6.8\r\nsqrt( n*var( diff_m6.7_m6.8 ) )\r\n\r\n## R code 7.28\r\n40.0 + c(-1,1)*10.4*2.6\r\n\r\n## R code 7.29\r\nplot( compare( m6.6 , m6.7 , m6.8 ) )\r\n\r\n## R code 7.30\r\nset.seed(92)\r\nwaic_m6.6 <- WAIC( m6.6 , pointwise=TRUE )$WAIC\r\ndiff_m6.6_m6.8 <- waic_m6.6 - waic_m6.8\r\nsqrt( n*var( diff_m6.6_m6.8 ) )\r\n\r\n## R code 7.31\r\nset.seed(93)\r\ncompare( m6.6 , m6.7 , m6.8 )@dSE\r\n\r\n## R code 7.32\r\nlibrary(rethinking)\r\ndata(WaffleDivorce)\r\nd <- WaffleDivorce\r\nd$A <- standardize( d$MedianAgeMarriage )\r\nd$D <- standardize( d$Divorce )\r\nd$M <- standardize( d$Marriage )\r\n\r\nm5.1 <- quap(\r\n alist(\r\n D ~ dnorm( mu , sigma ) ,\r\n mu <- a + bA * A ,\r\n a ~ dnorm( 0 , 0.2 ) ,\r\n bA ~ dnorm( 0 , 0.5 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data = d )\r\n\r\nm5.2 <- quap(\r\n alist(\r\n D ~ dnorm( mu , sigma ) ,\r\n mu <- a + bM * M ,\r\n a ~ dnorm( 0 , 0.2 ) ,\r\n bM ~ dnorm( 0 , 0.5 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data = d )\r\n\r\nm5.3 <- quap(\r\n alist(\r\n D ~ dnorm( mu , sigma ) ,\r\n mu <- a + bM*M + bA*A ,\r\n a ~ dnorm( 0 , 0.2 ) ,\r\n bM ~ dnorm( 0 , 0.5 ) ,\r\n bA ~ dnorm( 0 , 0.5 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data = d )\r\n\r\n## R code 7.33\r\nset.seed(24071847)\r\ncompare( m5.1 , m5.2 , m5.3 , func=PSIS )\r\n\r\n## R code 7.34\r\nset.seed(24071847)\r\nPSIS_m5.3 <- PSIS(m5.3,pointwise=TRUE)\r\nset.seed(24071847)\r\nWAIC_m5.3 <- WAIC(m5.3,pointwise=TRUE)\r\nplot( PSIS_m5.3$k , WAIC_m5.3$penalty , xlab=\"PSIS Pareto k\" ,\r\n ylab=\"WAIC penalty\" , col=rangi2 , lwd=2 )\r\n\r\n## R code 7.35\r\nm5.3t <- quap(\r\n alist(\r\n D ~ dstudent( 2 , mu , sigma ) ,\r\n mu <- a + bM*M + bA*A ,\r\n a ~ dnorm( 0 , 0.2 ) ,\r\n bM ~ dnorm( 0 , 0.5 ) ,\r\n bA ~ dnorm( 0 , 0.5 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data = d )\r\n\r\n## R code 8.1\r\nlibrary(rethinking)\r\ndata(rugged)\r\nd <- rugged\r\n\r\n# make log version of outcome\r\nd$log_gdp <- log( d$rgdppc_2000 )\r\n\r\n# extract countries with GDP data\r\ndd <- d[ complete.cases(d$rgdppc_2000) , ]\r\n\r\n# rescale variables\r\ndd$log_gdp_std <- dd$log_gdp / mean(dd$log_gdp)\r\ndd$rugged_std <- dd$rugged / max(dd$rugged)\r\n\r\n## R code 8.2\r\nm8.1 <- quap(\r\n alist(\r\n log_gdp_std ~ dnorm( mu , sigma ) ,\r\n mu <- a + b*( rugged_std - 0.215 ) ,\r\n a ~ dnorm( 1 , 1 ) ,\r\n b ~ dnorm( 0 , 1 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=dd )\r\n\r\n## R code 8.3\r\nset.seed(7)\r\nprior <- extract.prior( m8.1 )\r\n\r\n# set up the plot dimensions\r\nplot( NULL , xlim=c(0,1) , ylim=c(0.5,1.5) ,\r\n xlab=\"ruggedness\" , ylab=\"log GDP\" )\r\nabline( h=min(dd$log_gdp_std) , lty=2 )\r\nabline( h=max(dd$log_gdp_std) , lty=2 )\r\n\r\n# draw 50 lines from the prior\r\nrugged_seq <- seq( from=-0.1 , to=1.1 , length.out=30 )\r\nmu <- link( m8.1 , post=prior , data=data.frame(rugged_std=rugged_seq) )\r\nfor ( i in 1:50 ) lines( rugged_seq , mu[i,] , col=col.alpha(\"black\",0.3) )\r\n\r\n## R code 8.4\r\nsum( abs(prior$b) > 0.6 ) / length(prior$b)\r\n\r\n## R code 8.5\r\nm8.1 <- quap(\r\n alist(\r\n log_gdp_std ~ dnorm( mu , sigma ) ,\r\n mu <- a + b*( rugged_std - 0.215 ) ,\r\n a ~ dnorm( 1 , 0.1 ) ,\r\n b ~ dnorm( 0 , 0.3 ) ,\r\n sigma ~ dexp(1)\r\n ) , data=dd )\r\n\r\n## R code 8.6\r\nprecis( m8.1 )\r\n\r\n## R code 8.7\r\n# make variable to index Africa (1) or not (2)\r\ndd$cid <- ifelse( dd$cont_africa==1 , 1 , 2 )\r\n\r\n## R code 8.8\r\nm8.2 <- quap(\r\n alist(\r\n log_gdp_std ~ dnorm( mu , sigma ) ,\r\n mu <- a[cid] + b*( rugged_std - 0.215 ) ,\r\n a[cid] ~ dnorm( 1 , 0.1 ) ,\r\n b ~ dnorm( 0 , 0.3 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=dd )\r\n\r\n## R code 8.9\r\ncompare( m8.1 , m8.2 )\r\n\r\n## R code 8.10\r\nprecis( m8.2 , depth=2 )\r\n\r\n## R code 8.11\r\npost <- extract.samples(m8.2)\r\ndiff_a1_a2 <- post$a[,1] - post$a[,2]\r\nPI( diff_a1_a2 )\r\n\r\n## R code 8.12\r\nrugged.seq <- seq( from=-0.1 , to=1.1 , length.out=30 )\r\n# compute mu over samples, fixing cid=2 and then cid=1\r\nmu.NotAfrica <- link( m8.2 ,\r\n data=data.frame( cid=2 , rugged_std=rugged.seq ) )\r\nmu.Africa <- link( m8.2 ,\r\n data=data.frame( cid=1 , rugged_std=rugged.seq ) )\r\n# summarize to means and intervals\r\nmu.NotAfrica_mu <- apply( mu.NotAfrica , 2 , mean )\r\nmu.NotAfrica_ci <- apply( mu.NotAfrica , 2 , PI , prob=0.97 )\r\nmu.Africa_mu <- apply( mu.Africa , 2 , mean )\r\nmu.Africa_ci <- apply( mu.Africa , 2 , PI , prob=0.97 )\r\n\r\n## R code 8.13\r\nm8.3 <- quap(\r\n alist(\r\n log_gdp_std ~ dnorm( mu , sigma ) ,\r\n mu <- a[cid] + b[cid]*( rugged_std - 0.215 ) ,\r\n a[cid] ~ dnorm( 1 , 0.1 ) ,\r\n b[cid] ~ dnorm( 0 , 0.3 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=dd )\r\n\r\n## R code 8.14\r\nprecis( m8.5 , depth=2 )\r\n\r\n## R code 8.15\r\ncompare( m8.1 , m8.2 , m8.3 , func=PSIS )\r\n\r\n## R code 8.16\r\nplot( PSIS( m8.3 , pointwise=TRUE )$k )\r\n\r\n## R code 8.17\r\n# plot Africa - cid=1\r\nd.A1 <- dd[ dd$cid==1 , ]\r\nplot( d.A1$rugged_std , d.A1$log_gdp_std , pch=16 , col=rangi2 ,\r\n xlab=\"ruggedness (standardized)\" , ylab=\"log GDP (as proportion of mean)\" ,\r\n xlim=c(0,1) )\r\nmu <- link( m8.3 , data=data.frame( cid=1 , rugged_std=rugged_seq ) )\r\nmu_mean <- apply( mu , 2 , mean )\r\nmu_ci <- apply( mu , 2 , PI , prob=0.97 )\r\nlines( rugged_seq , mu_mean , lwd=2 )\r\nshade( mu_ci , rugged_seq , col=col.alpha(rangi2,0.3) )\r\nmtext(\"African nations\")\r\n\r\n# plot non-Africa - cid=2\r\nd.A0 <- dd[ dd$cid==2 , ]\r\nplot( d.A0$rugged_std , d.A0$log_gdp_std , pch=1 , col=\"black\" ,\r\n xlab=\"ruggedness (standardized)\" , ylab=\"log GDP (as proportion of mean)\" ,\r\n xlim=c(0,1) )\r\nmu <- link( m8.3 , data=data.frame( cid=2 , rugged_std=rugged_seq ) )\r\nmu_mean <- apply( mu , 2 , mean )\r\nmu_ci <- apply( mu , 2 , PI , prob=0.97 )\r\nlines( rugged_seq , mu_mean , lwd=2 )\r\nshade( mu_ci , rugged_seq )\r\nmtext(\"Non-African nations\")\r\n\r\n## R code 8.18\r\nrugged_seq <- seq(from=-0.2,to=1.2,length.out=30)\r\nmuA <- link( m8.3 , data=data.frame(cid=1,rugged_std=rugged_seq) )\r\nmuN <- link( m8.3 , data=data.frame(cid=2,rugged_std=rugged_seq) )\r\ndelta <- muA - muN\r\n\r\n## R code 8.19\r\nlibrary(rethinking)\r\ndata(tulips)\r\nd <- tulips\r\nstr(d)\r\n\r\n## R code 8.20\r\nd$blooms_std <- d$blooms / max(d$blooms)\r\nd$water_cent <- d$water - mean(d$water)\r\nd$shade_cent <- d$shade - mean(d$shade)\r\n\r\n## R code 8.21\r\na <- rnorm( 1e4 , 0.5 , 1 ); sum( a < 0 | a > 1 ) / length( a )\r\n\r\n## R code 8.22\r\na <- rnorm( 1e4 , 0.5 , 0.25 ); sum( a < 0 | a > 1 ) / length( a )\r\n\r\n## R code 8.23\r\nm8.4 <- quap(\r\n alist(\r\n blooms_std ~ dnorm( mu , sigma ) ,\r\n mu <- a + bw*water_cent + bs*shade_cent ,\r\n a ~ dnorm( 0.5 , 0.25 ) ,\r\n bw ~ dnorm( 0 , 0.25 ) ,\r\n bs ~ dnorm( 0 , 0.25 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=d )\r\n\r\n## R code 8.24\r\nm8.5 <- quap(\r\n alist(\r\n blooms_std ~ dnorm( mu , sigma ) ,\r\n mu <- a + bw*water_cent + bs*shade_cent + bws*water_cent*shade_cent ,\r\n a ~ dnorm( 0.5 , 0.25 ) ,\r\n bw ~ dnorm( 0 , 0.25 ) ,\r\n bs ~ dnorm( 0 , 0.25 ) ,\r\n bws ~ dnorm( 0 , 0.25 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=d )\r\n\r\n## R code 8.25\r\npar(mfrow=c(1,3)) # 3 plots in 1 row\r\nfor ( s in -1:1 ) {\r\n idx <- which( d$shade_cent==s )\r\n plot( d$water_cent[idx] , d$blooms_std[idx] , xlim=c(-1,1) , ylim=c(0,1) ,\r\n xlab=\"water\" , ylab=\"blooms\" , pch=16 , col=rangi2 )\r\n mu <- link( m8.4 , data=data.frame( shade_cent=s , water_cent=-1:1 ) )\r\n for ( i in 1:20 ) lines( -1:1 , mu[i,] , col=col.alpha(\"black\",0.3) )\r\n}\r\n\r\n## R code 8.26\r\nset.seed(7)\r\nprior <- extract.prior(m8.5)\r\n\r\n## R code 8.27\r\nd$lang.per.cap <- d$num.lang / d$k.pop\r\n\r\n## R code 9.1\r\nnum_weeks <- 1e5\r\npositions <- rep(0,num_weeks)\r\ncurrent <- 10\r\nfor ( i in 1:num_weeks ) {\r\n ## record current position\r\n positions[i] <- current\r\n ## flip coin to generate proposal\r\n proposal <- current + sample( c(-1,1) , size=1 )\r\n ## now make sure he loops around the archipelago\r\n if ( proposal < 1 ) proposal <- 10\r\n if ( proposal > 10 ) proposal <- 1\r\n ## move?\r\n prob_move <- proposal/current\r\n current <- ifelse( runif(1) < prob_move , proposal , current )\r\n}\r\n\r\n## R code 9.2\r\nplot( 1:100 , positions[1:100] )\r\n\r\n## R code 9.3\r\nplot( table( positions ) )\r\n\r\n## R code 9.4\r\nD <- 10\r\nT <- 1e3\r\nY <- rmvnorm(T,rep(0,D),diag(D))\r\nrad_dist <- function( Y ) sqrt( sum(Y^2) )\r\nRd <- sapply( 1:T , function(i) rad_dist( Y[i,] ) )\r\ndens( Rd )\r\n\r\n## R code 9.5\r\n# U needs to return neg-log-probability\r\nU <- function( q , a=0 , b=1 , k=0 , d=1 ) {\r\n muy <- q[1]\r\n mux <- q[2]\r\n U <- sum( dnorm(y,muy,1,log=TRUE) ) + sum( dnorm(x,mux,1,log=TRUE) ) +\r\n dnorm(muy,a,b,log=TRUE) + dnorm(mux,k,d,log=TRUE)\r\n return( -U )\r\n}\r\n\r\n## R code 9.6\r\n# gradient function\r\n# need vector of partial derivatives of U with respect to vector q\r\nU_gradient <- function( q , a=0 , b=1 , k=0 , d=1 ) {\r\n muy <- q[1]\r\n mux <- q[2]\r\n G1 <- sum( y - muy ) + (a - muy)/b^2 #dU/dmuy\r\n G2 <- sum( x - mux ) + (k - mux)/d^2 #dU/dmux\r\n return( c( -G1 , -G2 ) ) # negative bc energy is neg-log-prob\r\n}\r\n# test data\r\nset.seed(7)\r\ny <- rnorm(50)\r\nx <- rnorm(50)\r\nx <- as.numeric(scale(x))\r\ny <- as.numeric(scale(y))\r\n\r\n## R code 9.7\r\nlibrary(shape) # for fancy arrows\r\nQ <- list()\r\nQ$q <- c(-0.1,0.2)\r\npr <- 0.3\r\nplot( NULL , ylab=\"muy\" , xlab=\"mux\" , xlim=c(-pr,pr) , ylim=c(-pr,pr) )\r\nstep <- 0.03\r\nL <- 11 # 0.03/28 for U-turns --- 11 for working example\r\nn_samples <- 4\r\npath_col <- col.alpha(\"black\",0.5)\r\npoints( Q$q[1] , Q$q[2] , pch=4 , col=\"black\" )\r\nfor ( i in 1:n_samples ) {\r\n Q <- HMC2( U , U_gradient , step , L , Q$q )\r\n if ( n_samples < 10 ) {\r\n for ( j in 1:L ) {\r\n K0 <- sum(Q$ptraj[j,]^2)/2 # kinetic energy\r\n lines( Q$traj[j:(j+1),1] , Q$traj[j:(j+1),2] , col=path_col , lwd=1+2*K0 )\r\n }\r\n points( Q$traj[1:L+1,] , pch=16 , col=\"white\" , cex=0.35 )\r\n Arrows( Q$traj[L,1] , Q$traj[L,2] , Q$traj[L+1,1] , Q$traj[L+1,2] ,\r\n arr.length=0.35 , arr.adj = 0.7 )\r\n text( Q$traj[L+1,1] , Q$traj[L+1,2] , i , cex=0.8 , pos=4 , offset=0.4 )\r\n }\r\n points( Q$traj[L+1,1] , Q$traj[L+1,2] , pch=ifelse( Q$accept==1 , 16 , 1 ) ,\r\n col=ifelse( abs(Q$dH)>0.1 , \"red\" , \"black\" ) )\r\n}\r\n\r\n## R code 9.8\r\nHMC2 <- function (U, grad_U, epsilon, L, current_q) {\r\n q = current_q\r\n p = rnorm(length(q),0,1) # random flick - p is momentum.\r\n current_p = p\r\n # Make a half step for momentum at the beginning\r\n p = p - epsilon * grad_U(q) / 2\r\n # initialize bookkeeping - saves trajectory\r\n qtraj <- matrix(NA,nrow=L+1,ncol=length(q))\r\n ptraj <- qtraj\r\n qtraj[1,] <- current_q\r\n ptraj[1,] <- p\r\n\r\n## R code 9.9\r\n # Alternate full steps for position and momentum\r\n for ( i in 1:L ) {\r\n q = q + epsilon * p # Full step for the position\r\n # Make a full step for the momentum, except at end of trajectory\r\n if ( i!=L ) {\r\n p = p - epsilon * grad_U(q)\r\n ptraj[i+1,] <- p\r\n }\r\n qtraj[i+1,] <- q\r\n }\r\n\r\n## R code 9.10\r\n # Make a half step for momentum at the end\r\n p = p - epsilon * grad_U(q) / 2\r\n ptraj[L+1,] <- p\r\n # Negate momentum at end of trajectory to make the proposal symmetric\r\n p = -p\r\n # Evaluate potential and kinetic energies at start and end of trajectory\r\n current_U = U(current_q)\r\n current_K = sum(current_p^2) / 2\r\n proposed_U = U(q)\r\n proposed_K = sum(p^2) / 2\r\n # Accept or reject the state at end of trajectory, returning either\r\n # the position at the end of the trajectory or the initial position\r\n accept <- 0\r\n if (runif(1) < exp(current_U-proposed_U+current_K-proposed_K)) {\r\n new_q <- q # accept\r\n accept <- 1\r\n } else new_q <- current_q # reject\r\n return(list( q=new_q, traj=qtraj, ptraj=ptraj, accept=accept ))\r\n}\r\n\r\n## R code 9.11\r\nlibrary(rethinking)\r\ndata(rugged)\r\nd <- rugged\r\nd$log_gdp <- log(d$rgdppc_2000)\r\ndd <- d[ complete.cases(d$rgdppc_2000) , ]\r\ndd$log_gdp_std <- dd$log_gdp / mean(dd$log_gdp)\r\ndd$rugged_std <- dd$rugged / max(dd$rugged)\r\ndd$cid <- ifelse( dd$cont_africa==1 , 1 , 2 )\r\n\r\n## R code 9.12\r\nm8.3 <- quap(\r\n alist(\r\n log_gdp_std ~ dnorm( mu , sigma ) ,\r\n mu <- a[cid] + b[cid]*( rugged_std - 0.215 ) ,\r\n a[cid] ~ dnorm( 1 , 0.1 ) ,\r\n b[cid] ~ dnorm( 0 , 0.3 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=dd )\r\nprecis( m8.3 , depth=2 )\r\n\r\n## R code 9.13\r\ndat_slim <- list(\r\n log_gdp_std = dd$log_gdp_std,\r\n rugged_std = dd$rugged_std,\r\n cid = as.integer( dd$cid )\r\n)\r\nstr(dat_slim)\r\n\r\n## R code 9.14\r\nm9.1 <- ulam(\r\n alist(\r\n log_gdp_std ~ dnorm( mu , sigma ) ,\r\n mu <- a[cid] + b[cid]*( rugged_std - 0.215 ) ,\r\n a[cid] ~ dnorm( 1 , 0.1 ) ,\r\n b[cid] ~ dnorm( 0 , 0.3 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=dat_slim , chains=1 )\r\n\r\n## R code 9.15\r\nprecis( m9.1 , depth=2 )\r\n\r\n## R code 9.16\r\nm9.1 <- ulam(\r\n alist(\r\n log_gdp_std ~ dnorm( mu , sigma ) ,\r\n mu <- a[cid] + b[cid]*( rugged_std - 0.215 ) ,\r\n a[cid] ~ dnorm( 1 , 0.1 ) ,\r\n b[cid] ~ dnorm( 0 , 0.3 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=dat_slim , chains=4 , cores=4 )\r\n\r\n## R code 9.17\r\nshow( m9.1 )\r\n\r\n## R code 9.18\r\nprecis( m9.1 , 2 )\r\n\r\n## R code 9.19\r\npairs( m9.1 )\r\n\r\n## R code 9.20\r\ntraceplot( m9.1 )\r\n\r\n## R code 9.21\r\ntrankplot( m9.1 )\r\n\r\n## R code 9.22\r\ny <- c(-1,1)\r\nset.seed(11)\r\nm9.2 <- ulam(\r\n alist(\r\n y ~ dnorm( mu , sigma ) ,\r\n mu <- alpha ,\r\n alpha ~ dnorm( 0 , 1000 ) ,\r\n sigma ~ dexp( 0.0001 )\r\n ) , data=list(y=y) , chains=3 )\r\n\r\n## R code 9.23\r\nprecis( m9.2 )\r\n\r\n## R code 9.24\r\nset.seed(11)\r\nm9.3 <- ulam(\r\n alist(\r\n y ~ dnorm( mu , sigma ) ,\r\n mu <- alpha ,\r\n alpha ~ dnorm( 1 , 10 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=list(y=y) , chains=3 )\r\nprecis( m9.3 )\r\n\r\n## R code 9.25\r\nset.seed(41)\r\ny <- rnorm( 100 , mean=0 , sd=1 )\r\n\r\n## R code 9.26\r\nset.seed(384)\r\nm9.4 <- ulam(\r\n alist(\r\n y ~ dnorm( mu , sigma ) ,\r\n mu <- a1 + a2 ,\r\n a1 ~ dnorm( 0 , 1000 ),\r\n a2 ~ dnorm( 0 , 1000 ),\r\n sigma ~ dexp( 1 )\r\n ) , data=list(y=y) , chains=3 )\r\nprecis( m9.4 )\r\n\r\n## R code 9.27\r\nm9.5 <- ulam(\r\n alist(\r\n y ~ dnorm( mu , sigma ) ,\r\n mu <- a1 + a2 ,\r\n a1 ~ dnorm( 0 , 10 ),\r\n a2 ~ dnorm( 0 , 10 ),\r\n sigma ~ dexp( 1 )\r\n ) , data=list(y=y) , chains=3 )\r\nprecis( m9.5 )\r\n\r\n## R code 9.28\r\nmp <- ulam(\r\n alist(\r\n a ~ dnorm(0,1),\r\n b ~ dcauchy(0,1)\r\n ), data=list(y=1) , chains=1 )\r\n\r\n## R code 9.29\r\nm5.8s <- ulam(\r\n alist(\r\n height ~ dnorm( mu , sigma ) ,\r\n mu <- a + bl*leg_left + br*leg_right ,\r\n a ~ dnorm( 10 , 100 ) ,\r\n bl ~ dnorm( 2 , 10 ) ,\r\n br ~ dnorm( 2 , 10 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=d, chains=4,\r\n start=list(a=10,bl=0,br=0.1,sigma=1) )\r\n\r\n## R code 9.30\r\nm5.8s2 <- ulam(\r\n alist(\r\n height ~ dnorm( mu , sigma ) ,\r\n mu <- a + bl*leg_left + br*leg_right ,\r\n a ~ dnorm( 10 , 100 ) ,\r\n bl ~ dnorm( 2 , 10 ) ,\r\n br ~ dnorm( 2 , 10 ) ,\r\n sigma ~ dexp( 1 )\r\n ) , data=d, chains=4,\r\n constraints=list(br=\"lower=0\"),\r\n start=list(a=10,bl=0,br=0.1,sigma=1) )\r\n\r\n## R code 10.1\r\np <- list()\r\np$A <- c(0,0,10,0,0)\r\np$B <- c(0,1,8,1,0)\r\np$C <- c(0,2,6,2,0)\r\np$D <- c(1,2,4,2,1)\r\np$E <- c(2,2,2,2,2)\r\n\r\n## R code 10.2\r\np_norm <- lapply( p , function(q) q/sum(q))\r\n\r\n## R code 10.3\r\n( H <- sapply( p_norm , function(q) -sum(ifelse(q==0,0,q*log(q))) ) )\r\n\r\n## R code 10.4\r\nways <- c(1,90,1260,37800,113400)\r\nlogwayspp <- log(ways)/10\r\n\r\n## R code 10.5\r\n# build list of the candidate distributions\r\np <- list()\r\np[[1]] <- c(1/4,1/4,1/4,1/4)\r\np[[2]] <- c(2/6,1/6,1/6,2/6)\r\np[[3]] <- c(1/6,2/6,2/6,1/6)\r\np[[4]] <- c(1/8,4/8,2/8,1/8)\r\n\r\n# compute expected value of each\r\nsapply( p , function(p) sum(p*c(0,1,1,2)) )\r\n\r\n## R code 10.6\r\n# compute entropy of each distribution\r\nsapply( p , function(p) -sum( p*log(p) ) )\r\n\r\n## R code 10.7\r\np <- 0.7\r\n( A <- c( (1-p)^2 , p*(1-p) , (1-p)*p , p^2 ) )\r\n\r\n## R code 10.8\r\n-sum( A*log(A) )\r\n\r\n## R code 10.9\r\nsim.p <- function(G=1.4) {\r\n x123 <- runif(3)\r\n x4 <- ( (G)*sum(x123)-x123[2]-x123[3] )/(2-G)\r\n z <- sum( c(x123,x4) )\r\n p <- c( x123 , x4 )/z\r\n list( H=-sum( p*log(p) ) , p=p )\r\n}\r\n\r\n## R code 10.10\r\nH <- replicate( 1e5 , sim.p(1.4) )\r\ndens( as.numeric(H[1,]) , adj=0.1 )\r\n\r\n## R code 10.11\r\nentropies <- as.numeric(H[1,])\r\ndistributions <- H[2,]\r\n\r\n## R code 10.12\r\nmax(entropies)\r\n\r\n## R code 10.13\r\ndistributions[ which.max(entropies) ]\r\n\r\n## R code 11.1\r\nlibrary(rethinking)\r\ndata(chimpanzees)\r\nd <- chimpanzees\r\n\r\n## R code 11.2\r\nd$treatment <- 1 + d$prosoc_left + 2*d$condition\r\n\r\n## R code 11.3\r\nxtabs( ~ treatment + prosoc_left + condition , d )\r\n\r\n## R code 11.4\r\nm11.1 <- quap(\r\n alist(\r\n pulled_left ~ dbinom( 1 , p ) ,\r\n logit(p) <- a ,\r\n a ~ dnorm( 0 , 10 )\r\n ) , data=d )\r\n\r\n## R code 11.5\r\nset.seed(1999)\r\nprior <- extract.prior( m11.1 , n=1e4 )\r\n\r\n## R code 11.6\r\np <- inv_logit( prior$a )\r\ndens( p , adj=0.1 )\r\n\r\nd <- read.csv(\"squirrel-ai.csv\")\r\n\r\n\r\n## R code 11.7\r\nm_sqAI <- quap(\r\n alist(\r\n I ~ dbinom( 1 , p ) ,\r\n logit(p) <- a + b[A] ,\r\n a ~ dnorm( 0 , 1.5 ),\r\n b[A] ~ dnorm(0, 10 )\r\n ) , data=d )\r\nset.seed(42)\r\nprior <- extract.prior( m_sqAI , n=1e4 )\r\np <- sapply( 1:4 , function(k) inv_logit( prior$a + prior$b[,k] ) )\r\n\r\n## R code 11.8\r\ndens( abs( p[,1] - p[,2] ) , adj=0.1 )\r\n\r\n## R code 11.9\r\nm11.3 <- quap(\r\n alist(\r\n pulled_left ~ dbinom( 1 , p ) ,\r\n logit(p) <- a + b[treatment] ,\r\n a ~ dnorm( 0 , 1.5 ),\r\n b[treatment] ~ dnorm( 0 , 0.5 )\r\n ) , data=d )\r\nset.seed(1999)\r\nprior <- extract.prior( m11.3 , n=1e4 )\r\np <- sapply( 1:4 , function(k) inv_logit( prior$a + prior$b[,k] ) )\r\nmean( abs( p[,1] - p[,2] ) )\r\n\r\n## R code 11.10\r\n# trimmed data list\r\ndat_list <- list(\r\n pulled_left = d$pulled_left,\r\n actor = d$actor,\r\n treatment = as.integer(d$treatment) )\r\n\r\n## R code 11.11\r\nm11.4 <- ulam(\r\n alist(\r\n pulled_left ~ dbinom( 1 , p ) ,\r\n logit(p) <- a[actor] + b[treatment] ,\r\n a[actor] ~ dnorm( 0 , 1.5 ),\r\n b[treatment] ~ dnorm( 0 , 0.5 )\r\n ) , data=dat_list , chains=4 , log_lik=TRUE )\r\nprecis( m11.4 , depth=2 )\r\n\r\n## R code 11.12\r\npost <- extract.samples(m_sqAI)\r\np_sqAI <- inv_logit( post$a )\r\nplot( precis( as.data.frame(p_sqAI) ) , xlim=c(0,1) )\r\n\r\n## R code 11.13\r\nlabs <- c( \"adult\",\"juvenile\" )\r\nplot( precis( m_sqAI , depth=2 , pars=\"b\" ) , labels=labs )\r\n\r\n## R code 11.14\r\ndiffs <- list(\r\n db13 = post$b[,1] - post$b[,3],\r\n db24 = post$b[,2] - post$b[,4] )\r\nplot( precis(diffs) )\r\n\r\n## R code 11.15\r\npl <- by( d$pulled_left , list( d$actor , d$treatment ) , mean )\r\npl[1,]\r\n\r\n## R code 11.16\r\nplot( NULL , xlim=c(1,28) , ylim=c(0,1) , xlab=\"\" ,\r\n ylab=\"proportion left lever\" , xaxt=\"n\" , yaxt=\"n\" )\r\naxis( 2 , at=c(0,0.5,1) , labels=c(0,0.5,1) )\r\nabline( h=0.5 , lty=2 )\r\nfor ( j in 1:7 ) abline( v=(j-1)*4+4.5 , lwd=0.5 )\r\nfor ( j in 1:7 ) text( (j-1)*4+2.5 , 1.1 , concat(\"actor \",j) , xpd=TRUE )\r\nfor ( j in (1:7)[-2] ) {\r\n lines( (j-1)*4+c(1,3) , pl[j,c(1,3)] , lwd=2 , col=rangi2 )\r\n lines( (j-1)*4+c(2,4) , pl[j,c(2,4)] , lwd=2 , col=rangi2 )\r\n}\r\npoints( 1:28 , t(pl) , pch=16 , col=\"white\" , cex=1.7 )\r\npoints( 1:28 , t(pl) , pch=c(1,1,16,16) , col=rangi2 , lwd=2 )\r\nyoff <- 0.01\r\ntext( 1 , pl[1,1]-yoff , \"R/N\" , pos=1 , cex=0.8 )\r\ntext( 2 , pl[1,2]+yoff , \"L/N\" , pos=3 , cex=0.8 )\r\ntext( 3 , pl[1,3]-yoff , \"R/P\" , pos=1 , cex=0.8 )\r\ntext( 4 , pl[1,4]+yoff , \"L/P\" , pos=3 , cex=0.8 )\r\nmtext( \"observed proportions\\n\" )\r\n\r\n## R code 11.17\r\ndat <- list( actor=rep(1:7,each=4) , treatment=rep(1:4,times=7) )\r\np_post <- link( m11.4 , data=dat )\r\np_mu <- apply( p_post , 2 , mean )\r\np_ci <- apply( p_post , 2 , PI )\r\n\r\n## R code 11.18\r\nd$side <- d$prosoc_left + 1 # right 1, left 2\r\nd$cond <- d$condition + 1 # no partner 1, partner 2\r\n\r\n## R code 11.19\r\ndat_list2 <- list(\r\n pulled_left = d$pulled_left,\r\n actor = d$actor,\r\n side = d$side,\r\n cond = d$cond )\r\nm11.5 <- ulam(\r\n alist(\r\n pulled_left ~ dbinom( 1 , p ) ,\r\n logit(p) <- a[actor] + bs[side] + bc[cond] ,\r\n a[actor] ~ dnorm( 0 , 1.5 ),\r\n bs[side] ~ dnorm( 0 , 0.5 ),\r\n bc[cond] ~ dnorm( 0 , 0.5 )\r\n ) , data=dat_list2 , chains=4 , log_lik=TRUE )\r\n\r\n## R code 11.20\r\ncompare( m11.5 , m11.4 , func=PSIS )\r\n\r\n## R code 11.21\r\npost <- extract.samples( m11.4 , clean=FALSE )\r\nstr(post)\r\n\r\n## R code 11.22\r\nm11.4_stan_code <- stancode(m11.4)\r\nm11.4_stan <- stan( model_code=m11.4_stan_code , data=dat_list , chains=4 )\r\ncompare( m11.4_stan , m11.4 )\r\n\r\n## R code 11.23\r\npost <- extract.samples(m11.4)\r\nmean( exp(post$b[,4]-post$b[,2]) )\r\n\r\n## R code 11.24\r\ndata(chimpanzees)\r\nd <- chimpanzees\r\nd$treatment <- 1 + d$prosoc_left + 2*d$condition\r\nd$side <- d$prosoc_left + 1 # right 1, left 2\r\nd$cond <- d$condition + 1 # no partner 1, partner 2\r\nd_aggregated <- aggregate(\r\n d$pulled_left ,\r\n list( treatment=d$treatment , actor=d$actor ,\r\n side=d$side , cond=d$cond ) ,\r\n sum )\r\ncolnames(d_aggregated)[5] <- \"left_pulls\"\r\n\r\n## R code 11.25\r\ndat <- with( d_aggregated , list(\r\n left_pulls = left_pulls,\r\n treatment = treatment,\r\n actor = actor,\r\n side = side,\r\n cond = cond ) )\r\n\r\nm11.6 <- ulam(\r\n alist(\r\n left_pulls ~ dbinom( 18 , p ) ,\r\n logit(p) <- a[actor] + b[treatment] ,\r\n a[actor] ~ dnorm( 0 , 1.5 ) ,\r\n b[treatment] ~ dnorm( 0 , 0.5 )\r\n ) , data=dat , chains=4 , log_lik=TRUE )\r\n\r\n## R code 11.26\r\ncompare( m11.6 , m11.4 , func=PSIS )\r\n\r\n## R code 11.27\r\n# deviance of aggregated 6-in-9\r\n-2*dbinom(6,9,0.2,log=TRUE)\r\n# deviance of dis-aggregated\r\n-2*sum(dbern(c(1,1,1,1,1,1,0,0,0),0.2,log=TRUE))\r\n\r\n## R code 11.28\r\nlibrary(rethinking)\r\ndata(UCBadmit)\r\nd <- UCBadmit\r\n\r\n## R code 11.29\r\ndat_list <- list(\r\n admit = d$admit,\r\n applications = d$applications,\r\n gid = ifelse( d$applicant.gender==\"male\" , 1 , 2 )\r\n)\r\nm11.7 <- ulam(\r\n alist(\r\n admit ~ dbinom( applications , p ) ,\r\n logit(p) <- a[gid] ,\r\n a[gid] ~ dnorm( 0 , 1.5 )\r\n ) , data=dat_list , chains=4 )\r\nprecis( m11.7 , depth=2 )\r\n\r\n## R code 11.30\r\npost <- extract.samples(m11.7)\r\ndiff_a <- post$a[,1] - post$a[,2]\r\ndiff_p <- inv_logit(post$a[,1]) - inv_logit(post$a[,2])\r\nprecis( list( diff_a=diff_a , diff_p=diff_p ) )\r\n\r\n## R code 11.31\r\npostcheck( m11.7 )\r\n# draw lines connecting points from same dept\r\nfor ( i in 1:6 ) {\r\n x <- 1 + 2*(i-1)\r\n y1 <- d$admit[x]/d$applications[x]\r\n y2 <- d$admit[x+1]/d$applications[x+1]\r\n lines( c(x,x+1) , c(y1,y2) , col=rangi2 , lwd=2 )\r\n text( x+0.5 , (y1+y2)/2 + 0.05 , d$dept[x] , cex=0.8 , col=rangi2 )\r\n}\r\n\r\n## R code 11.32\r\ndat_list$dept_id <- rep(1:6,each=2)\r\nm11.8 <- ulam(\r\n alist(\r\n admit ~ dbinom( applications , p ) ,\r\n logit(p) <- a[gid] + delta[dept_id] ,\r\n a[gid] ~ dnorm( 0 , 1.5 ) ,\r\n delta[dept_id] ~ dnorm( 0 , 1.5 )\r\n ) , data=dat_list , chains=4 , iter=4000 )\r\nprecis( m11.8 , depth=2 )\r\n\r\n## R code 11.33\r\npost <- extract.samples(m11.8)\r\ndiff_a <- post$a[,1] - post$a[,2]\r\ndiff_p <- inv_logit(post$a[,1]) - inv_logit(post$a[,2])\r\nprecis( list( diff_a=diff_a , diff_p=diff_p ) )\r\n\r\n## R code 11.34\r\npg <- with( dat_list , sapply( 1:6 , function(k)\r\n applications[dept_id==k]/sum(applications[dept_id==k]) ) )\r\nrownames(pg) <- c(\"male\",\"female\")\r\ncolnames(pg) <- unique(d$dept)\r\nround( pg , 2 )\r\n\r\n## R code 11.35\r\ny <- rbinom(1e5,1000,1/1000)\r\nc( mean(y) , var(y) )\r\n\r\n## R code 11.36\r\nlibrary(rethinking)\r\ndata(Kline)\r\nd <- Kline\r\nd\r\n\r\n## R code 11.37\r\nd$P <- scale( log(d$population) )\r\nd$contact_id <- ifelse( d$contact==\"high\" , 2 , 1 )\r\n\r\n## R code 11.38\r\ncurve( dlnorm( x , 0 , 10 ) , from=0 , to=100 , n=200 )\r\n\r\n## R code 11.39\r\na <- rnorm(1e4,0,10)\r\nlambda <- exp(a)\r\nmean( lambda )\r\n\r\n## R code 11.40\r\ncurve( dlnorm( x , 3 , 0.5 ) , from=0 , to=100 , n=200 )\r\n\r\n## R code 11.41\r\nN <- 100\r\na <- rnorm( N , 3 , 0.5 )\r\nb <- rnorm( N , 0 , 10 )\r\nplot( NULL , xlim=c(-2,2) , ylim=c(0,100) )\r\nfor ( i in 1:N ) curve( exp( a[i] + b[i]*x ) , add=TRUE , col=grau() )\r\n\r\n## R code 11.42\r\nset.seed(10)\r\nN <- 100\r\na <- rnorm( N , 3 , 0.5 )\r\nb <- rnorm( N , 0 , 0.2 )\r\nplot( NULL , xlim=c(-2,2) , ylim=c(0,100) )\r\nfor ( i in 1:N ) curve( exp( a[i] + b[i]*x ) , add=TRUE , col=grau() )\r\n\r\n## R code 11.43\r\nx_seq <- seq( from=log(100) , to=log(200000) , length.out=100 )\r\nlambda <- sapply( x_seq , function(x) exp( a + b*x ) )\r\nplot( NULL , xlim=range(x_seq) , ylim=c(0,500) , xlab=\"log population\" ,\r\n ylab=\"total tools\" )\r\nfor ( i in 1:N ) lines( x_seq , lambda[i,] , col=grau() , lwd=1.5 )\r\n\r\n## R code 11.44\r\nplot( NULL , xlim=range(exp(x_seq)) , ylim=c(0,500) , xlab=\"population\" ,\r\n ylab=\"total tools\" )\r\nfor ( i in 1:N ) lines( exp(x_seq) , lambda[i,] , col=grau() , lwd=1.5 )\r\n\r\n## R code 11.45\r\ndat <- list(\r\n T = d$total_tools ,\r\n P = d$P ,\r\n cid = d$contact_id )\r\n\r\n# intercept only\r\nm11.9 <- ulam(\r\n alist(\r\n T ~ dpois( lambda ),\r\n log(lambda) <- a,\r\n a ~ dnorm( 3 , 0.5 )\r\n ), data=dat , chains=4 , log_lik=TRUE )\r\n\r\n# interaction model\r\nm11.10 <- ulam(\r\n alist(\r\n T ~ dpois( lambda ),\r\n log(lambda) <- a[cid] + b[cid]*P,\r\n a[cid] ~ dnorm( 3 , 0.5 ),\r\n b[cid] ~ dnorm( 0 , 0.2 )\r\n ), data=dat , chains=4 , log_lik=TRUE )\r\n\r\n## R code 11.46\r\ncompare( m11.9 , m11.10 , func=PSIS )\r\n\r\n## R code 11.47\r\nk <- PSIS( m11.10 , pointwise=TRUE )$k\r\nplot( dat$P , dat$T , xlab=\"log population (std)\" , ylab=\"total tools\" ,\r\n col=rangi2 , pch=ifelse( dat$cid==1 , 1 , 16 ) , lwd=2 ,\r\n ylim=c(0,75) , cex=1+normalize(k) )\r\n\r\n# set up the horizontal axis values to compute predictions at\r\nns <- 100\r\nP_seq <- seq( from=-1.4 , to=3 , length.out=ns )\r\n\r\n# predictions for cid=1 (low contact)\r\nlambda <- link( m11.10 , data=data.frame( P=P_seq , cid=1 ) )\r\nlmu <- apply( lambda , 2 , mean )\r\nlci <- apply( lambda , 2 , PI )\r\nlines( P_seq , lmu , lty=2 , lwd=1.5 )\r\nshade( lci , P_seq , xpd=TRUE )\r\n\r\n# predictions for cid=2 (high contact)\r\nlambda <- link( m11.10 , data=data.frame( P=P_seq , cid=2 ) )\r\nlmu <- apply( lambda , 2 , mean )\r\nlci <- apply( lambda , 2 , PI )\r\nlines( P_seq , lmu , lty=1 , lwd=1.5 )\r\nshade( lci , P_seq , xpd=TRUE )\r\n\r\n## R code 11.48\r\nplot( d$population , d$total_tools , xlab=\"population\" , ylab=\"total tools\" ,\r\n col=rangi2 , pch=ifelse( dat$cid==1 , 1 , 16 ) , lwd=2 ,\r\n ylim=c(0,75) , cex=1+normalize(k) )\r\n\r\nns <- 100\r\nP_seq <- seq( from=-5 , to=3 , length.out=ns )\r\n# 1.53 is sd of log(population)\r\n# 9 is mean of log(population)\r\npop_seq <- exp( P_seq*1.53 + 9 )\r\n\r\nlambda <- link( m11.10 , data=data.frame( P=P_seq , cid=1 ) )\r\nlmu <- apply( lambda , 2 , mean )\r\nlci <- apply( lambda , 2 , PI )\r\nlines( pop_seq , lmu , lty=2 , lwd=1.5 )\r\nshade( lci , pop_seq , xpd=TRUE )\r\n\r\nlambda <- link( m11.10 , data=data.frame( P=P_seq , cid=2 ) )\r\nlmu <- apply( lambda , 2 , mean )\r\nlci <- apply( lambda , 2 , PI )\r\nlines( pop_seq , lmu , lty=1 , lwd=1.5 )\r\nshade( lci , pop_seq , xpd=TRUE )\r\n\r\n## R code 11.49\r\ndat2 <- list( T=d$total_tools, P=d$population, cid=d$contact_id )\r\nm11.11 <- ulam(\r\n alist(\r\n T ~ dpois( lambda ),\r\n lambda <- exp(a[cid])*P^b[cid]/g,\r\n a[cid] ~ dnorm(1,1),\r\n b[cid] ~ dexp(1),\r\n g ~ dexp(1)\r\n ), data=dat2 , chains=4 , log_lik=TRUE )\r\n\r\n## R code 11.50\r\nnum_days <- 30\r\ny <- rpois( num_days , 1.5 )\r\n\r\n## R code 11.51\r\nnum_weeks <- 4\r\ny_new <- rpois( num_weeks , 0.5*7 )\r\n\r\n## R code 11.52\r\ny_all <- c( y , y_new )\r\nexposure <- c( rep(1,30) , rep(7,4) )\r\nmonastery <- c( rep(0,30) , rep(1,4) )\r\nd <- data.frame( y=y_all , days=exposure , monastery=monastery )\r\n\r\n## R code 11.53\r\n# compute the offset\r\nd$log_days <- log( d$days )\r\n\r\n# fit the model\r\nm11.12 <- quap(\r\n alist(\r\n y ~ dpois( lambda ),\r\n log(lambda) <- log_days + a + b*monastery,\r\n a ~ dnorm( 0 , 1 ),\r\n b ~ dnorm( 0 , 1 )\r\n ), data=d )\r\n\r\n## R code 11.54\r\npost <- extract.samples( m11.12 )\r\nlambda_old <- exp( post$a )\r\nlambda_new <- exp( post$a + post$b )\r\nprecis( data.frame( lambda_old , lambda_new ) )\r\n\r\n## R code 11.55\r\n# simulate career choices among 500 individuals\r\nN <- 500 # number of individuals\r\nincome <- c(1,2,5) # expected income of each career\r\nscore <- 0.5*income # scores for each career, based on income\r\n# next line converts scores to probabilities\r\np <- softmax(score[1],score[2],score[3])\r\n\r\n# now simulate choice\r\n# outcome career holds event type values, not counts\r\ncareer <- rep(NA,N) # empty vector of choices for each individual\r\n# sample chosen career for each individual\r\nset.seed(34302)\r\nfor ( i in 1:N ) career[i] <- sample( 1:3 , size=1 , prob=p )\r\n\r\n## R code 11.56\r\ncode_m11.13 <- \"\r\ndata{\r\n int N; // number of individuals\r\n int K; // number of possible careers\r\n int career[N]; // outcome\r\n vector[K] career_income;\r\n}\r\nparameters{\r\n vector[K-1] a; // intercepts\r\n real b; // association of income with choice\r\n}\r\nmodel{\r\n vector[K] p;\r\n vector[K] s;\r\n a ~ normal( 0 , 1 );\r\n b ~ normal( 0 , 0.5 );\r\n s[1] = a[1] + b*career_income[1];\r\n s[2] = a[2] + b*career_income[2];\r\n s[3] = 0; // pivot\r\n p = softmax( s );\r\n career ~ categorical( p );\r\n}\r\n\"\r\n\r\n## R code 11.57\r\ndat_list <- list( N=N , K=3 , career=career , career_income=income )\r\nm11.13 <- stan( model_code=code_m11.13 , data=dat_list , chains=4 )\r\nprecis( m11.13 , 2 )\r\n\r\n## R code 11.58\r\npost <- extract.samples( m11.13 )\r\n\r\n# set up logit scores\r\ns1 <- with( post , a[,1] + b*income[1] )\r\ns2_orig <- with( post , a[,2] + b*income[2] )\r\ns2_new <- with( post , a[,2] + b*income[2]*2 )\r\n\r\n# compute probabilities for original and counterfactual\r\np_orig <- sapply( 1:length(post$b) , function(i)\r\n softmax( c(s1[i],s2_orig[i],0) ) )\r\np_new <- sapply( 1:length(post$b) , function(i)\r\n softmax( c(s1[i],s2_new[i],0) ) )\r\n\r\n# summarize\r\np_diff <- p_new[2,] - p_orig[2,]\r\nprecis( p_diff )\r\n\r\n## R code 11.59\r\nN <- 500\r\n# simulate family incomes for each individual\r\nfamily_income <- runif(N)\r\n# assign a unique coefficient for each type of event\r\nb <- c(-2,0,2)\r\ncareer <- rep(NA,N) # empty vector of choices for each individual\r\nfor ( i in 1:N ) {\r\n score <- 0.5*(1:3) + b*family_income[i]\r\n p <- softmax(score[1],score[2],score[3])\r\n career[i] <- sample( 1:3 , size=1 , prob=p )\r\n}\r\n\r\ncode_m11.14 <- \"\r\ndata{\r\n int N; // number of observations\r\n int K; // number of outcome values\r\n int career[N]; // outcome\r\n real family_income[N];\r\n}\r\nparameters{\r\n vector[K-1] a; // intercepts\r\n vector[K-1] b; // coefficients on family income\r\n}\r\nmodel{\r\n vector[K] p;\r\n vector[K] s;\r\n a ~ normal(0,1.5);\r\n b ~ normal(0,1);\r\n for ( i in 1:N ) {\r\n for ( j in 1:(K-1) ) s[j] = a[j] + b[j]*family_income[i];\r\n s[K] = 0; // the pivot\r\n p = softmax( s );\r\n career[i] ~ categorical( p );\r\n }\r\n}\r\n\"\r\n\r\ndat_list <- list( N=N , K=3 , career=career , family_income=family_income )\r\nm11.14 <- stan( model_code=code_m11.14 , data=dat_list , chains=4 )\r\nprecis( m11.14 , 2 )\r\n\r\n## R code 11.60\r\nlibrary(rethinking)\r\ndata(UCBadmit)\r\nd <- UCBadmit\r\n\r\n## R code 11.61\r\n# binomial model of overall admission probability\r\nm_binom <- quap(\r\n alist(\r\n admit ~ dbinom(applications,p),\r\n logit(p) <- a,\r\n a ~ dnorm( 0 , 1.5 )\r\n ), data=d )\r\n\r\n# Poisson model of overall admission rate and rejection rate\r\n# 'reject' is a reserved word in Stan, cannot use as variable name\r\ndat <- list( admit=d$admit , rej=d$reject )\r\nm_pois <- ulam(\r\n alist(\r\n admit ~ dpois(lambda1),\r\n rej ~ dpois(lambda2),\r\n log(lambda1) <- a1,\r\n log(lambda2) <- a2,\r\n c(a1,a2) ~ dnorm(0,1.5)\r\n ), data=dat , chains=3 , cores=3 )\r\n\r\n## R code 11.62\r\ninv_logit(coef(m_binom))\r\n\r\n## R code 11.63\r\nk <- coef(m_pois)\r\na1 <- k['a1']; a2 <- k['a2']\r\nexp(a1)/(exp(a1)+exp(a2))\r\n\r\n## R code 12.1\r\npbar <- 0.5\r\ntheta <- 5\r\ncurve( dbeta2(x,pbar,theta) , from=0 , to=1 ,\r\n xlab=\"probability\" , ylab=\"Density\" )\r\n\r\n## R code 12.2\r\nlibrary(rethinking)\r\ndata(UCBadmit)\r\nd <- UCBadmit\r\nd$gid <- ifelse( d$applicant.gender==\"male\" , 1L , 2L )\r\ndat <- list( A=d$admit , N=d$applications , gid=d$gid )\r\nm12.1 <- ulam(\r\n alist(\r\n A ~ dbetabinom( N , pbar , theta ),\r\n logit(pbar) <- a[gid],\r\n a[gid] ~ dnorm( 0 , 1.5 ),\r\n transpars> theta <<- phi + 2.0,\r\n phi ~ dexp(1)\r\n ), data=dat , chains=4 )\r\n\r\n## R code 12.3\r\npost <- extract.samples( m12.1 )\r\npost$da <- post$a[,1] - post$a[,2]\r\nprecis( post , depth=2 )\r\n\r\n## R code 12.4\r\ngid <- 2\r\n# draw posterior mean beta distribution\r\ncurve( dbeta2(x,mean(logistic(post$a[,gid])),mean(post$theta)) , from=0 , to=1 ,\r\n ylab=\"Density\" , xlab=\"probability admit\", ylim=c(0,3) , lwd=2 )\r\n\r\n# draw 50 beta distributions sampled from posterior\r\nfor ( i in 1:50 ) {\r\n p <- logistic( post$a[i,gid] )\r\n theta <- post$theta[i]\r\n curve( dbeta2(x,p,theta) , add=TRUE , col=col.alpha(\"black\",0.2) )\r\n}\r\nmtext( \"distribution of female admission rates\" )\r\n\r\n## R code 12.5\r\npostcheck( m12.1 )\r\n\r\n## R code 12.6\r\nlibrary(rethinking)\r\ndata(Kline)\r\nd <- Kline\r\nd$P <- standardize( log(d$population) )\r\nd$contact_id <- ifelse( d$contact==\"high\" , 2L , 1L )\r\n\r\ndat2 <- list(\r\n T = d$total_tools,\r\n P = d$population,\r\n cid = d$contact_id )\r\n\r\nm12.2 <- ulam(\r\n alist(\r\n T ~ dgampois( lambda , phi ),\r\n lambda <- exp(a[cid])*P^b[cid] / g,\r\n a[cid] ~ dnorm(1,1),\r\n b[cid] ~ dexp(1),\r\n g ~ dexp(1),\r\n phi ~ dexp(1)\r\n ), data=dat2 , chains=4 , log_lik=TRUE )\r\n\r\n## R code 12.7\r\n# define parameters\r\nprob_drink <- 0.2 # 20% of days\r\nrate_work <- 1 # average 1 manuscript per day\r\n\r\n# sample one year of production\r\nN <- 365\r\n\r\n# simulate days monks drink\r\nset.seed(365)\r\ndrink <- rbinom( N , 1 , prob_drink )\r\n\r\n# simulate manuscripts completed\r\ny <- (1-drink)*rpois( N , rate_work )\r\n\r\n## R code 12.8\r\nsimplehist( y , xlab=\"manuscripts completed\" , lwd=4 )\r\nzeros_drink <- sum(drink)\r\nzeros_work <- sum(y==0 & drink==0)\r\nzeros_total <- sum(y==0)\r\nlines( c(0,0) , c(zeros_work,zeros_total) , lwd=4 , col=rangi2 )\r\n\r\n## R code 12.9\r\nm12.3 <- ulam(\r\n alist(\r\n y ~ dzipois( p , lambda ),\r\n logit(p) <- ap,\r\n log(lambda) <- al,\r\n ap ~ dnorm( -1.5 , 1 ),\r\n al ~ dnorm( 1 , 0.5 )\r\n ) , data=list(y=y) , chains=4 )\r\nprecis( m12.3 )\r\n\r\n## R code 12.10\r\npost <- extract.samples( m12.3 )\r\nmean( inv_logit( post$ap ) ) # probability drink\r\nmean( exp( post$al ) ) # rate finish manuscripts, when not drinking\r\n\r\n## R code 12.11\r\nm12.3_alt <- ulam(\r\n alist(\r\n y|y>0 ~ custom( log1m(p) + poisson_lpmf(y|lambda) ),\r\n y|y==0 ~ custom( log_mix( p , 0 , poisson_lpmf(0|lambda) ) ),\r\n logit(p) <- ap,\r\n log(lambda) <- al,\r\n ap ~ dnorm(-1.5,1),\r\n al ~ dnorm(1,0.5)\r\n ) , data=list(y=as.integer(y)) , chains=4 )\r\n\r\n## R code 12.12\r\nlibrary(rethinking)\r\ndata(Trolley)\r\nd <- Trolley\r\n\r\n## R code 12.13\r\nsimplehist( d$response , xlim=c(1,7) , xlab=\"response\" )\r\n\r\n## R code 12.14\r\n# discrete proportion of each response value\r\npr_k <- table( d$response ) / nrow(d)\r\n\r\n# cumsum converts to cumulative proportions\r\ncum_pr_k <- cumsum( pr_k )\r\n\r\n# plot\r\nplot( 1:7 , cum_pr_k , type=\"b\" , xlab=\"response\" ,\r\nylab=\"cumulative proportion\" , ylim=c(0,1) )\r\n\r\n## R code 12.15\r\nlogit <- function(x) log(x/(1-x)) # convenience function\r\nround( lco <- logit( cum_pr_k ) , 2 )\r\n\r\n## R code 12.16\r\nm12.4 <- ulam(\r\n alist(\r\n R ~ dordlogit( 0 , cutpoints ),\r\n cutpoints ~ dnorm( 0 , 1.5 )\r\n ) , data=list( R=d$response ), chains=4 , cores=4 )\r\n\r\n## R code 12.17\r\nm12.4q <- quap(\r\n alist(\r\n response ~ dordlogit( 0 , c(a1,a2,a3,a4,a5,a6) ),\r\n c(a1,a2,a3,a4,a5,a6) ~ dnorm( 0 , 1.5 )\r\n ) , data=d , start=list(a1=-2,a2=-1,a3=0,a4=1,a5=2,a6=2.5) )\r\n\r\n## R code 12.18\r\nprecis( m12.4 , depth=2 )\r\n\r\n## R code 12.19\r\nround( inv_logit(coef(m12.4)) , 3 )\r\n\r\n## R code 12.20\r\nround( pk <- dordlogit( 1:7 , 0 , coef(m12.4) ) , 2 )\r\n\r\n## R code 12.21\r\nsum( pk*(1:7) )\r\n\r\n## R code 12.22\r\nround( pk <- dordlogit( 1:7 , 0 , coef(m12.4)-0.5 ) , 2 )\r\n\r\n## R code 12.23\r\nsum( pk*(1:7) )\r\n\r\n## R code 12.24\r\ndat <- list(\r\n R = d$response,\r\n A = d$action,\r\n I = d$intention,\r\n C = d$contact )\r\nm12.5 <- ulam(\r\n alist(\r\n R ~ dordlogit( phi , cutpoints ),\r\n phi <- bA*A + bC*C + BI*I ,\r\n BI <- bI + bIA*A + bIC*C ,\r\n c(bA,bI,bC,bIA,bIC) ~ dnorm( 0 , 0.5 ),\r\n cutpoints ~ dnorm( 0 , 1.5 )\r\n ) , data=dat , chains=4 , cores=4 )\r\nprecis( m12.5 )\r\n\r\n## R code 12.25\r\nplot( precis(m12.5) , xlim=c(-1.4,0) )\r\n\r\n## R code 12.26\r\nplot( NULL , type=\"n\" , xlab=\"intention\" , ylab=\"probability\" ,\r\n xlim=c(0,1) , ylim=c(0,1) , xaxp=c(0,1,1) , yaxp=c(0,1,2) )\r\n\r\n## R code 12.27\r\nkA <- 0 # value for action\r\nkC <- 0 # value for contact\r\nkI <- 0:1 # values of intention to calculate over\r\npdat <- data.frame(A=kA,C=kC,I=kI)\r\nphi <- link( m12.5 , data=pdat )$phi\r\n\r\n## R code 12.28\r\npost <- extract.samples( m12.5 )\r\nfor ( s in 1:50 ) {\r\n pk <- pordlogit( 1:6 , phi[s,] , post$cutpoints[s,] )\r\n for ( i in 1:6 ) lines( kI , pk[,i] , col=grau(0.1) )\r\n}\r\n\r\n## R code 12.29\r\nkA <- 0 # value for action\r\nkC <- 1 # value for contact\r\nkI <- 0:1 # values of intention to calculate over\r\npdat <- data.frame(A=kA,C=kC,I=kI)\r\ns <- sim( m12.5 , data=pdat )\r\nsimplehist( s , xlab=\"response\" )\r\n\r\n## R code 12.30\r\nlibrary(rethinking)\r\ndata(Trolley)\r\nd <- Trolley\r\nlevels(d$edu)\r\n\r\n## R code 12.31\r\nedu_levels <- c( 6 , 1 , 8 , 4 , 7 , 2 , 5 , 3 )\r\nd$edu_new <- edu_levels[ d$edu ]\r\n\r\n## R code 12.32\r\nlibrary(gtools)\r\nset.seed(1805)\r\ndelta <- rdirichlet( 10 , alpha=rep(2,7) )\r\nstr(delta)\r\n\r\n## R code 12.33\r\nh <- 3\r\nplot( NULL , xlim=c(1,7) , ylim=c(0,0.4) , xlab=\"index\" , ylab=\"probability\" )\r\nfor ( i in 1:nrow(delta) ) lines( 1:7 , delta[i,] , type=\"b\" ,\r\n pch=ifelse(i==h,16,1) , lwd=ifelse(i==h,4,1.5) ,\r\n col=ifelse(i==h,\"black\",col.alpha(\"black\",0.7)) )\r\n\r\n## R code 12.34\r\ndat <- list(\r\n R = d$response ,\r\n action = d$action,\r\n intention = d$intention,\r\n contact = d$contact,\r\n E = as.integer( d$edu_new ), # edu_new as an index\r\n alpha = rep( 2 , 7 ) ) # delta prior\r\n\r\nm12.6 <- ulam(\r\n alist(\r\n R ~ ordered_logistic( phi , kappa ),\r\n phi <- bE*sum( delta_j[1:E] ) + bA*action + bI*intention + bC*contact,\r\n kappa ~ normal( 0 , 1.5 ),\r\n c(bA,bI,bC,bE) ~ normal( 0 , 1 ),\r\n vector[8]: delta_j <<- append_row( 0 , delta ),\r\n simplex[7]: delta ~ dirichlet( alpha )\r\n ), data=dat , chains=4 , cores=4 )\r\n\r\n## R code 12.35\r\nprecis( m12.6 , depth=2 , omit=\"kappa\" )\r\n\r\n## R code 12.36\r\ndelta_labels <- c(\"Elem\",\"MidSch\",\"SHS\",\"HSG\",\"SCol\",\"Bach\",\"Mast\",\"Grad\")\r\npairs( m12.6 , pars=\"delta\" , labels=delta_labels )\r\n\r\n## R code 12.37\r\ndat$edu_norm <- normalize( d$edu_new )\r\nm12.7 <- ulam(\r\n alist(\r\n R ~ ordered_logistic( mu , cutpoints ),\r\n mu <- bE*edu_norm + bA*action + bI*intention + bC*contact,\r\n c(bA,bI,bC,bE) ~ normal( 0 , 1 ),\r\n cutpoints ~ normal( 0 , 1.5 )\r\n ), data=dat , chains=4 , cores=4 )\r\nprecis( m12.7 )\r\n\r\n## R code 12.38\r\nlibrary(rethinking)\r\ndata(Hurricanes)\r\n\r\n## R code 13.1\r\nlibrary(rethinking)\r\ndata(reedfrogs)\r\nd <- reedfrogs\r\nstr(d)\r\n\r\n## R code 13.2\r\n# make the tank cluster variable\r\nd$tank <- 1:nrow(d)\r\n\r\ndat <- list(\r\n S = d$surv,\r\n N = d$density,\r\n tank = d$tank )\r\n\r\n# approximate posterior\r\nm13.1 <- ulam(\r\n alist(\r\n S ~ dbinom( N , p ) ,\r\n logit(p) <- a[tank] ,\r\n a[tank] ~ dnorm( 0 , 1.5 )\r\n ), data=dat , chains=4 , log_lik=TRUE )\r\n\r\n## R code 13.3\r\nm13.2 <- ulam(\r\n alist(\r\n S ~ dbinom( N , p ) ,\r\n logit(p) <- a[tank] ,\r\n a[tank] ~ dnorm( a_bar , sigma ) ,\r\n a_bar ~ dnorm( 0 , 1.5 ) ,\r\n sigma ~ dexp( 1 )\r\n ), data=dat , chains=4 , log_lik=TRUE )\r\n\r\n## R code 13.4\r\ncompare( m13.1 , m13.2 )\r\n\r\n## R code 13.5\r\n# extract Stan samples\r\npost <- extract.samples(m13.2)\r\n\r\n# compute mean intercept for each tank\r\n# also transform to probability with logistic\r\nd$propsurv.est <- logistic( apply( post$a , 2 , mean ) )\r\n\r\n# display raw proportions surviving in each tank\r\nplot( d$propsurv , ylim=c(0,1) , pch=16 , xaxt=\"n\" ,\r\n xlab=\"tank\" , ylab=\"proportion survival\" , col=rangi2 )\r\naxis( 1 , at=c(1,16,32,48) , labels=c(1,16,32,48) )\r\n\r\n# overlay posterior means\r\npoints( d$propsurv.est )\r\n\r\n# mark posterior mean probability across tanks\r\nabline( h=mean(inv_logit(post$a_bar)) , lty=2 )\r\n\r\n# draw vertical dividers between tank densities\r\nabline( v=16.5 , lwd=0.5 )\r\nabline( v=32.5 , lwd=0.5 )\r\ntext( 8 , 0 , \"small tanks\" )\r\ntext( 16+8 , 0 , \"medium tanks\" )\r\ntext( 32+8 , 0 , \"large tanks\" )\r\n\r\n## R code 13.6\r\n# show first 100 populations in the posterior\r\nplot( NULL , xlim=c(-3,4) , ylim=c(0,0.35) ,\r\n xlab=\"log-odds survive\" , ylab=\"Density\" )\r\nfor ( i in 1:100 )\r\n curve( dnorm(x,post$a_bar[i],post$sigma[i]) , add=TRUE ,\r\n col=col.alpha(\"black\",0.2) )\r\n\r\n# sample 8000 imaginary tanks from the posterior distribution\r\nsim_tanks <- rnorm( 8000 , post$a_bar , post$sigma )\r\n\r\n# transform to probability and visualize\r\ndens( inv_logit(sim_tanks) , lwd=2 , adj=0.1 )\r\n\r\n## R code 13.7\r\na_bar <- 1.5\r\nsigma <- 1.5\r\nnponds <- 60\r\nNi <- as.integer( rep( c(5,10,25,35) , each=15 ) )\r\n\r\n## R code 13.8\r\nset.seed(5005)\r\na_pond <- rnorm( nponds , mean=a_bar , sd=sigma )\r\n\r\n## R code 13.9\r\ndsim <- data.frame( pond=1:nponds , Ni=Ni , true_a=a_pond )\r\n\r\n## R code 13.10\r\nclass(1:3)\r\nclass(c(1,2,3))\r\n\r\n## R code 13.11\r\ndsim$Si <- rbinom( nponds , prob=logistic(dsim$true_a) , size=dsim$Ni )\r\n\r\n## R code 13.12\r\ndsim$p_nopool <- dsim$Si / dsim$Ni\r\n\r\n## R code 13.13\r\ndat <- list( Si=dsim$Si , Ni=dsim$Ni , pond=dsim$pond )\r\nm13.3 <- ulam(\r\n alist(\r\n Si ~ dbinom( Ni , p ),\r\n logit(p) <- a_pond[pond],\r\n a_pond[pond] ~ dnorm( a_bar , sigma ),\r\n a_bar ~ dnorm( 0 , 1.5 ),\r\n sigma ~ dexp( 1 )\r\n ), data=dat , chains=4 )\r\n\r\n## R code 13.14\r\nprecis( m13.3 , depth=2 )\r\n\r\n## R code 13.15\r\npost <- extract.samples( m13.3 )\r\ndsim$p_partpool <- apply( inv_logit(post$a_pond) , 2 , mean )\r\n\r\n## R code 13.16\r\ndsim$p_true <- inv_logit( dsim$true_a )\r\n\r\n## R code 13.17\r\nnopool_error <- abs( dsim$p_nopool - dsim$p_true )\r\npartpool_error <- abs( dsim$p_partpool - dsim$p_true )\r\n\r\n## R code 13.18\r\nplot( 1:60 , nopool_error , xlab=\"pond\" , ylab=\"absolute error\" ,\r\n col=rangi2 , pch=16 )\r\npoints( 1:60 , partpool_error )\r\n\r\n## R code 13.19\r\nnopool_avg <- aggregate(nopool_error,list(dsim$Ni),mean)\r\npartpool_avg <- aggregate(partpool_error,list(dsim$Ni),mean)\r\n\r\n## R code 13.20\r\na <- 1.5\r\nsigma <- 1.5\r\nnponds <- 60\r\nNi <- as.integer( rep( c(5,10,25,35) , each=15 ) )\r\na_pond <- rnorm( nponds , mean=a , sd=sigma )\r\ndsim <- data.frame( pond=1:nponds , Ni=Ni , true_a=a_pond )\r\ndsim$Si <- rbinom( nponds,prob=inv_logit( dsim$true_a ),size=dsim$Ni )\r\ndsim$p_nopool <- dsim$Si / dsim$Ni\r\nnewdat <- list(Si=dsim$Si,Ni=dsim$Ni,pond=1:nponds)\r\nm13.3new <- stan( fit=m13.3@stanfit , data=newdat , chains=4 )\r\n\r\npost <- extract.samples( m13.3new )\r\ndsim$p_partpool <- apply( inv_logit(post$a_pond) , 2 , mean )\r\ndsim$p_true <- inv_logit( dsim$true_a )\r\nnopool_error <- abs( dsim$p_nopool - dsim$p_true )\r\npartpool_error <- abs( dsim$p_partpool - dsim$p_true )\r\nplot( 1:60 , nopool_error , xlab=\"pond\" , ylab=\"absolute error\" , col=rangi2 , pch=16 )\r\npoints( 1:60 , partpool_error )\r\n\r\n## R code 13.21\r\nlibrary(rethinking)\r\ndata(chimpanzees)\r\nd <- chimpanzees\r\nd$treatment <- 1 + d$prosoc_left + 2*d$condition\r\n\r\ndat_list <- list(\r\n pulled_left = d$pulled_left,\r\n actor = d$actor,\r\n block_id = d$block,\r\n treatment = as.integer(d$treatment) )\r\n\r\nset.seed(13)\r\nm13.4 <- ulam(\r\n alist(\r\n pulled_left ~ dbinom( 1 , p ) ,\r\n logit(p) <- a[actor] + g[block_id] + b[treatment] ,\r\n b[treatment] ~ dnorm( 0 , 0.5 ),\r\n ## adaptive priors\r\n a[actor] ~ dnorm( a_bar , sigma_a ),\r\n g[block_id] ~ dnorm( 0 , sigma_g ),\r\n ## hyper-priors\r\n a_bar ~ dnorm( 0 , 1.5 ),\r\n sigma_a ~ dexp(1),\r\n sigma_g ~ dexp(1)\r\n ) , data=dat_list , chains=4 , cores=4 , log_lik=TRUE )\r\n\r\n## R code 13.22\r\nprecis( m13.4 , depth=2 )\r\nplot( precis(m13.4,depth=2) ) # also plot\r\n\r\n## R code 13.23\r\nset.seed(14)\r\nm13.5 <- ulam(\r\n alist(\r\n pulled_left ~ dbinom( 1 , p ) ,\r\n logit(p) <- a[actor] + b[treatment] ,\r\n b[treatment] ~ dnorm( 0 , 0.5 ),\r\n a[actor] ~ dnorm( a_bar , sigma_a ),\r\n a_bar ~ dnorm( 0 , 1.5 ),\r\n sigma_a ~ dexp(1)\r\n ) , data=dat_list , chains=4 , cores=4 , log_lik=TRUE )\r\n\r\n## R code 13.24\r\ncompare( m13.4 , m13.5 )\r\n\r\n## R code 13.25\r\nset.seed(15)\r\nm13.6 <- ulam(\r\n alist(\r\n pulled_left ~ dbinom( 1 , p ) ,\r\n logit(p) <- a[actor] + g[block_id] + b[treatment] ,\r\n b[treatment] ~ dnorm( 0 , sigma_b ),\r\n a[actor] ~ dnorm( a_bar , sigma_a ),\r\n g[block_id] ~ dnorm( 0 , sigma_g ),\r\n a_bar ~ dnorm( 0 , 1.5 ),\r\n sigma_a ~ dexp(1),\r\n sigma_g ~ dexp(1),\r\n sigma_b ~ dexp(1)\r\n ) , data=dat_list , chains=4 , cores=4 , log_lik=TRUE )\r\ncoeftab( m13.4 , m13.6 )\r\n\r\n## R code 13.26\r\nm13.7 <- ulam(\r\n alist(\r\n v ~ normal(0,3),\r\n x ~ normal(0,exp(v))\r\n ), data=list(N=1) , chains=4 )\r\nprecis( m13.7 )\r\n\r\n## R code 13.27\r\nm13.7nc <- ulam(\r\n alist(\r\n v ~ normal(0,3),\r\n z ~ normal(0,1),\r\n gq> real[1]:x <<- z*exp(v)\r\n ), data=list(N=1) , chains=4 )\r\nprecis( m13.7nc )\r\n\r\n## R code 13.28\r\nset.seed(13)\r\nm13.4b <- ulam( m13.4 , chains=4 , cores=4 , control=list(adapt_delta=0.99) )\r\ndivergent(m13.4b)\r\n\r\n## R code 13.29\r\nset.seed(13)\r\nm13.4nc <- ulam(\r\n alist(\r\n pulled_left ~ dbinom( 1 , p ) ,\r\n logit(p) <- a_bar + z[actor]*sigma_a + # actor intercepts\r\n x[block_id]*sigma_g + # block intercepts\r\n b[treatment] ,\r\n b[treatment] ~ dnorm( 0 , 0.5 ),\r\n z[actor] ~ dnorm( 0 , 1 ),\r\n x[block_id] ~ dnorm( 0 , 1 ),\r\n a_bar ~ dnorm( 0 , 1.5 ),\r\n sigma_a ~ dexp(1),\r\n sigma_g ~ dexp(1),\r\n gq> vector[actor]:a <<- a_bar + z*sigma_a,\r\n gq> vector[block_id]:g <<- x*sigma_g\r\n ) , data=dat_list , chains=4 , cores=4 )\r\n\r\n## R code 13.30\r\nprecis_c <- precis( m13.4 , depth=2 )\r\nprecis_nc <- precis( m13.4nc , depth=2 )\r\npars <- c( paste(\"a[\",1:7,\"]\",sep=\"\") , paste(\"g[\",1:6,\"]\",sep=\"\") ,\r\n paste(\"b[\",1:4,\"]\",sep=\"\") , \"a_bar\" , \"sigma_a\" , \"sigma_g\" )\r\nneff_table <- cbind( precis_c[pars,\"n_eff\"] , precis_nc[pars,\"n_eff\"] )\r\nplot( neff_table , xlim=range(neff_table) , ylim=range(neff_table) ,\r\n xlab=\"n_eff (centered)\" , ylab=\"n_eff (non-centered)\" , lwd=2 )\r\nabline( a=0 , b=1 , lty=2 )\r\n\r\n## R code 13.31\r\nchimp <- 2\r\nd_pred <- list(\r\n actor = rep(chimp,4),\r\n treatment = 1:4,\r\n block_id = rep(1,4)\r\n)\r\np <- link( m13.4 , data=d_pred )\r\np_mu <- apply( p , 2 , mean )\r\np_ci <- apply( p , 2 , PI )\r\n\r\n## R code 13.32\r\npost <- extract.samples(m13.4)\r\nstr(post)\r\n\r\n## R code 13.33\r\ndens( post$a[,5] )\r\n\r\n## R code 13.34\r\np_link <- function( treatment , actor=1 , block_id=1 ) {\r\n logodds <- with( post ,\r\n a[,actor] + g[,block_id] + b[,treatment] )\r\n return( inv_logit(logodds) )\r\n}\r\n\r\n## R code 13.35\r\np_raw <- sapply( 1:4 , function(i) p_link( i , actor=2 , block_id=1 ) )\r\np_mu <- apply( p_raw , 2 , mean )\r\np_ci <- apply( p_raw , 2 , PI )\r\n\r\n## R code 13.36\r\np_link_abar <- function( treatment ) {\r\n logodds <- with( post , a_bar + b[,treatment] )\r\n return( inv_logit(logodds) )\r\n}\r\n\r\n## R code 13.37\r\npost <- extract.samples(m13.4)\r\np_raw <- sapply( 1:4 , function(i) p_link_abar( i ) )\r\np_mu <- apply( p_raw , 2 , mean )\r\np_ci <- apply( p_raw , 2 , PI )\r\n\r\nplot( NULL , xlab=\"treatment\" , ylab=\"proportion pulled left\" ,\r\n ylim=c(0,1) , xaxt=\"n\" , xlim=c(1,4) )\r\naxis( 1 , at=1:4 , labels=c(\"R/N\",\"L/N\",\"R/P\",\"L/P\") )\r\nlines( 1:4 , p_mu )\r\nshade( p_ci , 1:4 )\r\n\r\n## R code 13.38\r\na_sim <- with( post , rnorm( length(post$a_bar) , a_bar , sigma_a ) )\r\np_link_asim <- function( treatment ) {\r\n logodds <- with( post , a_sim + b[,treatment] )\r\n return( inv_logit(logodds) )\r\n}\r\np_raw_asim <- sapply( 1:4 , function(i) p_link_asim( i ) )\r\n\r\n## R code 13.39\r\nplot( NULL , xlab=\"treatment\" , ylab=\"proportion pulled left\" ,\r\n ylim=c(0,1) , xaxt=\"n\" , xlim=c(1,4) )\r\naxis( 1 , at=1:4 , labels=c(\"R/N\",\"L/N\",\"R/P\",\"L/P\") )\r\nfor ( i in 1:100 ) lines( 1:4 , p_raw_asim[i,] , col=grau(0.25) , lwd=2 )\r\n\r\n## R code 13.40\r\n## R code 13.41\r\n## R code 14.1\r\na <- 3.5 # average morning wait time\r\nb <- (-1) # average difference afternoon wait time\r\nsigma_a <- 1 # std dev in intercepts\r\nsigma_b <- 0.5 # std dev in slopes\r\nrho <- (-0.7) # correlation between intercepts and slopes\r\n\r\n## R code 14.2\r\nMu <- c( a , b )\r\n\r\n## R code 14.3\r\ncov_ab <- sigma_a*sigma_b*rho\r\nSigma <- matrix( c(sigma_a^2,cov_ab,cov_ab,sigma_b^2) , ncol=2 )\r\n\r\n## R code 14.4\r\nmatrix( c(1,2,3,4) , nrow=2 , ncol=2 )\r\n\r\n## R code 14.5\r\nsigmas <- c(sigma_a,sigma_b) # standard deviations\r\nRho <- matrix( c(1,rho,rho,1) , nrow=2 ) # correlation matrix\r\n\r\n# now matrix multiply to get covariance matrix\r\nSigma <- diag(sigmas) %*% Rho %*% diag(sigmas)\r\n\r\n## R code 14.6\r\nN_cafes <- 20\r\n\r\n## R code 14.7\r\nlibrary(MASS)\r\nset.seed(5) # used to replicate example\r\nvary_effects <- mvrnorm( N_cafes , Mu , Sigma )\r\n\r\n## R code 14.8\r\na_cafe <- vary_effects[,1]\r\nb_cafe <- vary_effects[,2]\r\n\r\nd <- tibble( a_cafe = a_cafe, b_cafe = b_cafe)\r\n\r\nplt <- d %>% \r\n ggplot( aes(b_cafe, a_cafe) ) +\r\n geom_point( color = \"blue\" ) +\r\n xlab( \"intercepts (a_cafe)\" ) + ylab( \"slopes (n_cafe)\" ) + \r\n geom_density_2d()\r\nplt\r\n\r\n## R code 14.9\r\nplot( a_cafe , b_cafe , col=rangi2 ,\r\n xlab=\"intercepts (a_cafe)\" , ylab=\"slopes (b_cafe)\" )\r\n\r\n# overlay population distribution\r\nlibrary(ellipse)\r\nfor ( l in c(0.1,0.3,0.5,0.8,0.99) )\r\n lines(ellipse(Sigma,centre=Mu,level=l),col=col.alpha(\"black\",0.2))\r\n\r\n## R code 14.10\r\nset.seed(22)\r\nN_visits <- 10\r\nafternoon <- rep(0:1,N_visits*N_cafes/2)\r\ncafe_id <- rep( 1:N_cafes , each=N_visits )\r\nmu <- a_cafe[cafe_id] + b_cafe[cafe_id]*afternoon\r\nsigma <- 0.5 # std dev within cafes\r\nwait <- rnorm( N_visits*N_cafes , mu , sigma )\r\nd <- data.frame( cafe=cafe_id , afternoon=afternoon , wait=wait )\r\n\r\nplot( cafe_id , wait , col=rangi2 ,\r\n xlab=\"cafe\" , ylab=\"wait time\" )\r\n\r\n# overlay population distribution\r\nlibrary(ellipse)\r\nfor ( l in 1:20 )\r\n lines(ellipse(Sigma,centre=mu,level=l),col=col.alpha(\"black\",0.2))\r\n\r\nplt <- d %>% \r\n ggplot( aes( cafe_id, wait, group = afternoon )) +\r\n geom_point() +\r\n geom_density_2d()\r\nplt\r\n\r\n## R code 14.11\r\nR <- rlkjcorr( 1e4 , K=2 , eta=2 )\r\ndens( R[,1,2] , xlab=\"correlation\" )\r\n\r\n## R code 14.12\r\nset.seed(867530)\r\nm14.1 <- ulam(\r\n alist(\r\n wait ~ normal( mu , sigma ),\r\n mu <- a_cafe[cafe] + b_cafe[cafe]*afternoon,\r\n c(a_cafe,b_cafe)[cafe] ~ multi_normal( c(a,b) , Rho , sigma_cafe ),\r\n a ~ normal(5,2),\r\n b ~ normal(-1,0.5),\r\n sigma_cafe ~ exponential(1),\r\n sigma ~ exponential(1),\r\n Rho ~ lkj_corr(2)\r\n ) , data=d , chains=1 )\r\n\r\n## R code 14.13\r\npost <- extract.samples(m14.1)\r\ndens( post$Rho[,1,2] , xlim=c(-1,1) ) # posterior\r\nR <- rlkjcorr( 1e4 , K=2 , eta=2 ) # prior\r\ndens( R[,1,2] , add=TRUE , lty=2 )\r\n\r\n## R code 14.14\r\n# compute unpooled estimates directly from data\r\na1 <- sapply( 1:N_cafes ,\r\n function(i) mean(wait[cafe_id==i & afternoon==0]) )\r\nb1 <- sapply( 1:N_cafes ,\r\n function(i) mean(wait[cafe_id==i & afternoon==1]) ) - a1\r\n\r\n# extract posterior means of partially pooled estimates\r\npost <- extract.samples(m14.1)\r\na2 <- apply( post$a_cafe , 2 , mean )\r\nb2 <- apply( post$b_cafe , 2 , mean )\r\n\r\n# plot both and connect with lines\r\nplot( a1 , b1 , xlab=\"intercept\" , ylab=\"slope\" ,\r\n pch=16 , col=rangi2 , ylim=c( min(b1)-0.1 , max(b1)+0.1 ) ,\r\n xlim=c( min(a1)-0.1 , max(a1)+0.1 ) )\r\npoints( a2 , b2 , pch=1 )\r\nfor ( i in 1:N_cafes ) lines( c(a1[i],a2[i]) , c(b1[i],b2[i]) )\r\n\r\n## R code 14.15\r\n# compute posterior mean bivariate Gaussian\r\nMu_est <- c( mean(post$a) , mean(post$b) )\r\nrho_est <- mean( post$Rho[,1,2] )\r\nsa_est <- mean( post$sigma_cafe[,1] )\r\nsb_est <- mean( post$sigma_cafe[,2] )\r\ncov_ab <- sa_est*sb_est*rho_est\r\nSigma_est <- matrix( c(sa_est^2,cov_ab,cov_ab,sb_est^2) , ncol=2 )\r\n\r\n# draw contours\r\nlibrary(ellipse)\r\nfor ( l in c(0.1,0.3,0.5,0.8,0.99) )\r\n lines(ellipse(Sigma_est,centre=Mu_est,level=l),\r\n col=col.alpha(\"black\",0.2))\r\n\r\n## R code 14.16\r\n# convert varying effects to waiting times\r\nwait_morning_1 <- (a1)\r\nwait_afternoon_1 <- (a1 + b1)\r\nwait_morning_2 <- (a2)\r\nwait_afternoon_2 <- (a2 + b2)\r\n\r\n# plot both and connect with lines\r\nplot( wait_morning_1 , wait_afternoon_1 , xlab=\"morning wait\" ,\r\n ylab=\"afternoon wait\" , pch=16 , col=rangi2 ,\r\n ylim=c( min(wait_afternoon_1)-0.1 , max(wait_afternoon_1)+0.1 ) ,\r\n xlim=c( min(wait_morning_1)-0.1 , max(wait_morning_1)+0.1 ) )\r\npoints( wait_morning_2 , wait_afternoon_2 , pch=1 )\r\nfor ( i in 1:N_cafes )\r\n lines( c(wait_morning_1[i],wait_morning_2[i]) ,\r\n c(wait_afternoon_1[i],wait_afternoon_2[i]) )\r\nabline( a=0 , b=1 , lty=2 )\r\n\r\n## R code 14.17\r\n# now shrinkage distribution by simulation\r\nv <- mvrnorm( 1e4 , Mu_est , Sigma_est )\r\nv[,2] <- v[,1] + v[,2] # calculate afternoon wait\r\nSigma_est2 <- cov(v)\r\nMu_est2 <- Mu_est\r\nMu_est2[2] <- Mu_est[1]+Mu_est[2]\r\n\r\n# draw contours\r\nlibrary(ellipse)\r\nfor ( l in c(0.1,0.3,0.5,0.8,0.99) )\r\n lines(ellipse(Sigma_est2,centre=Mu_est2,level=l),\r\n col=col.alpha(\"black\",0.5))\r\n\r\n## R code 14.18\r\nlibrary(rethinking)\r\ndata(chimpanzees)\r\nd <- chimpanzees\r\nd$block_id <- d$block\r\nd$treatment <- 1L + d$prosoc_left + 2L*d$condition\r\n\r\ndat <- list(\r\n L = d$pulled_left,\r\n tid = d$treatment,\r\n actor = d$actor,\r\n block_id = as.integer(d$block_id) )\r\n\r\nset.seed(4387510)\r\nm14.2 <- ulam(\r\n alist(\r\n L ~ dbinom(1,p),\r\n logit(p) <- g[tid] + alpha[actor,tid] + beta[block_id,tid],\r\n\r\n # adaptive priors\r\n vector[4]:alpha[actor] ~ multi_normal(0,Rho_actor,sigma_actor),\r\n vector[4]:beta[block_id] ~ multi_normal(0,Rho_block,sigma_block),\r\n\r\n # fixed priors\r\n g[tid] ~ dnorm(0,1),\r\n sigma_actor ~ dexp(1),\r\n Rho_actor ~ dlkjcorr(4),\r\n sigma_block ~ dexp(1),\r\n Rho_block ~ dlkjcorr(4)\r\n ) , data=dat , chains=4 , cores=4 )\r\n\r\n## R code 14.19\r\nset.seed(4387510)\r\nm14.3 <- ulam(\r\n alist(\r\n L ~ binomial(1,p),\r\n logit(p) <- g[tid] + alpha[actor,tid] + beta[block_id,tid],\r\n\r\n # adaptive priors - non-centered\r\n transpars> matrix[actor,4]:alpha <-\r\n compose_noncentered( sigma_actor , L_Rho_actor , z_actor ),\r\n transpars> matrix[block_id,4]:beta <-\r\n compose_noncentered( sigma_block , L_Rho_block , z_block ),\r\n matrix[4,actor]:z_actor ~ normal( 0 , 1 ),\r\n matrix[4,block_id]:z_block ~ normal( 0 , 1 ),\r\n\r\n # fixed priors\r\n g[tid] ~ normal(0,1),\r\n vector[4]:sigma_actor ~ dexp(1),\r\n cholesky_factor_corr[4]:L_Rho_actor ~ lkj_corr_cholesky( 2 ),\r\n vector[4]:sigma_block ~ dexp(1),\r\n cholesky_factor_corr[4]:L_Rho_block ~ lkj_corr_cholesky( 2 ),\r\n\r\n # compute ordinary correlation matrixes from Cholesky factors\r\n gq> matrix[4,4]:Rho_actor <<- Chol_to_Corr(L_Rho_actor),\r\n gq> matrix[4,4]:Rho_block <<- Chol_to_Corr(L_Rho_block)\r\n ) , data=dat , chains=4 , cores=4 , log_lik=TRUE )\r\n\r\n## R code 14.20\r\n# extract n_eff values for each model\r\nneff_nc <- precis(m14.3,3,pars=c(\"alpha\",\"beta\"))$n_eff\r\nneff_c <- precis(m14.2,3,pars=c(\"alpha\",\"beta\"))$n_eff\r\nplot( neff_c , neff_nc , xlab=\"centered (default)\" ,\r\n ylab=\"non-centered (cholesky)\" , lwd=1.5 )\r\nabline(a=0,b=1,lty=2)\r\n\r\n## R code 14.21\r\nprecis( m14.3 , depth=2 , pars=c(\"sigma_actor\",\"sigma_block\") )\r\n\r\n## R code 14.22\r\n# compute mean for each actor in each treatment\r\npl <- by( d$pulled_left , list( d$actor , d$treatment ) , mean )\r\n\r\n# generate posterior predictions using link\r\ndatp <- list(\r\n actor=rep(1:7,each=4) ,\r\n tid=rep(1:4,times=7) ,\r\n block_id=rep(5,times=4*7) )\r\np_post <- link( m14.3 , data=datp )\r\np_mu <- apply( p_post , 2 , mean )\r\np_ci <- apply( p_post , 2 , PI )\r\n\r\n# set up plot\r\nplot( NULL , xlim=c(1,28) , ylim=c(0,1) , xlab=\"\" ,\r\n ylab=\"proportion left lever\" , xaxt=\"n\" , yaxt=\"n\" )\r\naxis( 2 , at=c(0,0.5,1) , labels=c(0,0.5,1) )\r\nabline( h=0.5 , lty=2 )\r\nfor ( j in 1:7 ) abline( v=(j-1)*4+4.5 , lwd=0.5 )\r\nfor ( j in 1:7 ) text( (j-1)*4+2.5 , 1.1 , concat(\"actor \",j) , xpd=TRUE )\r\n\r\nxo <- 0.1 # offset distance to stagger raw data and predictions\r\n# raw data\r\nfor ( j in (1:7)[-2] ) {\r\n lines( (j-1)*4+c(1,3)-xo , pl[j,c(1,3)] , lwd=2 , col=rangi2 )\r\n lines( (j-1)*4+c(2,4)-xo , pl[j,c(2,4)] , lwd=2 , col=rangi2 )\r\n}\r\npoints( 1:28-xo , t(pl) , pch=16 , col=\"white\" , cex=1.7 )\r\npoints( 1:28-xo , t(pl) , pch=c(1,1,16,16) , col=rangi2 , lwd=2 )\r\n\r\nyoff <- 0.175\r\ntext( 1-xo , pl[1,1]-yoff , \"R/N\" , pos=1 , cex=0.8 )\r\ntext( 2-xo , pl[1,2]+yoff , \"L/N\" , pos=3 , cex=0.8 )\r\ntext( 3-xo , pl[1,3]-yoff , \"R/P\" , pos=1 , cex=0.8 )\r\ntext( 4-xo , pl[1,4]+yoff , \"L/P\" , pos=3 , cex=0.8 )\r\n\r\n# posterior predictions\r\nfor ( j in (1:7)[-2] ) {\r\n lines( (j-1)*4+c(1,3)+xo , p_mu[(j-1)*4+c(1,3)] , lwd=2 )\r\n lines( (j-1)*4+c(2,4)+xo , p_mu[(j-1)*4+c(2,4)] , lwd=2 )\r\n}\r\nfor ( i in 1:28 ) lines( c(i,i)+xo , p_ci[,i] , lwd=1 )\r\npoints( 1:28+xo , p_mu , pch=16 , col=\"white\" , cex=1.3 )\r\npoints( 1:28+xo , p_mu , pch=c(1,1,16,16) )\r\n\r\n## R code 14.23\r\nset.seed(73)\r\nN <- 500\r\nU_sim <- rnorm( N )\r\nQ_sim <- sample( 1:4 , size=N , replace=TRUE )\r\nE_sim <- rnorm( N , U_sim + Q_sim )\r\nW_sim <- rnorm( N , U_sim + 0*E_sim )\r\ndat_sim <- list(\r\n W=standardize(W_sim) ,\r\n E=standardize(E_sim) ,\r\n Q=standardize(Q_sim) )\r\n\r\n## R code 14.24\r\nm14.4 <- ulam(\r\n alist(\r\n W ~ dnorm( mu , sigma ),\r\n mu <- aW + bEW*E,\r\n aW ~ dnorm( 0 , 0.2 ),\r\n bEW ~ dnorm( 0 , 0.5 ),\r\n sigma ~ dexp( 1 )\r\n ) , data=dat_sim , chains=4 , cores=4 )\r\nprecis( m14.4 )\r\n\r\n## R code 14.25\r\nm14.5 <- ulam(\r\n alist(\r\n W ~ dnorm( mu , sigma ),\r\n mu <- aW + bEW*E + bQW*Q,\r\n aW ~ dnorm( 0 , 0.2 ),\r\n bEW ~ dnorm( 0 , 0.5 ),\r\n bQW ~ dnorm( 0 , 0.5 ),\r\n sigma ~ dexp( 1 )\r\n ) , data=dat_sim , chains=4 , cores=4 )\r\nprecis( m14.5 )\r\n\r\n## R code 14.26\r\nm14.6 <- ulam(\r\n alist(\r\n c(W,E) ~ multi_normal( c(muW,muE) , Rho , Sigma ),\r\n muW <- aW + bEW*E,\r\n muE <- aE + bQE*Q,\r\n c(aW,aE) ~ normal( 0 , 0.2 ),\r\n c(bEW,bQE) ~ normal( 0 , 0.5 ),\r\n Rho ~ lkj_corr( 2 ),\r\n Sigma ~ exponential( 1 )\r\n ), data=dat_sim , chains=4 , cores=4 )\r\nprecis( m14.6 , depth=3 )\r\n\r\n## R code 14.27\r\nm14.4x <- ulam( m14.4 , data=dat_sim , chains=4 , cores=4 )\r\nm14.6x <- ulam( m14.6 , data=dat_sim , chains=4 , cores=4 )\r\n\r\n## R code 14.28\r\nset.seed(73)\r\nN <- 500\r\nU_sim <- rnorm( N )\r\nQ_sim <- sample( 1:4 , size=N , replace=TRUE )\r\nE_sim <- rnorm( N , U_sim + Q_sim )\r\nW_sim <- rnorm( N , -U_sim + 0.2*E_sim )\r\ndat_sim <- list(\r\n W=standardize(W_sim) ,\r\n E=standardize(E_sim) ,\r\n Q=standardize(Q_sim) )\r\n\r\n## R code 14.29\r\nlibrary(dagitty)\r\ndagIV <- dagitty( \"dag{ Q -> E <- U -> W <- E }\" )\r\ninstrumentalVariables( dagIV , exposure=\"E\" , outcome=\"W\" )\r\n\r\n## R code 14.30\r\nlibrary(rethinking)\r\ndata(KosterLeckie)\r\n\r\n## R code 14.31\r\nkl_data <- list(\r\n N = nrow(kl_dyads),\r\n N_households = max(kl_dyads$hidB),\r\n did = kl_dyads$did,\r\n hidA = kl_dyads$hidA,\r\n hidB = kl_dyads$hidB,\r\n giftsAB = kl_dyads$giftsAB,\r\n giftsBA = kl_dyads$giftsBA\r\n)\r\n\r\nm14.7 <- ulam(\r\n alist(\r\n giftsAB ~ poisson( lambdaAB ),\r\n giftsBA ~ poisson( lambdaBA ),\r\n log(lambdaAB) <- a + gr[hidA,1] + gr[hidB,2] + d[did,1] ,\r\n log(lambdaBA) <- a + gr[hidB,1] + gr[hidA,2] + d[did,2] ,\r\n a ~ normal(0,1),\r\n\r\n ## gr matrix of varying effects\r\n vector[2]:gr[N_households] ~ multi_normal(0,Rho_gr,sigma_gr),\r\n Rho_gr ~ lkj_corr(4),\r\n sigma_gr ~ exponential(1),\r\n\r\n ## dyad effects\r\n transpars> matrix[N,2]:d <-\r\n compose_noncentered( rep_vector(sigma_d,2) , L_Rho_d , z ),\r\n matrix[2,N]:z ~ normal( 0 , 1 ),\r\n cholesky_factor_corr[2]:L_Rho_d ~ lkj_corr_cholesky( 8 ),\r\n sigma_d ~ exponential(1),\r\n\r\n ## compute correlation matrix for dyads\r\n gq> matrix[2,2]:Rho_d <<- Chol_to_Corr( L_Rho_d )\r\n ), data=kl_data , chains=4 , cores=4 , iter=2000 )\r\n\r\n## R code 14.32\r\nprecis( m14.7 , depth=3 , pars=c(\"Rho_gr\",\"sigma_gr\") )\r\n\r\n## R code 14.33\r\npost <- extract.samples( m14.7 )\r\ng <- sapply( 1:25 , function(i) post$a + post$gr[,i,1] )\r\nr <- sapply( 1:25 , function(i) post$a + post$gr[,i,2] )\r\nEg_mu <- apply( exp(g) , 2 , mean )\r\nEr_mu <- apply( exp(r) , 2 , mean )\r\n\r\n## R code 14.34\r\nplot( NULL , xlim=c(0,8.6) , ylim=c(0,8.6) , xlab=\"generalized giving\" ,\r\n ylab=\"generalized receiving\" , lwd=1.5 )\r\nabline(a=0,b=1,lty=2)\r\n\r\n# ellipses\r\nlibrary(ellipse)\r\nfor ( i in 1:25 ) {\r\n Sigma <- cov( cbind( g[,i] , r[,i] ) )\r\n Mu <- c( mean(g[,i]) , mean(r[,i]) )\r\n for ( l in c(0.5) ) {\r\n el <- ellipse( Sigma , centre=Mu , level=l )\r\n lines( exp(el) , col=col.alpha(\"black\",0.5) )\r\n }\r\n}\r\n# household means\r\npoints( Eg_mu , Er_mu , pch=21 , bg=\"white\" , lwd=1.5 )\r\n\r\n## R code 14.35\r\nprecis( m14.7 , depth=3 , pars=c(\"Rho_d\",\"sigma_d\") )\r\n\r\n## R code 14.36\r\ndy1 <- apply( post$d[,,1] , 2 , mean )\r\ndy2 <- apply( post$d[,,2] , 2 , mean )\r\nplot( dy1 , dy2 )\r\n\r\n## R code 14.37\r\n# load the distance matrix\r\nlibrary(rethinking)\r\ndata(islandsDistMatrix)\r\n\r\n# display (measured in thousands of km)\r\nDmat <- islandsDistMatrix\r\ncolnames(Dmat) <- c(\"Ml\",\"Ti\",\"SC\",\"Ya\",\"Fi\",\"Tr\",\"Ch\",\"Mn\",\"To\",\"Ha\")\r\nround(Dmat,1)\r\n\r\n## R code 14.38\r\n# linear\r\ncurve( exp(-1*x) , from=0 , to=4 , lty=2 )\r\n# squared\r\ncurve( exp(-1*x^2) , add=TRUE )\r\n\r\n## R code 14.39\r\ndata(Kline2) # load the ordinary data, now with coordinates\r\nd <- Kline2\r\nd$society <- 1:10 # index observations\r\n\r\ndat_list <- list(\r\n T = d$total_tools,\r\n P = d$population,\r\n society = d$society,\r\n Dmat=islandsDistMatrix )\r\n\r\nm14.8 <- ulam(\r\n alist(\r\n T ~ dpois(lambda),\r\n lambda <- (a*P^b/g)*exp(k[society]),\r\n vector[10]:k ~ multi_normal( 0 , SIGMA ),\r\n matrix[10,10]:SIGMA <- cov_GPL2( Dmat , etasq , rhosq , 0.01 ),\r\n c(a,b,g) ~ dexp( 1 ),\r\n etasq ~ dexp( 2 ),\r\n rhosq ~ dexp( 0.5 )\r\n ), data=dat_list , chains=4 , cores=4 , iter=2000 )\r\n\r\n## R code 14.40\r\nprecis( m14.8 , depth=3 )\r\n\r\n## R code 14.41\r\npost <- extract.samples(m14.8)\r\n\r\n# plot the posterior median covariance function\r\nplot( NULL , xlab=\"distance (thousand km)\" , ylab=\"covariance\" ,\r\n xlim=c(0,10) , ylim=c(0,2) )\r\n\r\n# compute posterior mean covariance\r\nx_seq <- seq( from=0 , to=10 , length.out=100 )\r\npmcov <- sapply( x_seq , function(x) post$etasq*exp(-post$rhosq*x^2) )\r\npmcov_mu <- apply( pmcov , 2 , mean )\r\nlines( x_seq , pmcov_mu , lwd=2 )\r\n\r\n# plot 50 functions sampled from posterior\r\nfor ( i in 1:50 )\r\n curve( post$etasq[i]*exp(-post$rhosq[i]*x^2) , add=TRUE ,\r\n col=col.alpha(\"black\",0.3) )\r\n\r\n## R code 14.42\r\n# compute posterior median covariance among societies\r\nK <- matrix(0,nrow=10,ncol=10)\r\nfor ( i in 1:10 )\r\n for ( j in 1:10 )\r\n K[i,j] <- median(post$etasq) *\r\n exp( -median(post$rhosq) * islandsDistMatrix[i,j]^2 )\r\ndiag(K) <- median(post$etasq) + 0.01\r\n\r\n## R code 14.43\r\n# convert to correlation matrix\r\nRho <- round( cov2cor(K) , 2 )\r\n# add row/col names for convenience\r\ncolnames(Rho) <- c(\"Ml\",\"Ti\",\"SC\",\"Ya\",\"Fi\",\"Tr\",\"Ch\",\"Mn\",\"To\",\"Ha\")\r\nrownames(Rho) <- colnames(Rho)\r\nRho\r\n\r\n## R code 14.44\r\n# scale point size to logpop\r\npsize <- d$logpop / max(d$logpop)\r\npsize <- exp(psize*1.5)-2\r\n\r\n# plot raw data and labels\r\nplot( d$lon2 , d$lat , xlab=\"longitude\" , ylab=\"latitude\" ,\r\n col=rangi2 , cex=psize , pch=16 , xlim=c(-50,30) )\r\nlabels <- as.character(d$culture)\r\ntext( d$lon2 , d$lat , labels=labels , cex=0.7 , pos=c(2,4,3,3,4,1,3,2,4,2) )\r\n\r\n# overlay lines shaded by Rho\r\nfor( i in 1:10 )\r\n for ( j in 1:10 )\r\n if ( i < j )\r\n lines( c( d$lon2[i],d$lon2[j] ) , c( d$lat[i],d$lat[j] ) ,\r\n lwd=2 , col=col.alpha(\"black\",Rho[i,j]^2) )\r\n\r\n## R code 14.45\r\n# compute posterior median relationship, ignoring distance\r\nlogpop.seq <- seq( from=6 , to=14 , length.out=30 )\r\nlambda <- sapply( logpop.seq , function(lp) exp( post$a + post$bp*lp ) )\r\nlambda.median <- apply( lambda , 2 , median )\r\nlambda.PI80 <- apply( lambda , 2 , PI , prob=0.8 )\r\n\r\n# plot raw data and labels\r\nplot( d$logpop , d$total_tools , col=rangi2 , cex=psize , pch=16 ,\r\n xlab=\"log population\" , ylab=\"total tools\" )\r\ntext( d$logpop , d$total_tools , labels=labels , cex=0.7 ,\r\n pos=c(4,3,4,2,2,1,4,4,4,2) )\r\n\r\n# display posterior predictions\r\nlines( logpop.seq , lambda.median , lty=2 )\r\nlines( logpop.seq , lambda.PI80[1,] , lty=2 )\r\nlines( logpop.seq , lambda.PI80[2,] , lty=2 )\r\n\r\n# overlay correlations\r\nfor( i in 1:10 )\r\n for ( j in 1:10 )\r\n if ( i < j )\r\n lines( c( d$logpop[i],d$logpop[j] ) ,\r\n c( d$total_tools[i],d$total_tools[j] ) ,\r\n lwd=2 , col=col.alpha(\"black\",Rho[i,j]^2) )\r\n\r\n## R code 14.46\r\nm14.8nc <- ulam(\r\n alist(\r\n T ~ dpois(lambda),\r\n lambda <- (a*P^b/g)*exp(k[society]),\r\n\r\n # non-centered Gaussian Process prior\r\n transpars> vector[10]: k <<- L_SIGMA * z,\r\n vector[10]: z ~ normal( 0 , 1 ),\r\n transpars> matrix[10,10]: L_SIGMA <<- cholesky_decompose( SIGMA ),\r\n transpars> matrix[10,10]: SIGMA <- cov_GPL2( Dmat , etasq , rhosq , 0.01 ),\r\n\r\n c(a,b,g) ~ dexp( 1 ),\r\n etasq ~ dexp( 2 ),\r\n rhosq ~ dexp( 0.5 )\r\n ), data=dat_list , chains=4 , cores=4 , iter=2000 )\r\n\r\n## R code 14.47\r\nlibrary(rethinking)\r\ndata(Primates301)\r\ndata(Primates301_nex)\r\n\r\n# plot it using ape package - install.packages('ape') if needed\r\nlibrary(ape)\r\nplot( ladderize(Primates301_nex) , type=\"fan\" , font=1 , no.margin=TRUE ,\r\n label.offset=1 , cex=0.5 )\r\n\r\n## R code 14.48\r\nd <- Primates301\r\nd$name <- as.character(d$name)\r\ndstan <- d[ complete.cases( d$group_size , d$body , d$brain ) , ]\r\nspp_obs <- dstan$name\r\n\r\n## R code 14.49\r\ndat_list <- list(\r\n N_spp = nrow(dstan),\r\n M = standardize(log(dstan$body)),\r\n B = standardize(log(dstan$brain)),\r\n G = standardize(log(dstan$group_size)),\r\n Imat = diag(nrow(dstan)) )\r\n\r\nm14.9 <- ulam(\r\n alist(\r\n B ~ multi_normal( mu , SIGMA ),\r\n mu <- a + bM*M + bG*G,\r\n matrix[N_spp,N_spp]: SIGMA <- Imat * sigma_sq,\r\n a ~ normal( 0 , 1 ),\r\n c(bM,bG) ~ normal( 0 , 0.5 ),\r\n sigma_sq ~ exponential( 1 )\r\n ), data=dat_list , chains=4 , cores=4 )\r\nprecis( m14.9 )\r\n\r\n## R code 14.50\r\nlibrary(ape)\r\ntree_trimmed <- keep.tip( Primates301_nex, spp_obs )\r\nRbm <- corBrownian( phy=tree_trimmed )\r\nV <- vcv(Rbm)\r\nDmat <- cophenetic( tree_trimmed )\r\nplot( Dmat , V , xlab=\"phylogenetic distance\" , ylab=\"covariance\" )\r\n\r\n## R code 14.51\r\n# put species in right order\r\ndat_list$V <- V[ spp_obs , spp_obs ]\r\n# convert to correlation matrix\r\ndat_list$R <- dat_list$V / max(V)\r\n\r\n# Brownian motion model\r\nm14.10 <- ulam(\r\n alist(\r\n B ~ multi_normal( mu , SIGMA ),\r\n mu <- a + bM*M + bG*G,\r\n matrix[N_spp,N_spp]: SIGMA <- R * sigma_sq,\r\n a ~ normal( 0 , 1 ),\r\n c(bM,bG) ~ normal( 0 , 0.5 ),\r\n sigma_sq ~ exponential( 1 )\r\n ), data=dat_list , chains=4 , cores=4 )\r\nprecis( m14.10 )\r\n\r\n## R code 14.52\r\n# add scaled and reordered distance matrix\r\ndat_list$Dmat <- Dmat[ spp_obs , spp_obs ] / max(Dmat)\r\n\r\nm14.11 <- ulam(\r\n alist(\r\n B ~ multi_normal( mu , SIGMA ),\r\n mu <- a + bM*M + bG*G,\r\n matrix[N_spp,N_spp]: SIGMA <- cov_GPL1( Dmat , etasq , rhosq , 0.01 ),\r\n a ~ normal(0,1),\r\n c(bM,bG) ~ normal(0,0.5),\r\n etasq ~ half_normal(1,0.25),\r\n rhosq ~ half_normal(3,0.25)\r\n ), data=dat_list , chains=4 , cores=4 )\r\nprecis( m14.11 )\r\n\r\n## R code 14.53\r\npost <- extract.samples(m14.11)\r\nplot( NULL , xlim=c(0,max(dat_list$Dmat)) , ylim=c(0,1.5) ,\r\n xlab=\"phylogenetic distance\" , ylab=\"covariance\" )\r\n\r\n# posterior\r\nfor ( i in 1:30 )\r\n curve( post$etasq[i]*exp(-post$rhosq[i]*x) , add=TRUE , col=rangi2 )\r\n\r\n# prior mean and 89% interval\r\neta <- abs(rnorm(1e3,1,0.25))\r\nrho <- abs(rnorm(1e3,3,0.25))\r\nd_seq <- seq(from=0,to=1,length.out=50)\r\nK <- sapply( d_seq , function(x) eta*exp(-rho*x) )\r\nlines( d_seq , colMeans(K) , lwd=2 )\r\nshade( apply(K,2,PI) , d_seq )\r\ntext( 0.5 , 0.5 , \"prior\" )\r\ntext( 0.2 , 0.1 , \"posterior\" , col=rangi2 )\r\n\r\n## R code 14.54\r\nS <- matrix( c( sa^2 , sa*sb*rho , sa*sb*rho , sb^2 ) , nrow=2 )\r\n\r\n## R code 15.1\r\n# simulate a pancake and return randomly ordered sides\r\nsim_pancake <- function() {\r\n pancake <- sample(1:3,1)\r\n sides <- matrix(c(1,1,1,0,0,0),2,3)[,pancake]\r\n sample(sides)\r\n}\r\n\r\n# sim 10,000 pancakes\r\npancakes <- replicate( 1e4 , sim_pancake() )\r\nup <- pancakes[1,]\r\ndown <- pancakes[2,]\r\n\r\n# compute proportion 1/1 (BB) out of all 1/1 and 1/0\r\nnum_11_10 <- sum( up==1 )\r\nnum_11 <- sum( up==1 & down==1 )\r\nnum_11/num_11_10\r\n\r\n## R code 15.2\r\nlibrary(rethinking)\r\ndata(WaffleDivorce)\r\nd <- WaffleDivorce\r\n\r\n# points\r\nplot( d$Divorce ~ d$MedianAgeMarriage , ylim=c(4,15) ,\r\n xlab=\"Median age marriage\" , ylab=\"Divorce rate\" )\r\n\r\n# standard errors\r\nfor ( i in 1:nrow(d) ) {\r\n ci <- d$Divorce[i] + c(-1,1)*d$Divorce.SE[i]\r\n x <- d$MedianAgeMarriage[i]\r\n lines( c(x,x) , ci )\r\n}\r\n\r\n## R code 15.3\r\ndlist <- list(\r\n D_obs = standardize( d$Divorce ),\r\n D_sd = d$Divorce.SE / sd( d$Divorce ),\r\n M = standardize( d$Marriage ),\r\n A = standardize( d$MedianAgeMarriage ),\r\n N = nrow(d)\r\n)\r\n\r\nm15.1 <- ulam(\r\n alist(\r\n D_obs ~ dnorm( D_true , D_sd ),\r\n vector[N]:D_true ~ dnorm( mu , sigma ),\r\n mu <- a + bA*A + bM*M,\r\n a ~ dnorm(0,0.2),\r\n bA ~ dnorm(0,0.5),\r\n bM ~ dnorm(0,0.5),\r\n sigma ~ dexp(1)\r\n ) , data=dlist , chains=4 , cores=4 )\r\n\r\n## R code 15.4\r\nprecis( m15.1 , depth=2 )\r\n\r\n## R code 15.5\r\ndlist <- list(\r\n D_obs = standardize( d$Divorce ),\r\n D_sd = d$Divorce.SE / sd( d$Divorce ),\r\n M_obs = standardize( d$Marriage ),\r\n M_sd = d$Marriage.SE / sd( d$Marriage ),\r\n A = standardize( d$MedianAgeMarriage ),\r\n N = nrow(d)\r\n)\r\n\r\nm15.2 <- ulam(\r\n alist(\r\n D_obs ~ dnorm( D_true , D_sd ),\r\n vector[N]:D_true ~ dnorm( mu , sigma ),\r\n mu <- a + bA*A + bM*M_true[i],\r\n M_obs ~ dnorm( M_true , M_sd ),\r\n vector[N]:M_true ~ dnorm( 0 , 1 ),\r\n a ~ dnorm(0,0.2),\r\n bA ~ dnorm(0,0.5),\r\n bM ~ dnorm(0,0.5),\r\n sigma ~ dexp( 1 )\r\n ) , data=dlist , chains=4 , cores=4 )\r\n\r\n## R code 15.6\r\npost <- extract.samples( m15.2 )\r\nD_true <- apply( post$D_true , 2 , mean )\r\nM_true <- apply( post$M_true , 2 , mean )\r\nplot( dlist$M_obs , dlist$D_obs , pch=16 , col=rangi2 ,\r\n xlab=\"marriage rate (std)\" , ylab=\"divorce rate (std)\" )\r\npoints( M_true , D_true )\r\nfor ( i in 1:nrow(d) )\r\n lines( c( dlist$M_obs[i] , M_true[i] ) , c( dlist$D_obs[i] , D_true[i] ) )\r\n\r\n## R code 15.7\r\nN <- 500\r\nA <- rnorm(N)\r\nM <- rnorm(N,-A)\r\nD <- rnorm(N,A)\r\nA_obs <- rnorm(N,A)\r\n\r\n## R code 15.8\r\nN <- 100\r\nS <- rnorm( N )\r\nH <- rbinom( N , size=10 , inv_logit(S) )\r\n\r\n## R code 15.9\r\nD <- rbern( N ) # dogs completely random\r\nHm <- H\r\nHm[D==1] <- NA\r\n\r\n## R code 15.10\r\nD <- ifelse( S > 0 , 1 , 0 )\r\nHm <- H\r\nHm[D==1] <- NA\r\n\r\n## R code 15.11\r\nset.seed(501)\r\nN <- 1000\r\nX <- rnorm(N)\r\nS <- rnorm(N)\r\nH <- rbinom( N , size=10 , inv_logit( 2 + S - 2*X ) )\r\nD <- ifelse( X > 1 , 1 , 0 )\r\nHm <- H\r\nHm[D==1] <- NA\r\n\r\n## R code 15.12\r\ndat_list <- list(\r\n H = H,\r\n S = S )\r\n\r\nm15.3 <- ulam(\r\n alist(\r\n H ~ binomial( 10 , p ),\r\n logit(p) <- a + bS*S,\r\n a ~ normal( 0 , 1 ),\r\n bS ~ normal( 0 , 0.5 )\r\n ), data=dat_list , chains=4 )\r\nprecis( m15.3 )\r\n\r\n## R code 15.13\r\ndat_list0 <- list( H = H[D==0] , S = S[D==0] )\r\n\r\nm15.4 <- ulam(\r\n alist(\r\n H ~ binomial( 10 , p ),\r\n logit(p) <- a + bS*S,\r\n a ~ normal( 0 , 1 ),\r\n bS ~ normal( 0 , 0.5 )\r\n ), data=dat_list0 , chains=4 )\r\nprecis( m15.4 )\r\n\r\n## R code 15.14\r\nD <- ifelse( abs(X) < 1 , 1 , 0 )\r\n\r\n## R code 15.15\r\nN <- 100\r\nS <- rnorm(N)\r\nH <- rbinom( N , size=10 , inv_logit(S) )\r\nD <- ifelse( H < 5 , 1 , 0 )\r\nHm <- H; Hm[D==1] <- NA\r\n\r\n## R code 15.16\r\nlibrary(rethinking)\r\ndata(milk)\r\nd <- milk\r\nd$neocortex.prop <- d$neocortex.perc / 100\r\nd$logmass <- log(d$mass)\r\ndat_list <- list(\r\n K = standardize( d$kcal.per.g ),\r\n B = standardize( d$neocortex.prop ),\r\n M = standardize( d$logmass ) )\r\n\r\n## R code 15.17\r\nm15.5 <- ulam(\r\n alist(\r\n K ~ dnorm( mu , sigma ),\r\n mu <- a + bB*B + bM*M,\r\n B ~ dnorm( nu , sigma_B ),\r\n c(a,nu) ~ dnorm( 0 , 0.5 ),\r\n c(bB,bM) ~ dnorm( 0, 0.5 ),\r\n sigma_B ~ dexp( 1 ),\r\n sigma ~ dexp( 1 )\r\n ) , data=dat_list , chains=4 , cores=4 )\r\n\r\n## R code 15.18\r\nprecis( m15.5 , depth=2 )\r\n\r\n## R code 15.19\r\nobs_idx <- which( !is.na(d$neocortex.prop) )\r\ndat_list_obs <- list(\r\n K = dat_list$K[obs_idx],\r\n B = dat_list$B[obs_idx],\r\n M = dat_list$M[obs_idx] )\r\nm15.6 <- ulam(\r\n alist(\r\n K ~ dnorm( mu , sigma ),\r\n mu <- a + bB*B + bM*M,\r\n B ~ dnorm( nu , sigma_B ),\r\n c(a,nu) ~ dnorm( 0 , 0.5 ),\r\n c(bB,bM) ~ dnorm( 0, 0.5 ),\r\n sigma_B ~ dexp( 1 ),\r\n sigma ~ dexp( 1 )\r\n ) , data=dat_list_obs , chains=4 , cores=4 )\r\nprecis( m15.6 )\r\n\r\n## R code 15.20\r\nplot( coeftab(m15.5,m15.6) , pars=c(\"bB\",\"bM\") )\r\n\r\n## R code 15.21\r\npost <- extract.samples( m15.5 )\r\nB_impute_mu <- apply( post$B_impute , 2 , mean )\r\nB_impute_ci <- apply( post$B_impute , 2 , PI )\r\n\r\n# B vs K\r\nplot( dat_list$B , dat_list$K , pch=16 , col=rangi2 ,\r\n xlab=\"neocortex percent (std)\" , ylab=\"kcal milk (std)\" )\r\nmiss_idx <- which( is.na(dat_list$B) )\r\nKi <- dat_list$K[miss_idx]\r\npoints( B_impute_mu , Ki )\r\nfor ( i in 1:12 ) lines( B_impute_ci[,i] , rep(Ki[i],2) )\r\n\r\n# M vs B\r\nplot( dat_list$M , dat_list$B , pch=16 , col=rangi2 ,\r\n ylab=\"neocortex percent (std)\" , xlab=\"log body mass (std)\" )\r\nMi <- dat_list$M[miss_idx]\r\npoints( Mi , B_impute_mu )\r\nfor ( i in 1:12 ) lines( rep(Mi[i],2) , B_impute_ci[,i] )\r\n\r\n## R code 15.22\r\nm15.7 <- ulam(\r\n alist(\r\n # K as function of B and M\r\n K ~ dnorm( mu , sigma ),\r\n mu <- a + bB*B_merge + bM*M,\r\n\r\n # M and B correlation\r\n MB ~ multi_normal( c(muM,muB) , Rho_BM , Sigma_BM ),\r\n matrix[29,2]:MB <<- append_col( M , B_merge ),\r\n\r\n # define B_merge as mix of observed and imputed values\r\n vector[29]:B_merge <- merge_missing( B , B_impute ),\r\n\r\n # priors\r\n c(a,muB,muM) ~ dnorm( 0 , 0.5 ),\r\n c(bB,bM) ~ dnorm( 0, 0.5 ),\r\n sigma ~ dexp( 1 ),\r\n Rho_BM ~ lkj_corr(2),\r\n Sigma_BM ~ dexp(1)\r\n ) , data=dat_list , chains=4 , cores=4 )\r\nprecis( m15.7 , depth=3 , pars=c(\"bM\",\"bB\",\"Rho_BM\" ) )\r\n\r\n## R code 15.23\r\nB_missidx <- which( is.na( dat_list$B ) )\r\n\r\n## R code 15.24\r\ndata(Moralizing_gods)\r\nstr(Moralizing_gods)\r\n\r\n## R code 15.25\r\ntable( Moralizing_gods$moralizing_gods , useNA=\"always\" )\r\n\r\n## R code 15.26\r\nsymbol <- ifelse( Moralizing_gods$moralizing_gods==1 , 16 , 1 )\r\nsymbol <- ifelse( is.na(Moralizing_gods$moralizing_gods) , 4 , symbol )\r\ncolor <- ifelse( is.na(Moralizing_gods$moralizing_gods) , \"black\" , rangi2 )\r\nplot( Moralizing_gods$year , Moralizing_gods$population , pch=symbol ,\r\n col=color , xlab=\"Time (year)\" , ylab=\"Population size\" , lwd=1.5 )\r\n\r\n## R code 15.27\r\nwith( Moralizing_gods ,\r\n table( gods=moralizing_gods , literacy=writing , useNA=\"always\" ) )\r\n\r\n## R code 15.28\r\nhaw <- which( Moralizing_gods$polity==\"Big Island Hawaii\" )\r\ncolumns <- c(\"year\",\"writing\",\"moralizing_gods\")\r\nt( Moralizing_gods[ haw , columns ] )\r\n\r\n## R code 15.29\r\nset.seed(9)\r\nN_houses <- 100L\r\nalpha <- 5\r\nbeta <- (-3)\r\nk <- 0.5\r\nr <- 0.2\r\ncat <- rbern( N_houses , k )\r\nnotes <- rpois( N_houses , alpha + beta*cat )\r\nR_C <- rbern( N_houses , r )\r\ncat_obs <- cat\r\ncat_obs[R_C==1] <- (-9L)\r\ndat <- list(\r\n notes = notes,\r\n cat = cat_obs,\r\n RC = R_C,\r\n N = as.integer(N_houses) )\r\n\r\n## R code 15.30\r\nm15.8 <- ulam(\r\n alist(\r\n # singing bird model\r\n ## cat known present/absent:\r\n notes|RC==0 ~ poisson( lambda ),\r\n log(lambda) <- a + b*cat,\r\n ## cat NA:\r\n notes|RC==1 ~ custom( log_sum_exp(\r\n log(k) + poisson_lpmf( notes | exp(a + b) ),\r\n log(1-k) + poisson_lpmf( notes | exp(a) )\r\n ) ),\r\n\r\n # priors\r\n a ~ normal(0,1),\r\n b ~ normal(0,0.5),\r\n\r\n # sneaking cat model\r\n cat|RC==0 ~ bernoulli(k),\r\n k ~ beta(2,2)\r\n ), data=dat , chains=4 , cores=4 )\r\n\r\n## R code 15.31\r\nm15.9 <- ulam(\r\n alist(\r\n # singing bird model\r\n notes|RC==0 ~ poisson( lambda ),\r\n notes|RC==1 ~ custom( log_sum_exp(\r\n log(k) + poisson_lpmf( notes | exp(a + b) ),\r\n log(1-k) + poisson_lpmf( notes | exp(a) )\r\n ) ),\r\n log(lambda) <- a + b*cat,\r\n a ~ normal(0,1),\r\n b ~ normal(0,0.5),\r\n\r\n # sneaking cat model\r\n cat|RC==0 ~ bernoulli(k),\r\n k ~ beta(2,2),\r\n\r\n # imputed values\r\n gq> vector[N]:PrC1 <- exp(lpC1)/(exp(lpC1)+exp(lpC0)),\r\n gq> vector[N]:lpC1 <- log(k) + poisson_lpmf( notes[i] | exp(a+b) ),\r\n gq> vector[N]:lpC0 <- log(1-k) + poisson_lpmf( notes[i] | exp(a) )\r\n ), data=dat , chains=4 , cores=4 )\r\n\r\n## R code 15.32\r\nset.seed(100)\r\nx <- c( rnorm(10) , NA )\r\ny <- c( rnorm(10,x) , 100 )\r\nd <- list(x=x,y=y)\r\n\r\n## R code 15.33\r\n## R code 15.34\r\n## R code 15.35\r\n## R code 15.36\r\n## R code 15.37\r\n## R code 15.38\r\n## R code 15.39\r\n## R code 16.1\r\nlibrary(rethinking)\r\ndata(Howell1)\r\nd <- Howell1\r\n\r\n# scale observed variables\r\nd$w <- d$weight / mean(d$weight)\r\nd$h <- d$height / mean(d$height)\r\n\r\n## R code 16.2\r\nm16.1 <- ulam(\r\n alist(\r\n w ~ dlnorm( mu , sigma ),\r\n exp(mu) <- 3.141593 * k * p^2 * h^3,\r\n p ~ beta( 2 , 18 ),\r\n k ~ exponential( 0.5 ),\r\n sigma ~ exponential( 1 )\r\n ), data=d , chains=4 , cores=4 )\r\n\r\n## R code 16.3\r\nh_seq <- seq( from=0 , to=max(d$h) , length.out=30 )\r\nw_sim <- sim( m16.1 , data=list(h=h_seq) )\r\nmu_mean <- apply( w_sim , 2 , mean )\r\nw_CI <- apply( w_sim , 2 , PI )\r\nplot( d$h , d$w , xlim=c(0,max(d$h)) , ylim=c(0,max(d$w)) , col=rangi2 ,\r\n lwd=2 , xlab=\"height (scaled)\" , ylab=\"weight (scaled)\" )\r\nlines( h_seq , mu_mean )\r\nshade( w_CI , h_seq )\r\n\r\n## R code 16.4\r\nlibrary(rethinking)\r\ndata(Boxes)\r\nprecis(Boxes)\r\n\r\n## R code 16.5\r\ntable( Boxes$y ) / length( Boxes$y )\r\n\r\n## R code 16.6\r\nset.seed(7)\r\nN <- 30 # number of children\r\n\r\n# half are random\r\n# sample from 1,2,3 at random for each\r\ny1 <- sample( 1:3 , size=N/2 , replace=TRUE )\r\n\r\n# half follow majority\r\ny2 <- rep( 2 , N/2 )\r\n\r\n# combine and shuffle y1 and y2\r\ny <- sample( c(y1,y2) )\r\n\r\n# count the 2s\r\nsum(y==2)/N\r\n\r\n## R code 16.7\r\ndata(Boxes_model)\r\ncat(Boxes_model)\r\n\r\n## R code 16.8\r\n# prep data\r\ndat_list <- list(\r\n N = nrow(Boxes),\r\n y = Boxes$y,\r\n majority_first = Boxes$majority_first )\r\n\r\n# run the sampler\r\nm16.2 <- stan( model_code=Boxes_model , data=dat_list , chains=3 , cores=3 )\r\n\r\n# show marginal posterior for p\r\np_labels <- c(\"1 Majority\",\"2 Minority\",\"3 Maverick\",\"4 Random\",\r\n \"5 Follow First\")\r\nplot( precis(m16.2,2) , labels=p_labels )\r\n\r\n## R code 16.9\r\nlibrary(rethinking)\r\ndata(Panda_nuts)\r\n\r\n## R code 16.10\r\nN <- 1e4\r\nphi <- rlnorm( N , log(1) , 0.1 )\r\nk <- rlnorm( N , log(2), 0.25 )\r\ntheta <- rlnorm( N , log(5) , 0.25 )\r\n\r\n# relative grow curve\r\nplot( NULL , xlim=c(0,1.5) , ylim=c(0,1) , xaxt=\"n\" , xlab=\"age\" ,\r\n ylab=\"body mass\" )\r\nat <- c(0,0.25,0.5,0.75,1,1.25,1.5)\r\naxis( 1 , at=at , labels=round(at*max(Panda_nuts$age)) )\r\nfor ( i in 1:20 ) curve( (1-exp(-k[i]*x)) , add=TRUE , col=grau() , lwd=1.5 )\r\n\r\n# implied rate of nut opening curve\r\nplot( NULL , xlim=c(0,1.5) , ylim=c(0,1.2) , xaxt=\"n\" , xlab=\"age\" ,\r\n ylab=\"nuts per second\" )\r\nat <- c(0,0.25,0.5,0.75,1,1.25,1.5)\r\naxis( 1 , at=at , labels=round(at*max(Panda_nuts$age)) )\r\nfor ( i in 1:20 ) curve( phi[i]*(1-exp(-k[i]*x))^theta[i] , add=TRUE ,\r\n col=grau() , lwd=1.5 )\r\n\r\n## R code 16.11\r\ndat_list <- list(\r\n n = as.integer( Panda_nuts$nuts_opened ),\r\n age = Panda_nuts$age / max(Panda_nuts$age),\r\n seconds = Panda_nuts$seconds )\r\n\r\nm16.4 <- ulam(\r\n alist(\r\n n ~ poisson( lambda ),\r\n lambda <- seconds*phi*(1-exp(-k*age))^theta,\r\n phi ~ lognormal( log(1) , 0.1 ),\r\n k ~ lognormal( log(2) , 0.25 ),\r\n theta ~ lognormal( log(5) , 0.25 )\r\n ), data=dat_list , chains=4 )\r\n\r\n## R code 16.12\r\npost <- extract.samples(m16.4)\r\nplot( NULL , xlim=c(0,1) , ylim=c(0,1.5) , xlab=\"age\" ,\r\n ylab=\"nuts per second\" , xaxt=\"n\" )\r\nat <- c(0,0.25,0.5,0.75,1,1.25,1.5)\r\naxis( 1 , at=at , labels=round(at*max(Panda_nuts$age)) )\r\n\r\n# raw data\r\npts <- dat_list$n / dat_list$seconds\r\npoint_size <- normalize( dat_list$seconds )\r\npoints( jitter(dat_list$age) , pts , col=rangi2 , lwd=2 , cex=point_size*3 )\r\n\r\n# 30 posterior curves\r\nfor ( i in 1:30 ) with( post ,\r\n curve( phi[i]*(1-exp(-k[i]*x))^theta[i] , add=TRUE , col=grau() ) )\r\n\r\n## R code 16.13\r\nlibrary(rethinking)\r\ndata(Lynx_Hare)\r\nplot( 1:21 , Lynx_Hare[,3] , ylim=c(0,90) , xlab=\"year\" ,\r\n ylab=\"thousands of pelts\" , xaxt=\"n\" , type=\"l\" , lwd=1.5 )\r\nat <- c(1,11,21)\r\naxis( 1 , at=at , labels=Lynx_Hare$Year[at] )\r\nlines( 1:21 , Lynx_Hare[,2] , lwd=1.5 , col=rangi2 )\r\npoints( 1:21 , Lynx_Hare[,3] , bg=\"black\" , col=\"white\" , pch=21 , cex=1.4 )\r\npoints( 1:21 , Lynx_Hare[,2] , bg=rangi2 , col=\"white\" , pch=21 , cex=1.4 )\r\ntext( 17 , 80 , \"Lepus\" , pos=2 )\r\ntext( 19 , 50 , \"Lynx\" , pos=2 , col=rangi2 )\r\n\r\n## R code 16.14\r\nsim_lynx_hare <- function( n_steps , init , theta , dt=0.002 ) {\r\n L <- rep(NA,n_steps)\r\n H <- rep(NA,n_steps)\r\n L[1] <- init[1]\r\n H[1] <- init[2]\r\n for ( i in 2:n_steps ) {\r\n H[i] <- H[i-1] + dt*H[i-1]*( theta[1] - theta[2]*L[i-1] )\r\n L[i] <- L[i-1] + dt*L[i-1]*( theta[3]*H[i-1] - theta[4] )\r\n }\r\n return( cbind(L,H) )\r\n}\r\n\r\n## R code 16.15\r\ntheta <- c( 0.5 , 0.05 , 0.025 , 0.5 )\r\nz <- sim_lynx_hare( 1e4 , as.numeric(Lynx_Hare[1,2:3]) , theta )\r\n\r\nplot( z[,2] , type=\"l\" , ylim=c(0,max(z[,2])) , lwd=2 , xaxt=\"n\" ,\r\n ylab=\"number (thousands)\" , xlab=\"\" )\r\nlines( z[,1] , col=rangi2 , lwd=2 )\r\nmtext( \"time\" , 1 )\r\n\r\n## R code 16.16\r\nN <- 1e4\r\nHt <- 1e4\r\np <- rbeta(N,2,18)\r\nh <- rbinom( N , size=Ht , prob=p )\r\nh <- round( h/1000 , 2 )\r\ndens( h , xlab=\"thousand of pelts\" , lwd=2 )\r\n\r\n## R code 16.17\r\ndata(Lynx_Hare_model)\r\ncat(Lynx_Hare_model)\r\n\r\n## R code 16.18\r\ndat_list <- list(\r\n N = nrow(Lynx_Hare),\r\n pelts = Lynx_Hare[,2:3] )\r\n\r\nm16.5 <- stan( model_code=Lynx_Hare_model , data=dat_list , chains=3 ,\r\n cores=3 , control=list( adapt_delta=0.95 ) )\r\n\r\n## R code 16.19\r\npost <- extract.samples(m16.5)\r\npelts <- dat_list$pelts\r\nplot( 1:21 , pelts[,2] , pch=16 , ylim=c(0,120) , xlab=\"year\" ,\r\n ylab=\"thousands of pelts\" , xaxt=\"n\" )\r\nat <- c(1,11,21)\r\naxis( 1 , at=at , labels=Lynx_Hare$Year[at] )\r\npoints( 1:21 , pelts[,1] , col=rangi2 , pch=16 )\r\n# 21 time series from posterior\r\nfor ( s in 1:21 ) {\r\n lines( 1:21 , post$pelts_pred[s,,2] , col=col.alpha(\"black\",0.2) , lwd=2 )\r\n lines( 1:21 , post$pelts_pred[s,,1] , col=col.alpha(rangi2,0.3) , lwd=2 )\r\n}\r\n# text labels\r\ntext( 17 , 90 , \"Lepus\" , pos=2 )\r\ntext( 19 , 50 , \"Lynx\" , pos=2 , col=rangi2 )\r\n\r\n## R code 16.20\r\nplot( NULL , pch=16 , xlim=c(1,21) , ylim=c(0,500) , xlab=\"year\" ,\r\n ylab=\"thousands of animals\" , xaxt=\"n\" )\r\nat <- c(1,11,21)\r\naxis( 1 , at=at , labels=Lynx_Hare$Year[at] )\r\nfor ( s in 1:21 ) {\r\n lines( 1:21 , post$pop[s,,2] , col=col.alpha(\"black\",0.2) , lwd=2 )\r\n lines( 1:21 , post$pop[s,,1] , col=col.alpha(rangi2,0.4) , lwd=2 )\r\n}\r\n\r\n## R code 16.21\r\ndata(Lynx_Hare)\r\ndat_ar1 <- list(\r\n L = Lynx_Hare$Lynx[2:21],\r\n L_lag1 = Lynx_Hare$Lynx[1:20],\r\n H = Lynx_Hare$Hare[2:21],\r\n H_lag1 = Lynx_Hare$Hare[1:20] )\r\n\r\n", "meta": {"hexsha": "c978824f37498677a51e6f8e77819738332ab4a9", "size": 124648, "ext": "r", "lang": "R", 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YES\n2. YES", "lm_q1_score": 0.8902942377652496, "lm_q2_score": 0.8856314798554445, "lm_q1q2_score": 0.7884726032988131}} {"text": "# two samples (group) t.test\nttest.fun <- function(theta, x, y) {\n # parameters\n\tmu1 <- theta[1]\n\tsd1 <- theta[2]\n\tmu2 <- theta[3]\n\tsd2 <- theta[4]\n\tnu <- theta[5]\n\n # no negative standard deviations, right?!\n\tif(sd1 <=0 | sd2 <= 0) { return(-Inf) }\n\n # priors\n sigma <- sd(c(x,y))\n log.prior <- dnorm(mu1, sd = sigma*1e3, log=T) + # mu1 ~ N(0, sd*1e3)\n dunif(sd1, min= sigma*1e-3, max=sigma*1e3, log=T) + # sd1 ~ unif(sd*1e-3, sd*1e3)\n \t\t\t\t dnorm(mu2, sd = sigma*1e3, log=T) + # mu2 ~ N(0, sd*1e3)\n dunif(sd2, min= sigma*1e-3, max=sigma*1e3, log=T) + # sd2 ~ unif(sd*1e-3, sd*1e3)\n \t\t\t\t dexp((nu-1), 1/29, log=T) # nu ~ exp(1/29) + 1\n\n # likelihood\n\tlog.like <- sum(dt({x-mu1}/sd1, df=nu, log=T) - log(sd1)) + # x ~ T(mu1, sd1, nu) ~ t({x-mu}/sd, nu)/sd\n sum(dt({y-mu2}/sd2, df=nu, log=T) - log(sd2)) # y ~ T(mu1, sd1, nu) ~ t({x-mu}/sd, nu)/sd\n\n # posterior\n\tll <- log.like + log.prior\n\n\tifelse(is.na(ll) | is.nan(ll), -Inf, ll) # deal with the missing values\n}\n\n# one sample (group) t.test\n# or two dependent (paired) t.test\nttest.1g.fun <- function(theta, x) {\n # parameters\n\tmu <- theta[1]\n\tsd <- theta[2]\n\tnu <- theta[3]\n\n # no negative standard deviations, right?!\n\tif(sd <=0) { return(-Inf) }\n\n # priors\n log.prior <- dnorm(mu, sd = sd*1e3, log=T) + # mu ~ N(0, sd*1e3)\n dunif(sd, min= sd*1e-3, max=sd*1e3, log=T) + # sd1 ~ unif(sd*1e-3, sd*1e3)\n \t\t\t\t dexp((nu-1), 1/29, log=T) # nu ~ exp(1/29) + 1\n\n # likelihood\n\tlog.like <- sum(dt({x-mu}/sd, df=nu, log=T) - log(sd)) # x ~ T(mu, sd, nu) ~ t({x-mu}/sd, nu)/sd\n\n # posterior\n\tll <- log.like + log.prior\n\n\tifelse(is.na(ll) | is.nan(ll), -Inf, ll) # deal with the missing values\n}\n\n# accuracy goes 1/sqrt(nmc),\n# therefore may appropriate round(out, int(sqrt(nmc) % 10))\nbayes.t.test <- function(x, y=NULL, nmc=20000, nbi=20000) {\n if(is.null(y)) { # one group\n out <- bayes::mcmc(ttest.1g.fun, c(mean(x), sd(x), 5), nmc, nbi, x=x)\n colnames(out) <- c(\"mu\", \"sd\", \"nu\")\n } else { # two groups\n out <- bayes::mcmc(ttest.fun, c(mean(x), sd(x), mean(y), sd(y), 5), nmc, nbi, x=x, y=y)\n colnames(out) <- c(\"mu1\", \"sd1\", \"mu2\", \"sd2\", \"nu\")\n }\n return(out)\n}\n", "meta": {"hexsha": "707a719cae8de9e46b060d73f7fa9ddc2f9210d7", "size": 2540, "ext": "r", "lang": "R", "max_stars_repo_path": "R/best.r", "max_stars_repo_name": "MikeXL/bayes", "max_stars_repo_head_hexsha": "68912c47ae5df94973e960050cdef401676d5acb", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/best.r", "max_issues_repo_name": "MikeXL/bayes", "max_issues_repo_head_hexsha": "68912c47ae5df94973e960050cdef401676d5acb", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/best.r", "max_forks_repo_name": "MikeXL/bayes", "max_forks_repo_head_hexsha": "68912c47ae5df94973e960050cdef401676d5acb", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 37.3529411765, "max_line_length": 113, "alphanum_fraction": 0.4755905512, "num_tokens": 928, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9643214470715363, "lm_q2_score": 0.8175744828610095, "lm_q1q2_score": 0.7884046084012917}} {"text": "# Example : 5 Chapter : 8.3 Page No: 437\n# Linear Algebra in Economy\nA<-matrix(c(0,1,4,0),ncol=2)\nlambda<-eigen(A)$values\nprint(\"Lambda max is \")\nprint(lambda[1])\nI<-matrix(c(1,0,0,1),ncol=2)\nA1<-solve(I-A)\nprint(A1)\n#The answers may vary due to rounding off values\n", "meta": {"hexsha": "1858f8019212c932fc102f5feb3322fcc9347020", "size": 272, "ext": "r", "lang": "R", "max_stars_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.5/Ex8.3_5.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.5/Ex8.3_5.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.5/Ex8.3_5.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 24.7272727273, "max_line_length": 48, "alphanum_fraction": 0.6727941176, "num_tokens": 102, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9273632956467158, "lm_q2_score": 0.8499711794579723, "lm_q1q2_score": 0.7882320741868714}} {"text": "expected <- function(size) {\n result <- 0\n for (i in 1:size) {\n result <- result + factorial(size) / size^i / factorial(size -i)\n }\n result\n}\n\nknuth <- function(size) {\n v <- sample(1:size, size, replace = TRUE)\n\n visit <- vector('logical',size)\n place <- 1\n visit[[1]] <- TRUE\n steps <- 0\n\n repeat {\n place <- v[[place]]\n steps <- steps + 1\n if (visit[[place]]) break\n visit[[place]] <- TRUE\n }\n steps\n}\n\ncat(\" N average analytical (error)\\n\")\ncat(\"=== ========= ============ ==========\\n\")\nfor (num in 1:20) {\n average <- mean(replicate(1e6, knuth(num)))\n analytical <- expected(num)\n error <- abs(average/analytical-1)*100\n\n cat(sprintf(\"%3d%11.4f%14.4f ( %4.4f%%)\\n\", num, round(average,4), round(analytical,4), round(error,2)))\n}\n", "meta": {"hexsha": "511b92a354fce2c1cf63ad27f5807cbefd2ddfe5", "size": 780, "ext": "r", "lang": "R", "max_stars_repo_path": "Task/Average-loop-length/R/average-loop-length.r", "max_stars_repo_name": "LaudateCorpus1/RosettaCodeData", "max_stars_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-05-05T13:42:20.000Z", "max_stars_repo_stars_event_max_datetime": "2021-05-05T13:42:20.000Z", "max_issues_repo_path": "Task/Average-loop-length/R/average-loop-length.r", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Average-loop-length/R/average-loop-length.r", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.2857142857, "max_line_length": 107, "alphanum_fraction": 0.5512820513, "num_tokens": 258, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9458012671214071, "lm_q2_score": 0.8333246035907933, "lm_q1q2_score": 0.7881594659996166}} {"text": "get_l_a0_bernoulli <- function(y0, n0, cc, dd, a_0){\n ans <- lbeta(a_0 * y0 + cc, a_0 *(n0 -y0) + dd)-lbeta(cc, dd)\n return(ans)\n}\nposterior_a0_Bernoulli_2 <- function(a_0, y0, n0, y, n, cc, dd, delta, nu, log = FALSE){\n term1 <- get_l_a0_bernoulli(y0 = y0, n0 = n0, cc = cc, dd = dd, a_0 = a_0)\n term2 <- dbeta(a_0, shape1 = delta, shape2 = nu, log = TRUE)\n term3 <- lbeta(a_0 * y0 + y + cc - 1, a_0 * (n0 - y0) + dd + (n-y) - 1)\n ans <- -term1 + term2 + term3\n if(!log) ans <- exp(ans)\n return(ans)\n}\npost_a0_2 <- function(x) {\n posterior_a0_Bernoulli_2(a_0 = x, y0 = y_0, n0 = N_0,\n y = y, n = N, cc = cc, dd = dd, nu = nu, delta = delta)\n}\npost_a0_2 <- Vectorize(post_a0_2) \npost_a0_2 <- Vectorize(post_a0_2) \ncurve(post_a0_2)\n\nK2 <- integrate(post_a0_2, 0, 1)$value\nnorm_post_a0_2 <- function(x) post_a0_2(x)/K2\nnorm_post_a0_2 <- Vectorize(norm_post_a0_2)\ncurve(norm_post_a0_2)", "meta": {"hexsha": "0683396ef563d37b4bf97b7d1d192b6d84b0d1f4", "size": 920, "ext": "r", "lang": "R", "max_stars_repo_path": "code/extra/alternative_implementation_marginal_posterior_a0_Bernoulli.r", "max_stars_repo_name": "maxbiostat/propriety_power_priors", "max_stars_repo_head_hexsha": "43a9dc7bd007d5647bc453cd8a875e82c16ad6eb", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "code/extra/alternative_implementation_marginal_posterior_a0_Bernoulli.r", "max_issues_repo_name": "maxbiostat/propriety_power_priors", "max_issues_repo_head_hexsha": "43a9dc7bd007d5647bc453cd8a875e82c16ad6eb", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 7, "max_issues_repo_issues_event_min_datetime": "2020-05-29T19:11:11.000Z", "max_issues_repo_issues_event_max_datetime": "2020-08-29T15:58:08.000Z", "max_forks_repo_path": "code/extra/alternative_implementation_marginal_posterior_a0_Bernoulli.r", "max_forks_repo_name": "maxbiostat/propriety_power_priors", "max_forks_repo_head_hexsha": "43a9dc7bd007d5647bc453cd8a875e82c16ad6eb", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 38.3333333333, "max_line_length": 88, "alphanum_fraction": 0.6119565217, "num_tokens": 402, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9458012701768145, "lm_q2_score": 0.8333245932423308, "lm_q1q2_score": 0.7881594587581737}} {"text": "#Copyright (c) 2016 Riccardo Francescato\n#data from example page 144\na = 4 # number of rows \nb = 6 # number of columns \nN = a*b \nalpha = .05\nRawData= c(90.3,89.2, 98.2, 93.9, 87.4, 97.9,92.5, 89.5, 90.6, 94.7, 87.0, 95.8,85.5, 90.8, 89.6, 86.2, 88.0, 93.4,82.5, 89.5, 85.6, 87.4, 78.9, 90.7)\ndata = matrix(RawData,# the data elements \n\tnrow=a, # number of rows \n\tncol=b, # number of columns \n\tbyrow = TRUE) # fill matrix by rows\n\nSStot = sum(data^2) - sum(data)^2/N\nSStreat = 0\nfor(i in 1:a){\n\tSStreat = SStreat + sum(data[i,])^2\n}\nSStreat = SStreat *(1/b) - sum(data)^2/N\nSSblock = 0\nfor(i in 1:b){\n\tSSblock = SSblock + sum(data[,i])^2\n}\nSSblock = SSblock *(1/a) - sum(data)^2/N\nSSerr = SStot - SStreat - SSblock\nMStreat = SStreat/(a-1)\nMSblock = SSblock/(b-1)\nMSerr = SSerr/((a-1)*(b-1))\n\nF0 <- MStreat/MSerr\nFa <- qf(alpha,df1=a-1,df2=((a-1)*(b-1)),lower.tail=F)\n\nif(F0 > Fa) print(paste0(\" reject H0 \", F0)) else print(paste0(\" Accept H0 \", F0))\ncat(paste0(\" Treatments SS: \",SStreat,\" Df: \", a-1 ,\" MS: \",MStreat, \" F0: \",F0,\n\t\t\"\\n Blocks SS: \",SSblock,\" Df: \", b-1 ,\" MS: \",MSblock,\n\t\t\"\\n Error SS: \",SSerr,\" Df: \", (a-1)*(b-1) ,\" MS: \",MSerr,\n\t\t\"\\n Total SS: \",SStot,\" Df: \", (a*b)-1))\n\n\n\ndelivery.df = data.frame(\n Treatment = c(rep(\"1\", b), rep(\"2\", b), rep(\"3\", b), rep(\"4\", b)),\n Block = c(rep(c(\"1\", \"2\", \"3\", \"4\",\"5\",\"6\"), a)),\n Data = RawData\n)\ndelivery.mod1 = lm(Data ~ Treatment+Block, data = delivery.df)\nanova(delivery.mod1)", "meta": {"hexsha": "f4545d12568c958c0eebc0ce97bd57449c3d174a", "size": 1482, "ext": "r", "lang": "R", "max_stars_repo_path": "ANOVA_Block.r", "max_stars_repo_name": "RiccardoFrancescato/DataDesignScrips", "max_stars_repo_head_hexsha": "92d19d1cd5da9fb1486d53bc97c444714a3e5aa1", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "ANOVA_Block.r", "max_issues_repo_name": "RiccardoFrancescato/DataDesignScrips", "max_issues_repo_head_hexsha": "92d19d1cd5da9fb1486d53bc97c444714a3e5aa1", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "ANOVA_Block.r", "max_forks_repo_name": "RiccardoFrancescato/DataDesignScrips", "max_forks_repo_head_hexsha": "92d19d1cd5da9fb1486d53bc97c444714a3e5aa1", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 32.2173913043, "max_line_length": 150, "alphanum_fraction": 0.5701754386, "num_tokens": 652, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9458012686491107, "lm_q2_score": 0.8333245891029457, "lm_q1q2_score": 0.788159453570065}} {"text": "rm(list = ls(all = TRUE))\n\nlibrary(ggplot2)\n\n\n# Calculate the integral from 0 to 1 of:\n\n# f(x) = sqrt(1 - x ^ 2)\n\n\n# Case 1: \n# G(x) = sqrt(1 - x ^ 2) / ((3 / 2) * (1 - x ^ 2))\n# f(x) = (3 / 2) * (1 - x ^ 2)\n\nx = seq(0, 1, by = 0.001)\n\nf = function(x) {\n (3 / 2) * (1 - x ^ 2)}\n\noptimize(f, c(-100, 100), maximum = TRUE)\n\ny1 = 1.5 * dunif(x, 0, 1)\ny2 = f(x)\ndf <- data.frame(x, y1, y2)\n\ng <- ggplot(df, aes(x)) + \n geom_line(aes(y = y1), colour = \"red\") + \n geom_line(aes(y = y2), colour = \"green\")\ng\n\nx = seq(0, 10, by = 0.1)\n\nhx = function(x) {\n ((3 / 2) * (1 - x ^ 2)) / dunif(x, 0, 1)\n }\ny1 = hx(x)\ndf <- data.frame(x, y1)\ng <- ggplot(df, aes(x)) + \n geom_line(aes(y = y1), colour = \"blue\")\ng\n\noptimize(hx, c(0, 1), maximum = TRUE)\n## hx is maxed at x = 1.5\n\nsample.x = runif(10000,0,1)\naccept = c()\nsample.accept = c()\n\n\n\nfor(i in 1:length(sample.x)){\n U = runif(1, 0, 1)\n if(dunif(sample.x[i], 0, 1) * (1.5) * U <= f(sample.x[i])) { \n accept[i] = 'Yes'\n sample.accept[i] = sample.x[i]\n } \n else {\n accept[i] = 'No'\n sample.accept[i] = 0\n }\n}\n\n\n\nt = data.frame(sample.x, \n accept = factor(accept, levels = c('Yes', 'No')),\n sample.accept)\n\nt_acc = t[accept == 'Yes',]\n\n\nG = function(x) {\n (sqrt(1 - x ^ 2)) / ((1.5) * (1 - x ^ 2))\n}\n\nn_acc = length(which(t$accept == 'Yes'))\n\nI = sum(G(t_acc$sample.accept)) / n_acc\nI\n\nff = function(x) {\n (sqrt(1 - x ^ 2))\n}\n\nIreal = integrate(ff, 0, 1)\nIreal\n\n# Variance\nS = sqrt(sum((G(t_acc$sample.accept) \n - sum(G(t_acc$sample.accept)) / n_acc) ^ 2) / (n_acc - 1))\nS\n\n\n\n# Case 2:\n# G(x) = sqrt(1 - x ^ 2) / ((5 / 4) * (1 - x ^ 4))\n# f(x) = (5 / 4) * (1 - x ^ 4)\n\n\nx = seq(0, 1, by = 0.001)\n\nf = function(x) {\n (5 / 4) * (1 - x ^ 4)\n}\n\noptimize(f, c(-100, 100), maximum = TRUE)\n## f is maxed at x = 1.25\n\ny1 = 1.25 * dunif(x, 0, 1)\ny2 = f(x)\ndf <- data.frame(x, y1, y2)\n\ng <- ggplot(df, aes(x)) + \n geom_line(aes(y = y1), colour = \"red\") + \n geom_line(aes(y = y2), colour = \"green\")\ng\n\nx = seq(0, 10, by = 0.1)\n\nhx = function(x) {\n ((5 / 4) * (1 - x ^ 4)) / dunif(x, 0, 1)\n}\n\noptimize(hx, c(0, 1), maximum = TRUE)\n## hx is maxed at x = 1.25\n\ny1 = hx(x)\ndf <- data.frame(x, y1)\ng <- ggplot(df, aes(x)) + \n geom_line(aes(y = y1), colour = \"blue\")\ng\n\nsample.x = runif(10000,0,1)\naccept = c()\nsample.accept = c()\n\n\nfor(i in 1:length(sample.x)){\n U = runif(1, 0, 1)\n if(dunif(sample.x[i], 0, 1) * (1.25) * U <= f(sample.x[i])) { \n accept[i] = 'Yes'\n sample.accept[i] = sample.x[i]\n } \n else {\n accept[i] = 'No'\n sample.accept[i] = 0\n }\n}\n\n\n\nt = data.frame(sample.x, \n accept = factor(accept, levels = c('Yes', 'No')),\n sample.accept)\n\nt_acc = t[accept == 'Yes',]\n\n\nG = function(x) {\n sqrt(1 - x ^ 2) / ((5 / 4) * (1 - x ^ 4))\n}\n\nn_acc = length(which(t$accept == 'Yes'))\n\nI = sum(G(t_acc$sample.accept)) / n_acc\nI\n\nIreal = integrate(ff, 0, 1)\nIreal\n\n# Variance\nS2 = sqrt(sum((G(t_acc$sample.accept) \n - sum(G(t_acc$sample.accept)) / n_acc) ^ 2) / (n_acc - 1))\nS2\n\n\n# Case 3:\n# G(x) = sqrt(1 - x ^ 2) / ((3 / 4) * (2 - 2 * x ^ 2))\n# f(x) = (3 / 4) * (2 - 2 * x ^ 2)\n\n\nx = seq(0, 1, by = 0.001)\n\nf = function(x) {\n (3 / 4) * (2 - 2 * x ^ 2)\n}\n\noptimize(f, c(0, 1), maximum = TRUE)\n## f is maxed at x = 1.5\n\ny1 = 1.5 * dunif(x, 0, 1)\ny2 = f(x)\ndf <- data.frame(x, y1, y2)\n\ng <- ggplot(df, aes(x)) + \n geom_line(aes(y = y1), colour = \"red\") + \n geom_line(aes(y = y2), colour = \"green\")\ng\n\nx = seq(0, 10, by = 0.1)\n\nhx = function(x) {\n ((3 / 4) * (2 - 2 * x ^ 2)) / dunif(x, 0, 1)\n}\n\noptimize(hx, c(0, 1), maximum = TRUE)\n## hx is maxed at x = 1.5\n\ny1 = hx(x)\ndf <- data.frame(x, y1)\ng <- ggplot(df, aes(x)) + \n geom_line(aes(y = y1), colour = \"blue\")\ng\n\nsample.x = runif(10000,0,1)\naccept = c()\nsample.accept = c()\n\n\nfor(i in 1:length(sample.x)){\n U = runif(1, 0, 1)\n if(dunif(sample.x[i], 0, 1) * (1.5) * U <= f(sample.x[i])) { \n accept[i] = 'Yes'\n sample.accept[i] = sample.x[i]\n } \n else {\n accept[i] = 'No'\n sample.accept[i] = 0\n }\n}\n\n\n\nt = data.frame(sample.x, \n accept = factor(accept, levels = c('Yes', 'No')),\n sample.accept)\n\nt_acc = t[accept == 'Yes',]\n\n\nG = function(x) {\n sqrt(1 - x ^ 2) / ((3 / 4) * (2 - 2 * x ^ 2))\n}\n\nn_acc = length(which(t$accept == 'Yes'))\n\nI = sum(G(t_acc$sample.accept)) / n_acc\nI\n\nIreal = integrate(ff, 0, 1)\nIreal\n\n# Variance\nS3 = sqrt(sum((G(t_acc$sample.accept) \n - sum(G(t_acc$sample.accept)) / n_acc) ^ 2) / (n_acc - 1))\nS3\n\nS ; S2 ; S3\n\n# Using the importance integration method, the best decomposition \n# of the integral function is the one used in Case 2.\n", "meta": {"hexsha": "463a32953f4506e36bcd61973b15f602e0361e04", "size": 4631, "ext": "r", "lang": "R", "max_stars_repo_path": "playground/importance-integration.r", "max_stars_repo_name": "gonz4lex/data-science-projects", "max_stars_repo_head_hexsha": "7f83fdc5ead55ea620f7599f3359d4801adb99d3", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "playground/importance-integration.r", "max_issues_repo_name": "gonz4lex/data-science-projects", "max_issues_repo_head_hexsha": "7f83fdc5ead55ea620f7599f3359d4801adb99d3", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "playground/importance-integration.r", "max_forks_repo_name": "gonz4lex/data-science-projects", "max_forks_repo_head_hexsha": "7f83fdc5ead55ea620f7599f3359d4801adb99d3", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 17.6755725191, "max_line_length": 73, "alphanum_fraction": 0.5031310732, "num_tokens": 1909, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9433475715065793, "lm_q2_score": 0.8354835350552604, "lm_q1q2_score": 0.7881513638281119}} {"text": "library(tidyverse)\n\nbernstein = function(k,n){\n return(function(x){\n choose(n,k)*x^k*(1-x)^(n-k)}\n )\n}\n\nN = 5\na = sapply(0:N,function(x) bernstein(x,N))\n\nz = sapply(a, function(f){\n t = seq(0,1,0.02)\n return(f(t))\n})\n\nzd = data.frame(t = seq(0,1,0.02),z)\ngzd = gather(zd,\"key\",\"value\",-1)\np = ggplot(data =gzd) +geom_line(aes(x = t,y = value, color = key))\nprint(p)\n\n#---just use the dbinom to get it\nt = seq(0,1,0.02)\ns = sapply(t, function(p){dbinom(0:N,N,p)})\nss = data.frame(t = t, t(s))\ngss = gather(ss,\"key\",\"value\",-1)\np = ggplot(data =gss) +geom_line(aes(x = t,y = value, color = key))\nprint(p)\n\n\n#pick N+1 random points\nN = 3\nt = seq(0,1,0.02)\ns = sapply(t, function(p){dbinom(0:N,N,p)})\n\nx = runif(N+1,max = 10)\ny = runif(N+1,max = 10)\nbx = matrix(x,ncol = N+1) %*% s\nby = matrix(y,ncol = N+1) %*% s\nplot(x,y,col = \"red\")\nlines(x,y,col = \"grey\")\nlines(bx,by)\n\n#include the lower order\nN = 5\nt = seq(0,1,0.02)\ns.list = sapply(1:N,\n function(w){\n return(sapply(t,function(p){dbinom(0:w,w,p)}))\n })\n\n#x = runif(N+1,max = 10) \nx = c(2.6122230, 8.9649724, 2.3694770, 8.1857733, 0.1079161, 6.3198825)\n#y = runif(N+1,max = 10) \ny = c(9.127837, 8.970236, 2.930961, 3.065698, 6.277990, 8.775528)\n\nbx = matrix(x,ncol = N+1) %*% s.list[[N]]\nby = matrix(y,ncol = N+1) %*% s.list[[N]]\n\nplot(x,y,col = \"red\")\nlines(x,y,col = \"grey\")\nlines(bx,by)\ncolors = c('lightblue','pink','lightgreen')\n\nfor(k in seq(3,5)){\n bxq = matrix(x[1:k],ncol = k) %*% s.list[[k-1]]\n byq = matrix(y[1:k],ncol = k) %*% s.list[[k-1]]\n lines(bxq,byq,col = colors[k-2])\n}\n\nplot(x,y,col = \"red\")\ncolors = c('grey','lightblue','pink','lightgreen','black')\n\nfor(k in seq(2,6)){\n bxq = matrix(x[1:k],ncol = k) %*% s.list[[k-1]]\n byq = matrix(y[1:k],ncol = k) %*% s.list[[k-1]]\n lines(bxq,byq,col = colors[k-1])\n}\n\n\nplot(x,y,col = \"red\")\nlines(x,y,col = \"grey\")\nlines(bx,by)\ncolors = c('lightblue','pink','lightgreen')\nfor(k in seq(2,4)){\n for(j in 1:(N+1-k)){\n bxq = matrix(x[j:(j+k)],ncol = k+1) %*% s.list[[k]]\n byq = matrix(y[j:(j+k)],ncol = k+1) %*% s.list[[k]]\n lines(bxq,byq,col = colors[k-1] )\n }\n}\n", "meta": {"hexsha": "bf3a74c14649e80e7ef32586e43db58ae8109d58", "size": 2141, "ext": "r", "lang": "R", "max_stars_repo_path": "bezier_curve.r", "max_stars_repo_name": "surecalois/random_R_stuff", "max_stars_repo_head_hexsha": "1e3dc4cf0960effb581800ceb6020488aab26ae0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "bezier_curve.r", "max_issues_repo_name": "surecalois/random_R_stuff", "max_issues_repo_head_hexsha": "1e3dc4cf0960effb581800ceb6020488aab26ae0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "bezier_curve.r", "max_forks_repo_name": "surecalois/random_R_stuff", "max_forks_repo_head_hexsha": "1e3dc4cf0960effb581800ceb6020488aab26ae0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 23.2717391304, "max_line_length": 71, "alphanum_fraction": 0.5567491826, "num_tokens": 901, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9294404018582427, "lm_q2_score": 0.8479677622198946, "lm_q1q2_score": 0.7881354976804936}} {"text": "days = seq(from = 1, to = 260)\ntype = c(1,2)\nhomeWork = rnorm(260, mean=10, sd=1.5)\nworkHome = rnorm(260, mean=10, sd=2.0)\n\nconsumption = data.frame(days, type, consumption = c(homeWork, workHome))\n#write.csv(file=\"consumption.csv\", x=consumption)\n\nconsumption = read.csv(\"consumption.csv\")\n\nhomeWork = consumption[consumption$type == 1,]\nworkHome = consumption[consumption$type == 2,]\n\npng(filename=\"homeWork.plot.png\")\n plot(homeWork$day, homeWork$consumption)\ndev.off()\n\npng(filename=\"homeWork.hist.png\")\n hist(homeWork$consumption)\ndev.off()\n\npng(filename=\"workHome.plot.png\")\n plot(workHome$day, workHome$consumption)\ndev.off()\n\npng(filename=\"workHome.hist.png\")\n hist(workHome$consumption)\ndev.off()\n\nnormal.lik<-function(mu,sigma,y){\n sigma <- max(sigma, 0.0001)\n n<-length(y)\n logl <- sum(log(dnorm(y, mean = mu, sd = sigma)))/n\n return(-logl)\n}\nnormal.lik.muvar <- function (theta,y){\n normal.lik(theta[1],theta[2],y)\n}\nv.normal.lik <- function (mu, sigma, y){\n mapply(function(m,s) normal.lik(m,s,y), mu, sigma)\n}\n\nlibrary(RColorBrewer)\nplotMLE <- function(data, x, y, steps = 20, levels = 10000) {\n x = seq(x[1], x[2], length= 20)\n y = seq(y[1], y[2], length= 20)\n f = function(x, y) {\n v.normal.lik(x,y,data)\n }\n z = outer(x, y, f)\n z[is.na(z)] = 0\n contour(x,y,z,col=rev(brewer.pal(11, \"RdYlBu\")), nlevels = levels,\n xlab=\"mean\", ylab=\"standard deviation\")\n}\n\npng(filename=\"homeWork.likelihood.png\")\n plotMLE(homeWork$consumption, x=c(5,15),y=c(0,5), levels = 2000)\ndev.off()\noptim(c(12,4),normal.lik.muvar,y=homeWork$consumption,method=\"BFGS\") \npng(filename=\"homeWork.likelihood.withlines.png\")\n plotMLE(homeWork$consumption, x=c(5,15),y=c(0,5), levels = 2000)\n abline(h=1.70105, lty=2)\n abline(v=10.01983, lty=2)\ndev.off()\n\nplotGaussian <- function(start = -1, end = 1, u, sigma, scale, color = \"black\"){\n x <- seq(start, end, length=100)\n hx <- dnorm(x, mean = u, sd = sigma)*scale\n lines(x, hx, type=\"l\", lty=2, xlab=\"x value\", ylab=\"Density\", main=\"Gaussian\", col = color)\n}\nplotArea <- function(u, sigma, sigmaSize, color){\n x <- seq(-4, 4, length=100)\n hx <- dnorm(x, mean = u, sd = sigma)\n l <- -(sigma*sigmaSize)\n r <- (sigma*sigmaSize)\n i <- x >= l & x <= r\n polygon(c(l,x[i],r), c(0,hx[i],0), col=color)\n}\n\npng(filename=\"homeWork.hist.model.png\")\n plot.new()\n hist(homeWork$consumption)\n plotGaussian(5, 15, 10, 1.7, 250, \"red\")\ndev.off()\n\n#WORK HOME\n\npng(filename=\"workHome.likelihood.png\")\n plotMLE(workHome$consumption, x=c(5,15),y=c(0,5), levels = 2000)\ndev.off()\noptim(c(12,4),normal.lik.muvar,y=workHome$consumption,method=\"BFGS\") \npng(filename=\"workHome.likelihood.withlines.png\")\n plotMLE(workHome$consumption, x=c(5,15),y=c(0,5), levels = 2000)\n abline(h=1.7274, lty=2)\n abline(v=9.87, lty=2)\ndev.off()\n\n# DAILY\n\ndays = seq(from = 1, to = 260)\ndaily = homeWork$consumption + workHome$consumption\nconsumption = data.frame(days, consumption = daily)\npng(filename=\"daily.plot.png\")\n plot(consumption$day, consumption$consumption)\ndev.off()\n\noptim(c(12,4),normal.lik.muvar,y=consumption$consumption,method=\"BFGS\") \n\npng(filename=\"daily.hist.png\")\nplot.new()\n hist(consumption$consumption)\n plotGaussian(10, 30, 19.899697, 2.421108, 270, \"red\")\ndev.off()\n\npng(filename=\"daily.hist.png\")\nplot.new()\n hist(consumption$consumption)\n plotGaussian(10, 30, 19.899697, 2.421108, 270, \"red\")\n abline(v=25, lty=2, col =\"green\")\ndev.off()\n\npnorm(25, mean = 19.899697, sd = 2.421108)\npnorm(25, mean = 19.899697, sd = 2.421108, lower.tail = FALSE)\n", "meta": {"hexsha": "91bc873764310c36e7738d934aa45dead9df665f", "size": 3513, "ext": "r", "lang": "R", "max_stars_repo_path": "texts/math/Statistics/CarOutGas/generate.data.r", "max_stars_repo_name": 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"max_forks_repo_forks_event_min_datetime": "2018-09-20T01:07:39.000Z", "max_forks_repo_forks_event_max_datetime": "2019-02-22T14:55:38.000Z", "avg_line_length": 28.3306451613, "max_line_length": 93, "alphanum_fraction": 0.6692285796, "num_tokens": 1243, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9294403959948494, "lm_q2_score": 0.8479677545357568, "lm_q1q2_score": 0.7881354855665771}} {"text": "## 1. Indexing Vectors by Position ##\n\nfinal_scores <- c(88, 87.66667, 86, 91.33333, 84, 91, 89.33333)\nstem_grades<-final_scores[1:2]\nnon_stem_grades<-final_scores[3:7]\navg_stem_grades<-mean(stem_grades)\navg_non_stem_grades<-mean(non_stem_grades)\n\n## 2. Numeric and Character Data Types ##\n\ntypeof(final_scores)\nmath_chemistry<-c('math','chemistry')\ntypeof(math_chemistry)\nclass_names<-c('math','chemistry','writing','art','history','music','physical_education')\n\n## 3. Naming Elements of a Vector ##\n\nclass_names <- c(\"math\", \"chemistry\", \"writing\", \"art\", \"history\", \"music\", \"physical_education\")\nfinal_scores <- c(88, 87.66667, 86, 91.33333, 84, 91, 89.33333)\nnames(final_scores)<-class_names\nfinal_scores\n\n## 4. Indexing Vectors Using Names ##\n\nliberal_arts<-final_scores[c('writing','history')]\nfine_arts<-final_scores[c('art','music')]\nmean(liberal_arts)\nmean(fine_arts)\n\n## 5. Comparing Values And Logical Data Types ##\n\nliberal_arts <- final_scores[c(\"writing\", \"history\")]\nfine_arts <- final_scores[c(\"art\", \"music\")]\nmean(liberal_arts)>mean(fine_arts)\n\n## 6. Comparing Single Values Against Vectors ##\n\ngpa<-mean(final_scores)\nabove_average<-final_scores>gpa\nabove_average\n\n## 7. Logical Indexing ##\n\ngpa <- mean(final_scores)\nabove_average <- (gpa < final_scores)\nbest_grades<-final_scores[above_average]\nbest_grades\n\n## 8. Performing Arithmetic with Vectors ##\n\ntests <- c(76, 89, 78, 88, 79, 93, 89)\nhomework <- c(85, 90, 88, 79, 88, 95, 74)\nprojects <- c(77, 93, 87, 90, 77, 82, 80)\njohnny_scores<-(tests+homework+projects)/3\nmean(johnny_scores)\n\n## 9. Vector Recycling ##\n\ntests <- c(76, 89, 78)\nhomework <- c(85, 90, 88, 79, 88, 95, 74)\nprojects <- c(77, 93, 87, 90, 77, 82, 80)\nrecycling<-tests+homework+projects\n\n## 10. Appending Elements To A Vector ##\n\ntests <- c(76, 89, 78)\nhomework <- c(85, 90, 88, 79, 88, 95, 74)\nprojects <- c(77, 93, 87, 90, 77, 82, 80)\n\nclass_names <- c(\"math\", \"chemistry\", \"writing\", \"art\", \"history\", \"music\", \"physical_education\")\ntests<-c(tests,89,79,93,89)\nkate_grades<-(tests+homework+projects)/3\nnames(kate_grades)<-class_names\nkate_gpa<-mean(kate_grades)\nkate_low_grades<-kate_grades[(kate_gpa>kate_grades)]\nkate_low_grades", "meta": {"hexsha": "23b6b4f71de7c861d133e36189a02296af4c1e22", "size": 2177, "ext": "r", "lang": "R", "max_stars_repo_path": "Working With Vectors-333.r", "max_stars_repo_name": "saquibmehmood/Data-Projects", "max_stars_repo_head_hexsha": "136fbcd46f728e09c627f690fa1fa6c1d71c3ad2", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2020-11-29T10:41:57.000Z", "max_stars_repo_stars_event_max_datetime": "2020-11-29T10:41:57.000Z", "max_issues_repo_path": "Working With Vectors-333.r", "max_issues_repo_name": "saquib-mehmood/R_basics_to_advanced", "max_issues_repo_head_hexsha": "136fbcd46f728e09c627f690fa1fa6c1d71c3ad2", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Working With Vectors-333.r", "max_forks_repo_name": "saquib-mehmood/R_basics_to_advanced", "max_forks_repo_head_hexsha": "136fbcd46f728e09c627f690fa1fa6c1d71c3ad2", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 28.6447368421, "max_line_length": 97, "alphanum_fraction": 0.7124483234, "num_tokens": 761, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9314625088705931, "lm_q2_score": 0.8459424334245618, "lm_q1q2_score": 0.787963661397737}} {"text": "\n#' @include Bayesian_Bricks.r\n\n\n#' @title Density function of Inverse-Gamma distribution\n#' @description\n#' For a random variable x, the density function of Inverse-Gamma distribution is defined as:\n#' \\deqn{(rate^shape)/Gamma(shape) x^{-shape-1} exp(-rate/x)}\n#' @param x numeric, positive numeric values.\n#' @param shape numeric, the shape parameter of gamma distribution.\n#' @param scale numeric, the scale, or inverse-scale parameter of gamma distribution. The 'rate' parameter in Gamma is the 'scale' parameter in InvGamma\n#' @param LOG logical, return log density of LOG=TRUE, default TRUE.\n#' @return A numeric vector, the density values.\n#' @export\ndInvGamma <- function(x,shape,scale,LOG=TRUE){\n logp <- shape*log(scale) - lgamma(shape)+(-shape-1)*log(x) - scale/x\n if(!LOG) logp <- exp(logp)\n logp\n}\n\n#' @title Random number generation of Inverse-Gamma distribution\n#' @description\n#' Generation random samples from Inverse-Gamma distribution. For a random variable x, the density function is defined as:\n#' \\deqn{(rate^shape)/Gamma(shape) x^{-shape-1} exp(-rate/x)}\n#' Where Gamma() is the Gamma function.\n#' @param n integer, number of samples to be generated.\n#' @param shape numeric, the shape parameter of gamma distribution.\n#' @param scale numeric, the scale, or inverse-scale parameter of gamma distribution. The 'rate' parameter in Gamma is the 'scale' parameter in InvGamma.\n#' @return A numeric vector, samples of Inverse-Gamma distribution.\n#' @export\n#' @import stats\nrInvGamma <- function(n,shape,scale){\n 1/rgamma(n=n,shape = shape,rate = scale)\n}\n\n#' @title Random generation for Wishart distribution\n#' @description\n#' Generate random samples from Wishart distribution. For a random matrix x, the density function of Wishart distribution is defined as:\n#' \\deqn{(2^{(df p)/2} Gamma_p(df/2) |rate|^{-df/2})^{-1} |x|^{(df-p-1)/2} exp(-1/2 tr(x rate))}\n#' Where x is a pxp symmetric positive definite matrix, Gamma_p() is the multivariate Gamma function of dimension p.\n#' @param df numeric, the degree of freedom.\n#' @param rate matrix, a symmetric positive-definite matrix, the 'rate', or 'inverse-scale' parameter. The 'rate' parameter in Wishart is the 'scale' parameter in InvWishart\n#' @param scale, matrix, the inverse of rate. Only one of 'rate' and 'scale' should be non-NULL.\n#' @return A symmetric positive-definite matrix.\n#' @export\n#' @examples\n#' rate <- crossprod(matrix(rnorm(15),5,3)) #the prior inverse-scale\n#' m <- matrix(0,3,3)\n#' ## get 1000 samples and calculate the sample mean\n#' for(i in 1:100){\n#' m <- m+rWishart(df=5,rate=rate)/100\n#' }\n#' ## m should roughly equal to df*inverse(rate):\n#' m\n#' pdsInverse(rate)*5\n#' ## try generating samples with 'rate' parameter:\n#' scale <- pdsInverse(rate)\n#' m2 <- matrix(0,3,3)\n#' for(i in 1:100){\n#' m2 <- m2+rWishart(df=5,scale=scale)/100\n#' }\n#' ## m2 should roughly equal df*scale:\n#' m2\n#' 5*scale\n#' @references Smith, W. B., and R. R. Hocking. \"Algorithm as 53: Wishart variate generator.\" Journal of the Royal Statistical Society. Series C (Applied Statistics) 21.3 (1972): 341-345.\n#' @import stats\nrWishart <- function(df,rate=NULL,scale=NULL){\n if(missing(df)) stop(\"'df' not specified!\")\n if(is.null(rate) & is.null(scale)) stop(\"one of 'rate' or 'scale' should be non-NULL.\")\n if(!is.null(rate)){\n if(!.is(rate,\"matrix\")){\n stop(\"'rate' must be a matrix!\")\n }else if(nrow(rate)!=ncol(rate)){\n stop(\"'rate' must be a square matrix!\")\n }\n if(df1L){\n A[upper.tri(A)] <- rnorm(D*(D-1L)/2L)\n }\n\n if(!is.null(scale)){\n return(crossprod(A%*%chol(scale)))\n }else{\n return(crossprod(A%*%t(pdsInverse(S=rate,returnUpper = TRUE))))\n }\n}\n\n#' @title Density function of Wishart distribution\n#' @description\n#' For a random matrix x, the density function of Wishart distribution is defined as:\n#' \\deqn{(2^{(df p)/2} Gamma_p(df/2) |rate|^{-df/2})^{-1} |x|^{(df-p-1)/2} exp(-1/2 tr(x rate))}\n#' Where x is a pxp symmetric positive definite matrix, Gamma_p() is the multivariate Gamma function of dimension p.\n#' @param x matrix, a symmetric positive-definite matrix.\n#' @param df numeric, the degree of freedom.\n#' @param rate matrix, a symmetric positive-definite matrix, the 'rate', or 'inverse-scale' parameter. The 'rate' parameter in Wishart is the 'scale' parameter in InvWishart\n#' @param LOG logical, return log density of LOG=TRUE, default TRUE.\n#' @return A numeric vector, the density values.\n#' @export\n#' @examples\n#' ##generate a symmetric positive-definite matrix\n#' x <- crossprod(matrix(rnorm(15),5,3))\n#' rate <- crossprod(matrix(rnorm(15),5,3)) #the prior inverse-scale of x\n#' dWishart(x,df = 5,rate = rate,LOG = TRUE)\n#' dWishart(x,df = 5,rate = rate,LOG = FALSE)\n#' @references Wishart, John. \"The generalized product moment distribution in samples from a normal multivariate population.\" Biometrika (1928): 32-52.\n#' @references MARolA, K. V., JT KBNT, and J. M. Bibly. Multivariate analysis. AcadeInic Press, Londres, 1979.\ndWishart <- function(x,df,rate,LOG=TRUE){\n if(missing(df)|missing(rate)) stop(\"'n' or 'rate' not specified!\")\n if(!.is(x,\"matrix\")){\n stop(\"'x' must be a matrix!\")\n }else if(nrow(x)!=ncol(x)){\n stop(\"'x' must be a square matrix!\")\n }\n if(!.is(rate,\"matrix\")){\n stop(\"'rate' must be a matrix!\")\n }else if(nrow(rate)!=ncol(rate)){\n stop(\"'rate' must be a square matrix!\")\n }\n if(df=3.5,]\nlm2 <- lm(log(r)~log(pSize),data=ps2)\nrequire(car)\ndwt(lm2)\nabline(lm2,col=\"blue\")\ncoef(lm2)\n\n# the library segmented\n\nrequire(segmented)\n\nps$logr <- log(ps$r)\nps$logpSize <- log(ps$pSize)\nlm0 <- lm(logr~logpSize,data=ps)\nseg <- segmented(lm0, seg.Z = ~logpSize, psi=4)\nsummary(seg)\nslope(seg)\n\n# Function to calculate H\n\ncalcH <- function(B) { 2-2*abs(B)}\n\ncalcH(.1550) # H = 1.69\n\n# small patches are anti-persistent\n\ncalcH(.9036) # H = 0.19\n\n# Big patches are persistent\n\n# where is the breakpoint in ha\n\ncalcBreak <- function(B) { 0.1*exp(B)*0.65 } \n\ncalcBreak(3.35) # 1.85 ha\n\n# Read the data from 1985\n\nps <- read.table(\"patch1985.dat\",header=T)\nps$r <- rank(-ps$pSize)\nplot(r ~ pSize,data=ps)\nplot(log(r)~log(pSize),data=ps)\n\nlm0 <- lm(log(r)~log(pSize),data=ps)\n\ncoef(lm0)\n\nabline(lm0)\nrequire(car)\ndwt(lm0)\n\n# Exercise 2\n\nrequire(segmented)\n\nps$logr <- log(ps$r)\nps$logpSize <- log(ps$pSize)\nlm0 <- lm(logr~logpSize,data=ps)\nseg <- segmented(lm0, seg.Z = ~logpSize, psi=4)\nsummary(seg)\nslope(seg)\n\nplot(seg,col=\"green\",xlab=\"Log Patch Size\",ylab=\"Acum Freq\")\npoints(log(r)~log(pSize),data=ps,pch=2,cex=.5)\n\n\ncalcH(0.2676)\ncalcH(1.26)\n\ncalcBreak(2.708) # 0.97 ha\n\n\n# using ggplot2\n\nps <- read.table(\"patch1985.dat\",header=T)\nps$r <- rank(-ps$pSize)\nps$Year <- \"1985\"\nps1 <- read.table(\"patch1968.dat\",header=T)\nps1$r <- rank(-ps1$pSize)\nps1$Year <- \"1968\"\n\nps <- rbind(ps,ps1)\n# \nrequire(ggplot2)\nggplot(data=ps,aes(x=pSize,y=r,color=Year))+geom_point()\n\np <- ggplot(data=ps,aes(x=log(pSize),y=log(r),color=Year))+geom_point(aes(shape=Year))\n\np\n\nps$logpSize <- log(ps$pSize)\nps1 <- ps[ps$logpSize>3.35,]\n\np + geom_smooth(data=ps1,method=\"lm\")\n\nggsave(\"patch_Breaks.png\",width=2)\n\n\n# This suggest that the increase cattle load change the break, but not the patch process\n# Los parches mas grandes se mantuvieron estables los mas chicos cambiaron", "meta": {"hexsha": "124b574cef49f7a022fc518f57a03253685c0e80", "size": 2488, "ext": "r", "lang": "R", "max_stars_repo_path": "R/cursoR2.r", "max_stars_repo_name": "lsaravia/MultifractalsInR", "max_stars_repo_head_hexsha": "1dfe51dbd49f370551c45fd16fd37f4ce040b2ca", "max_stars_repo_licenses": ["CC-BY-3.0"], "max_stars_count": 3, "max_stars_repo_stars_event_min_datetime": "2015-08-11T04:34:37.000Z", "max_stars_repo_stars_event_max_datetime": "2017-03-17T12:25:35.000Z", "max_issues_repo_path": "R/cursoR2.r", "max_issues_repo_name": "lsaravia/MultifractalsInR", "max_issues_repo_head_hexsha": "1dfe51dbd49f370551c45fd16fd37f4ce040b2ca", "max_issues_repo_licenses": ["CC-BY-3.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/cursoR2.r", "max_forks_repo_name": "lsaravia/MultifractalsInR", "max_forks_repo_head_hexsha": "1dfe51dbd49f370551c45fd16fd37f4ce040b2ca", "max_forks_repo_licenses": ["CC-BY-3.0"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2017-03-17T12:26:28.000Z", "max_forks_repo_forks_event_max_datetime": "2020-02-11T20:31:32.000Z", "avg_line_length": 17.2777777778, "max_line_length": 88, "alphanum_fraction": 0.6772508039, "num_tokens": 900, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8991213853793452, "lm_q2_score": 0.8757869803008764, "lm_q1q2_score": 0.7874388030253173}} {"text": "# Packages used : pracma\r\n# To install pracma,type following in command line while connected to internet\r\n# install.packages(\"pracma\") \r\n# package can be included by command \" library(pracma) \"\r\n# for more information about pracma visit https://cran.r-project.org/web/packages/pracma/index.html\r\n\r\n# Example : 3.6A Chapter : 3.6 Page No: 190\r\n# Four Fundamental Spaces of given matrix\r\n\r\nlibrary(pracma)\r\nnullspacebasis <- function(A){\r\n R<-rref(A)\r\n m<-nrow(A)\r\n n<-ncol(A)\r\n pivotcol<-c() #vector to store the column numbers of pivot columns\r\n freecol<-c() #vector to store the column numbers of free columns\r\n i<-1\r\n j<-1\r\n \r\n # to find which columns are pivot and which are free\r\n while(i<=m & j<=n){\r\n if(R[i,j]==1){\r\n pivotcol<-c(pivotcol,j)\r\n i<-i+1\r\n j<-j+1\r\n }\r\n else{\r\n j<-j+1\r\n }\r\n }\r\n y<-length(pivotcol)\r\n freecol<-c(1:n)\r\n freecol<-freecol[!freecol%in%pivotcol]\r\n x<-length(freecol)\r\n N<-c()\r\n #find the basis for null space based on Row reduced echelon form of given matrix\r\n if(y==n){\r\n return(N)\r\n }\r\n for(i in 1:x){\r\n temp<-c(1:n)\r\n for(j in 1:x){\r\n temp[freecol[j]]<-0\r\n }\r\n temp[freecol[i]]<-1\r\n temp[freecol[i]]\r\n for(j in 1:y){\r\n temp[pivotcol[j]]<-R[j,freecol[i]]*-1\r\n }\r\n N<-c(N,temp)\r\n }\r\n N<-matrix(N,nrow=n,ncol=x)\r\n #Basis for the nullspace of given matrix\r\n return(N)\r\n}\r\nl<-matrix(c(1,2,5,0,1,0,0,0,1),ncol=3)\r\nu<-matrix(c(1,0,0,3,0,0,0,1,0,5,6,0),ncol=4)\r\nA<-l%*%u\r\nprint(\"Row space Basis of A\")\r\nprint(u[1,])\r\nprint(u[2,])\r\nprint(\"COlumn space Basis of A \")\r\nprint(l[,1])\r\nprint(l[,2])\r\nprint(\"Null space Basis of A\")\r\nN<-nullspacebasis(A)\r\nprint(N)\r\nprint(\"Null space Basis of A transpose\")\r\nNT<-nullspacebasis(t(A))\r\nprint(NT)\r\n", "meta": {"hexsha": "9bf248a9eea64a3a946ec0825f94659fe1aa73e2", "size": 1763, "ext": "r", "lang": "R", "max_stars_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH3/EX3.6.a/Ex3_3.6A.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH3/EX3.6.a/Ex3_3.6A.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH3/EX3.6.a/Ex3_3.6A.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 24.8309859155, "max_line_length": 100, "alphanum_fraction": 0.6035167328, "num_tokens": 605, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8991213772699435, "lm_q2_score": 0.8757869835428965, "lm_q1q2_score": 0.7874387988381785}} {"text": "y<-c(.593 ,.142, .329, .691 ,.231 ,.793 ,.519 ,.392, .418 )\r\nybar = mean(y)\r\nmu0 = 0.3\r\nsigma = sd(y)\r\nn = 9 # sample size \r\nz = abs((ybar- mu0)/(sigma/sqrt(n)))\r\nprint(z)\r\np_value=2*(1-pnorm(z))\r\nprint(p_value)\r\nalpha=0.01\r\nif(p_value>alpha){\r\n print(\"we fail to reject H0\")\r\n print(\" data do not support the research hypothesis(insufficient evidence).\")\r\n}else{\r\n print(\"reject H0\")\r\n}\r\n ", "meta": {"hexsha": "1ef29e4b307086064c77aba051e846676722ae02", "size": 406, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH5/EX5.15/Ex5_15.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH5/EX5.15/Ex5_15.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH5/EX5.15/Ex5_15.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 23.8823529412, "max_line_length": 80, "alphanum_fraction": 0.5886699507, "num_tokens": 138, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9473810525948927, "lm_q2_score": 0.8311430436757313, "lm_q1q2_score": 0.7874091715744372}} {"text": "'''\r\nSuppose the mean weight of King Penguins found in an Antarctic colony \r\nlast year was 15.4 kg. In a sample of 35 penguins same time this year in the same colony, \r\nthe mean penguin weight is 14.6 kg. Assume the population standard deviation is 2.5 kg. \r\nAt .05 significance level, can we reject the null hypothesis that the mean penguin\r\nweight does not differ from last year?\r\n'''\r\n#media muestral\r\nxbar = 14.6\r\n\r\n#valor de la hipotesis\r\nmu0 = 15.4\r\n\r\n#sd\r\nsigma = 2.5\r\n\r\nn = 35\r\n\r\nz = (xbar-mu0)/(sigma/sqrt(n))\r\n\r\nz #-1.89\r\n\r\nalpha = .05\r\n\r\nz.half.alpha = qnorm(1-alpha/2)\r\n\r\nc(-z.half.alpha,z.half.alpha)\r\n\r\n#-1.96 1.96\r\n\r\n#aceptamos la hipotesis\r\n\r\npval = 2*pnorm(z)\r\npval #pvalue para 2 colas 0.058\r\n", "meta": {"hexsha": "a84383e3c0018da4a34f80442ef6aed14db30fa8", "size": 711, "ext": "r", "lang": "R", "max_stars_repo_path": "Parcial/1. Prueba de hipotesis/TwoTailedMeanKnownVariance.r", "max_stars_repo_name": "jchudb93/Exp-Numerica", "max_stars_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Parcial/1. Prueba de hipotesis/TwoTailedMeanKnownVariance.r", "max_issues_repo_name": "jchudb93/Exp-Numerica", "max_issues_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Parcial/1. Prueba de hipotesis/TwoTailedMeanKnownVariance.r", "max_forks_repo_name": "jchudb93/Exp-Numerica", "max_forks_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 20.3142857143, "max_line_length": 91, "alphanum_fraction": 0.6779184248, "num_tokens": 231, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9518632316144273, "lm_q2_score": 0.8267117919359419, "lm_q1q2_score": 0.7869165578858998}} {"text": "### 多値判別分析の例\n### - Edgar Anderson's Iris Data\n\n## パッケージの読み込み (lda/qda)\nrequire(MASS) \nrequire(tidyverse) \nrequire(ggfortify)\nrequire(GGally)\n\n## データの読み込み (\"datasets::iris\"を用いる)\ndata(iris) # データセットの読み込み\n\n## データの内容を確認\nhelp(iris) # 内容の詳細を表示\nstr(iris) # データの構造を表示\n## print(iris) # 全データの表示\nhead(iris) # データの最初を表示\ntail(iris) # データの最後を表示\n\n## データの散布図: 図(a)\nggpairs(iris, columns=1:4, mapping=aes(colour=Species, alpha=.5)) +\n labs(title=\"Edgar Anderson's Iris Data\")\n\n## 3D表示 (Sepal.Widthを除く): 図(b)\nrequire(lattice)\ncloud(Sepal.Length ~ Petal.Length * Petal.Width,\n data=iris,　groups=Species, screen=list(z=30, x=-60),\n main=\"Edgar Anderson's Iris Data\")\n## cloud(Sepal.Length ~ Petal.Length * Petal.Width | Species,\n## data=iris, screen=list(x=-90, y=70), distance=.4, zoom=.6)\n\n## 特徴量とカテゴリによる線形判別関数の構成\nmodel <- lda(Species ~ ., data=iris)\nprint(model) # 結果を表示\n\n## 判別得点の散布図: 図(c)\n### 参考 https://www.r-bloggers.com/computing-and-visualizing-lda-in-r/\nmydata <- data.frame(iris,\n lda=predict(model, newdata=iris)$x)\nprop <- model$svd^2/sum(model$svd^2) # 判別の寄与率の計算\nggplot(mydata) +\n geom_point(aes(lda.LD1,lda.LD2,colour=Species)) +\n labs(x=paste0(\"LD1 (\", round(prop[1]*100,2),\"%)\"),\n y=paste0(\"LD1 (\", round(prop[2]*100,2),\"%)\")) +\n theme(legend.position=\"top\")\n\n## 主成分得点の散布図: 図(d)\nautoplot(prcomp(~ . -Species, data=iris, scale.=TRUE),\n data=iris, colour=\"Species\") + \n theme(legend.position=\"top\")\n\n## 訓練データと試験データによる線形判別の評価\n## set.seed(1234) # 実験の再現性を求める場合\nidx <- sample(1:150,75) # 訓練用データの番号をランダムに選ぶ\nwith(iris,table(Species[idx])) # 各種が何個ずつ選ばれたか表示\n\n## 線形判別式の作成\nmodel1 <- lda(Species ~ ., data=iris, subset=idx,\n prior=c(1/3,1/3,1/3)) \n## print(model1) # 結果を表示\n## ## データの分布をそのまま使う場合はpriorを指定しない\n## model1 <- lda(Species ~ ., data=iris, subset=idx) \n## ## モデルの更新を行う場合はupdateを使う (例: Petal.Length を除く)\n## model1 <- update(model1, . ~ . - Petal.Length) \n\n## 線形判別による予測\ntrue <- iris[-idx,5]\npredict1 <- predict(model1, newdata=iris[-idx,-5]) \ntable(true,predict=predict1$class) # 真のクラスラベルと予測結果の比較\nif(length(true!=predict1$class)>0) {# 誤ったデータがある場合\n which(true!=predict1$class) # 番号を表示\n predict1$posterior[true!=predict1$class,] # 事後確率を表示\n}\n## 線形判別の事後確率: 図(e)\ncloud(setosa ~ versicolor * virginica, \n data=data.frame(predict1$posterior),\n groups=true)\n\n## 訓練データと試験データによる2次判別の評価\n## 2次判別式の作成\nmodel2 <- qda(Species ~ ., data=iris, subset=idx,\n prior=c(1/3,1/3,1/3)) \n## print(model2) # 結果を表示\n\n## 2次判別による予測\npredict2 <- predict(model2, newdata=iris[-idx,-5]) \ntable(true,predict=predict2$class) # 真のクラスラベルと予測結果の比較\nif(length(true!=predict2$class)>0) {# 誤ったデータがある場合\n which(true!=predict2$class) # 番号を表示\n predict2$posterior[true!=predict2$class,] # 事後確率を表示\n}\n## 2次判別の事後確率: 図(f)\ncloud(setosa ~ versicolor * virginica, # 事後確率を図示\n data=data.frame(predict2$posterior),\n groups=true)\n", "meta": {"hexsha": "f558295b1449ad0bad1034e4f03a57376a955b83", "size": 2893, "ext": "r", "lang": "R", "max_stars_repo_path": "docs/code/d-iris.r", "max_stars_repo_name": "noboru-murata/multivariate-analysis", "max_stars_repo_head_hexsha": "645bff23d3868e5d7c245ef4af7d0ff9fe98e017", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "docs/code/d-iris.r", "max_issues_repo_name": "noboru-murata/multivariate-analysis", "max_issues_repo_head_hexsha": "645bff23d3868e5d7c245ef4af7d0ff9fe98e017", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "docs/code/d-iris.r", "max_forks_repo_name": "noboru-murata/multivariate-analysis", "max_forks_repo_head_hexsha": "645bff23d3868e5d7c245ef4af7d0ff9fe98e017", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 30.1354166667, "max_line_length": 69, "alphanum_fraction": 0.6647079157, "num_tokens": 1376, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9173026528034426, "lm_q2_score": 0.8577681013541611, "lm_q1q2_score": 0.7868329548623443}} {"text": "# 2.2\nexample(mean)\n\n# 1. Generamos dos vectores de datos desde sendas distribuciones normales\n# y los guardamos en sendos objetos 'x' e 'y'\nx <- rnorm(50)\ny <- rnorm(50, mean = 10, sd = 2)\n# Imprimimos en la consola el contenido de los objetos 'x' e 'y'\nx\ny\n# 2. Resumen descriptivo de los datos\nsummary(x)\nsummary(y)\n# 3. Histograma de x\nhist(x)\n# 4. Representamos la distribución conjunta de los datos (scatterplot)\nplot(x, y)\n# 5. Ajustamos una recta de regresión a los datos\nfit <- lm(y ~ x)\nsummary(fit)\n# 6. Superponemos la recta de regresión al gráfico anterior\nabline(fit)\n# 7. Creamos dos nuevos vectores con secuencias de valores\nx <- 1:10\ny <- seq(-pi, pi, length.out = 10)\n# 8. Escribimos una matriz con los vectores anteriores por columnas\ncbind(x, y)\n# 9. Escribimos una matriz con dos filas y cinco columnas con los elementos de x\nmatrix(x, 2, 5)\n# 10. Creamos una matriz con filas y columnas indexadas por x e y,\n# cuyos valores son cos(y)/(1 + x^2))\nf <- outer(x, y, function(x, y) cos(y) / (1 + x^2))\nf\n# 11. Dos representaciones tridimensional de f como función de x e y\n# primero un diagrama de contornos\ncontour(x, y, f)\n# añadimos más niveles\ncontour(x, y, f, nlevels = 15, add = TRUE)\n# y ahora un mapa de colores\nimage(x, y, f)\n# 12. Demostración de otras funciones gráficas\ndemo(graphics)\ndemo(persp)\n##############\n\n# 2.3\nx <- 5\ny <- 2 * x\nz <- log(y)\nk <- x * y * z\nls()\nrm(x, y)\nls()\nrm(list = ls())\nls()\n\n# matrix(data = NA, nrow = 1, ncol = 1, byrow = FALSE, dimnames = NULL)\nmatrix(pi, 1, 3)\n\n#########\n# 2.4\n0.3 - 0.1 == 0.2\n0.3 - 0.2\nall.equal(0.3 - 0.2, 0.1)", "meta": {"hexsha": "d7551e3b6e4e6a731032ab4c7ebfa0e1078f1d59", "size": 1593, "ext": "r", "lang": "R", "max_stars_repo_path": "clases/Clase 2022-02-24.r", "max_stars_repo_name": "LucasFA/EC", "max_stars_repo_head_hexsha": "a3822b94fc1c97f3096c9fd40cd3140ee85a5ac8", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "clases/Clase 2022-02-24.r", "max_issues_repo_name": "LucasFA/EC", "max_issues_repo_head_hexsha": "a3822b94fc1c97f3096c9fd40cd3140ee85a5ac8", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "clases/Clase 2022-02-24.r", "max_forks_repo_name": "LucasFA/EC", "max_forks_repo_head_hexsha": "a3822b94fc1c97f3096c9fd40cd3140ee85a5ac8", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 24.890625, "max_line_length": 80, "alphanum_fraction": 0.6641556811, "num_tokens": 594, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.893309411735131, "lm_q2_score": 0.880797085800514, "lm_q1q2_score": 0.7868243265744749}} {"text": "\r\n\r\n##source(url(\"http://www.stat.pitt.edu/stoffer/tsa2/Rcode/itall.R\"))\r\n##z<- as.matrix(read.table(\"C:/Users/mccj07/Documents/Media mix modeling/MMM_data.csv\", sep=\",\", header=T), 104, 4, byrow = TRUE)\r\n\r\n### Lets first generate some Random DAta\r\nx1=2000*10^arima.sim(n = 104, list(ar = c(0.8897, -0.178)),sd = sqrt(0.0796))\r\nx2=5000*10^arima.sim(n = 104, list(ar = c(0.9497, -0.1758)),sd = sqrt(0.1296))\r\nx3=1000*10^arima.sim(n = 104, list(ar = c(0.9197, -0.1258)),sd = sqrt(0.0696))\r\ny=10000*10^arima.sim(n = 104, list(ar = c(0.9097, -0.1458), ma = c(-0.279, 0.188)),sd = sqrt(0.1596))\r\n\r\ny=y+.75*x2+1.2*x1+.9*x3\r\n\r\nxxxy=cbind(x1,x2,x3,y) \r\nplot(xxxy,type='l')\r\n\r\nxxxy \r\n\r\n\r\n## Lets go ahead and log the data\r\ny1.l=log(y)\r\nx1.l=log(x1)\r\nx2.l=log(x2)\r\nx3.l=log(x3)\r\n\r\n## lets remove the mean for each series. \r\ny1.m=mean(y1.l)\r\nx1.m=mean(x1.l)\r\nx2.m=mean(x2.l)\r\nx3.m=mean(x3.l)\r\n\r\n\r\ny1a=y1.l-y1.m\r\nx1a=x1.l-x1.m\r\nx2a=x2.l-x2.m\r\nx3a=x3.l-x3.m\r\n\r\n## The two series X and Y must be made stationary before starting interpreting \r\n## the crosscorrelation function. Means of X and Y and variances of X and Y must \r\n## be constant over time. So the Autocorrelation Function of X and Y must be looked at \r\n## first of all and appropriate pre-transformations and differencing transformations \r\n## must be made until the ACF dies down quickly or has a cut off kind of behavior.\r\n\r\npar(mfcol=c(2,2))\r\nacf(y1a,lag=20)\r\nacf(x1a,lag=20)\r\npacf(y1a,lag=20)\r\npacf(x1a,lag=20)\r\n\r\npar(mfcol=c(2,2))\r\nacf(x2a,lag=20)\r\nacf(x3a,lag=20)\r\npacf(x2a,lag=20)\r\npacf(x3a,lag=20)\r\n\r\n## in this case we generated staionary time series . so all are stationary\r\n\r\n\r\n\r\nxxxya=cbind(x1a,x2a,x3a,y1a) \r\nlag.plot(xxxya, 4, do.lines=FALSE) \r\n\r\nx1_f=arima(x1a,order=c(2,0,0))\r\nx2_f=arima(x2a,order=c(2,0,0))\r\nx3_f=arima(x3a,order=c(2,0,0))\r\n\r\nx1_f\r\nx2_f\r\nx3_f\r\n\r\n\r\n###y1=arima(z[,1],order=c(2,0,0))\r\n### choos x2 as a filter \r\ntsdiag(x1_f, gof.lag=20)\r\ntsdiag(x2_f, gof.lag=20)\r\ntsdiag(x3_f, gof.lag=20)\r\n\r\n\r\nf1=c(1,-x2_f$coef[1:2])\r\n\r\n\r\ny1fil=filter(y1a, sides=1,f1)\r\ny1fil=y1fil[3:103]\r\n\r\nx1fil=filter(x1a, sides=1,f1)\r\nx1fil=x1fil[3:103]\r\nx2fil=filter(x1a, sides=1,f1)\r\nx2fil=x2fil[3:104]\r\nx3fil=filter(x1a, sides=1,f1)\r\nx3fil=x3fil[3:104]\r\n\r\n## Identify an ARIMA model for the input series X that you made stationary and apply this model to Y.\r\n\r\n## Get the residuals from the model for X and the residuals of the model for Y. This is called Prewhitening the series.\r\n\r\n\r\nccf(x1fil,y1fil, ylab = \"cross-correlation x1 and y\")\r\nccf(x2fil,y1fil, ylab = \"cross-correlation x2 and y\")\r\nccf(x3fil,y1fil, ylab = \"cross-correlation x3 and y\")\r\n\r\nx1f=x1_f$residuals[3:104]\r\nx2f=x2_f$residuals[3:104]\r\nx3f=x3_f$residuals[3:104]\r\n\r\n\r\n\r\n## Find the cross-correlation function between the residuals. This crosscorrelation function allows \r\n## us to find the impulse response function.\r\n\r\n### Use the estimates of the impulse response function to make guesses of the orders of the actual Y and X models.\r\n\r\nsource(\"C:/Users/mccj07/Documents/R/source/ccm.R\")\r\n\r\nxy=cbind(x1f,y1a[3:104],x2f,x3f) \r\n##<== Combine filtered series.\r\nccm(xy,20)\r\n\r\n## With the latter get initial estimates of the parameters. \r\n### Estimate the parameters for the Y and the X part of the model\r\n\r\n\r\n(fit2.gls = arima(y1a[3:104], order=c(2,0,2), xreg=cbind(x1f, x2f, x3f))) \r\nacf(fit2.gls$residuals)\r\npacf(fit2.gls$residuals)\r\n\r\n\r\nBox.test(resid(fit2.gls), 12, type=\"Ljung\")\r\npchisq(12.377, 10, lower=FALSE) \r\n\r\n\r\nx1.p=predict(x1_f, n.ahead=13, level=c(80,95))\r\nx2.p=predict(x2_f, n.ahead=13, level=c(80,95))\r\nx3.p=predict(x3_f, n.ahead=13, level=c(80,95))\r\n\r\nnewxreg=cbind(x1.p$pred,x2.p$pred,x3.p$pred)\r\ny.fore = predict(fit2.gls, n.ahead=13, newxreg=newxreg) \r\n\r\nexp(y.fore$pred)\r\ny.fore$pred+y1.m\r\n\r\n\r\nU = exp((y.fore$pred + 2*y.fore$se)+y1.m)\r\nL = exp((y.fore$pred - 2*y.fore$se)+y1.m)\r\nminy=min(y,L)\r\nmaxy=max(y,U)\r\nts.plot(y,exp(y.fore$pred+y1.m),col=1:2, ylim=c(miny,maxy))\r\nlines(U, col=\"blue\", lty=\"dashed\")\r\nlines(L, col=\"blue\", lty=\"dashed\")\r\n\r\nexy=ts(exp(y.fore$pred+y1.m),start=105)\r\n\r\npred.xxxy=cbind(exp(x1.p$pred+x1.m),exp(x2.p$pred+x2.m),exp(x3.p$pred+x3.m),exy)\r\n\r\npred.xxxy", "meta": {"hexsha": "b45a54198d58f7f3c3808ebddf3314ad5a2d3ae5", "size": 4147, "ext": "r", "lang": "R", "max_stars_repo_path": "Media mix model.r", "max_stars_repo_name": "ahmerinam/Sample-R-Codes", "max_stars_repo_head_hexsha": "62f83511b7bdc9a8a19cbd40b7b9b22028c9c42d", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Media mix model.r", "max_issues_repo_name": "ahmerinam/Sample-R-Codes", "max_issues_repo_head_hexsha": "62f83511b7bdc9a8a19cbd40b7b9b22028c9c42d", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Media mix model.r", "max_forks_repo_name": "ahmerinam/Sample-R-Codes", "max_forks_repo_head_hexsha": "62f83511b7bdc9a8a19cbd40b7b9b22028c9c42d", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.9285714286, "max_line_length": 130, "alphanum_fraction": 0.6650590789, "num_tokens": 1600, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9465966702001757, "lm_q2_score": 0.8311430457670241, "lm_q1q2_score": 0.7867572395830973}} {"text": "### 6.1-6\n\nbeforeData <- c(12, 15, 6, 20, 2, 5, 9, 16, 14, 17, 8, 5)\nafterData <- c(11, 13, 3, 21, 5, 7, 6, 10, 9, 72, 4, 1)\n\nnSamples <- length(beforeData)\ndf <- nSamples - 1\n\ndArray <- beforeData - afterData\ndSqArray <- dArray^2\n\ndOverline <- sum(dArray) / nSamples\nsD <- sqrt((sum(dSqArray - sum(dArray)^2/nSamples))/ df)\n\nt <- dOverline / (sD / sqrt(nSamples))\nprint(df)\nprint(t)\n\n### df = 11\ntCrit <- qt(0.975, df, ncp=0, lower.tail=TRUE, log.p=FALSE)\nprint(tCrit)\n\n### t = -0.6951115 -> H0 is rejected (the movie did not affect the people)\n", "meta": {"hexsha": "4450b324293a369e28c3fedffd8dbf120b90a58e", "size": 548, "ext": "r", "lang": "R", "max_stars_repo_path": "TASK3/sem3/coupSamp1.r", "max_stars_repo_name": "mortarsynth/StatisticalModelling", "max_stars_repo_head_hexsha": "ebb6c76cd8defa7dcb2a4d16515328b55989dedd", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "TASK3/sem3/coupSamp1.r", "max_issues_repo_name": "mortarsynth/StatisticalModelling", "max_issues_repo_head_hexsha": "ebb6c76cd8defa7dcb2a4d16515328b55989dedd", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "TASK3/sem3/coupSamp1.r", "max_forks_repo_name": "mortarsynth/StatisticalModelling", "max_forks_repo_head_hexsha": "ebb6c76cd8defa7dcb2a4d16515328b55989dedd", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.8333333333, "max_line_length": 76, "alphanum_fraction": 0.6149635036, "num_tokens": 234, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.970687766704745, "lm_q2_score": 0.8104789018037399, "lm_q1q2_score": 0.7867219551531867}} {"text": "rm(list = ls())\nlibrary(\"openssl\")\n\n## We are going to create a public key (n and e) and a private key(d) ####\n## Assign Prime Numbers ###\n\np = bignum(\"112481050639317229656723018120659623829736571015511322021617837187076258724819\")\nq = bignum(\"89185111938335771293328323333111422985697062149139368049232365065924632677343\")\n\n##Public Keys###\n\nn = p*q\nprint(n)\n\ne = bignum(\"65537\")\n\n###Private Keys###\n\nd = bignum_mod_inv(e, (p-1)*(q-1))\n\n### GRADER ATTENTION: Following command has been commented out because \"Private Key Info\" Please uncomment if needed ###\n#print(d)\n\nm=bignum(charToRaw(\"Bitcoin is a vehicle of freedom\")) \nprint(m)\n\nc = bignum_mod_exp(m,e,n)\n### GRADER ATTENTION: Following command has been commented out because \"Private Message Payload\" Please uncomment if needed ###\n#print(c)\n\nc_encoded = base64_encode(c)\n### GRADER ATTENTION: Following command has been commented out because \"Private Message Payload\" Please uncomment if needed ###\n#print(c_encoded)\n\n### This section of the code will decode the information into a readable form ###\nc_decoded = bignum(base64_decode(\"rGhkBLUmPQStyYGrhIcNxnhZw6GeGoFGswZuUihd+kPx21VtPSMmdBRQOkKw8uLPhsh0NV4qk27G/EFuVT2iAw==\"))\nm3 = bignum_mod_exp(c_decoded,d,n)\nm3_char = rawToChar(m3)\nprint(m3_char)\n\nm_hash = sha256(m3_char)\nprint(m_hash)\n\nhashed_num = bignum(charToRaw(m_hash))\nprint (hashed_num)\n\ns = bignum_mod_exp(hashed_num,d,n)\n\n### Verify ###\nm_verif = bignum_mod_exp(s,e,n)\nprint(m_verif)\n\n\n## Simple logic test if the signature was the same and valid ###\nif (m_verif == hashed_num)\n print(\"Success: The Signature Is Valid!\") \n\n\n", "meta": {"hexsha": "3076e114a89da5945d4f1fa0505f5500a8035290", "size": 1599, "ext": "r", "lang": "R", "max_stars_repo_path": "Cryptography/Cryptography.r", "max_stars_repo_name": "PeterShortino20/Fintech-Distributed-Ledger", "max_stars_repo_head_hexsha": "d85f526b4dfa70b809ce2558d7c75a2647c363e9", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Cryptography/Cryptography.r", "max_issues_repo_name": "PeterShortino20/Fintech-Distributed-Ledger", "max_issues_repo_head_hexsha": "d85f526b4dfa70b809ce2558d7c75a2647c363e9", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Cryptography/Cryptography.r", "max_forks_repo_name": "PeterShortino20/Fintech-Distributed-Ledger", "max_forks_repo_head_hexsha": "d85f526b4dfa70b809ce2558d7c75a2647c363e9", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 27.1016949153, "max_line_length": 127, "alphanum_fraction": 0.7517198249, "num_tokens": 466, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9648551515780318, "lm_q2_score": 0.8152324871074608, "lm_q1q2_score": 0.7865812649194049}} {"text": "##### Chapter 7: Neural Networks and Support Vector Machines -------------------\n\n# 활성 함수는 인공 뉴런이 들어오는 정보를 처리해서 네트워크를 통해 정보를 처리하는 메커니즘.\n# (로지스틱)시그모이드 함수를 자주 쓴다.\n# 선형 함수를 활성 함수로 쓰면 선형 회귀와 매우 유사한 신경망르 만든다.\n# 가우시안 활성 함수는 방사 기저 함수 네트워크라고 하는 모델을 만든다.\n# 이들 각각은 특정 학습 작업에 좀 더 적합한 강점을 가진다.\n# 여러 활성 함수의 경우, 출력 신호에 영향을 미치는 입력 값의 범위가 상대적으로 좁다는 것을 인식해야 한다.\n# ex) 시그모이드는 절대값이 5를 넘어가는 값은 거의 0이나 1이다.\n# 압축 문제에 대한 해결책은, 특징 값이 0 근처의 작은 범위 안으로 들어오게 모든 신경망 입력을 변환하는 것이다.\n# 이 과정에서 표준화나 정규화가 수반된다.\n\n# 네트워크 토폴로지(네트워크 패턴, 네트워크 구조)\n# 계층 갯수, 네트워크의 정보가 역방향으로 이동할 수 있는지 여부, 네트워크의 각 계층 별 노드 개수로 구별.\n# 다중 은닉 계층을 갖는 신경망을 DNN이라고 하며, 그런 신경망의 훈련을 딥러닝이라고 한다.\n\n# 신경망은 각 계층의 노드 개수로 복잡도에 변화를 줄 수 있다.\n# 입력 노드 개수는 입력 데이터의 특징 개수로 사전에 결정된다.\n# 비슷하게 출력 노드의 갯수는 모델링되는 출력 개수 또는 출력 클래스 레벨 개수로 사전에 결정된다.\n# 하지만 은닉 노드의 갯수는 모델을 훈련하기 전에 사용자가 결정한다.\n# 은닉 계층의 뉴런 갯수를 결정하는 신뢰할 많나 규칙은 없다.\n# 적합한 갯수는 다양한 요소 중, 입력 노드 수, 훈련 데이터양, 잡음 데이터양, 학습 작업의 복잡도에 따라 달라진다.\n# 뉴런 갯수가 아주 많으면 오버피팅 가능성!\n# 대부분의 경우 신경망은 적은 갯수의 은닉 노드 만으로도 엄청난 학습 능력 제공한다.\n\n# 네트워크는 경험으로 훈련된다. 신경망이 입력 데이터를 처리하면서 뉴런 사이에 연결은 강화되거나 약화된다.\n# 네트워크의 연결 가중치는 시간이 지나면서 관측되는 패턴을 반영하도록 조정된다.\n# 순방향 단계\n # 입력 계층부터 출력 계층까지 뉴런이 순차적으로 활성화되면서\n # 도중에 뉴런의 가중치와 활성 함수가 적용된다.\n # 마지막 계층에 도달하면 출력 신호가 생성된다.\n# 역방향 단계\n # 순방향 단계에서 만들어진 네트워크 출력 신호를 훈련 데이터의 실제 목표 값과 비교한다.\n # 네트워크 출력 신호와 실제 값의 차로 오차가 만들어지면,\n # 네트워크에서 역방향으로 전파되어 뉴런 사이에 연결 가중치를 수정하고, 미래의 오차를 줄인다.\n# 뉴런의 입력과 출력 사이의 관계가 복잡한데, 알고리즘이 가중치를 얼마나 바꿔야 하는지 어떻게 결정하는가?\n # 경사 하강법!\n # 역전파 알고리즘은 각 뉴런의 활성 함수를 미분해 들어오는 각 가중치 방향의 그래디언트를 식별한다.\n # 그래서 미분 가능한 활성 함수를 갖는 것이 중요하다.\n # 그래디언트는 가중치의 변화에 대해 오차의 감소 또는 증가 방향(경사)를 나타낸다.\n # 알고리즘은 오차가 최대한 감소하도록, \"학습률만큼\" 변경하려고 할 것이다.\n # 학습률이 커질수록 알고리즘은 더 빠르게 언덕을 내려온다.->훈련 시간을 줄일 수 있다.\n\n\n##### Part 1: Neural Networks -------------------\n## Example: Modeling the Strength of Concrete ----\n\n## Step 2: Exploring and preparing the data ----\n# read in data and examine structure\ngetwd()\nsetwd(\"D:/R_LAB/MLwR/Chapter 07\")\nconcrete <- read.csv(\"concrete.csv\")\nstr(concrete)\n\n# custom normalization function\nnormalize <- function(x) { \n return((x - min(x)) / (max(x) - min(x)))\n}\n# apply normalization to entire data frame\nconcrete_norm <- as.data.frame(lapply(concrete, normalize))\n# confirm that the range is now between zero and one\nsummary(concrete_norm$strength)\n# compared to the original minimum and maximum\nsummary(concrete$strength)\n# 모델을 훈련하기 전에 데이터에 적용한 모든 변환은 이후에 역으로 적용해서 원래 측정 단위로 되돌려야 한다.\n# 재조정을 용이하게 하려면 원래 데이터나, 원래 데이터의 요약 통계를 저장해 두는 것이 좋다.\n\n\n# create training and test data\n# 이미 임의로 정렬되어 있으므로, 데이터 프레임을 단순히 두 부분으로 나누면 된다.\nconcrete_train <- concrete_norm[1:773, ]\nconcrete_test <- concrete_norm[774:1030, ]\n\n## Step 3: Training a model on the data ----\n# train the neuralnet model\ninstall.packages(\"neuralnet\")\nlibrary(neuralnet) # 사용하기 쉬운 표준 신경망의 구현을 제공 & 네트워크 토폴로지 그리는 함수 제공.\n\n# simple ANN with only a single hidden neuron(은닉 노드 하나인 다층 순방향 네트워)\nset.seed(13123313) # to guarantee repeatable results\nconcrete_model <- neuralnet(formula = strength ~ cement + slag +\n ash + water + superplastic + \n coarseagg + fineagg + age,\n data = concrete_train)\n\n# visualize the network topology\nplot(concrete_model)\n# 은닉 노드가 하나인 신경망은, 선형 회귀 모델과 비슷할 수 있다.\n # 각 입력 노드와 은닉 노드의 가중치는 회귀 계수와 비슷하다.\n # 바이어스 항의 가중치는 절편과 비슷하다.\n# 아래 부분에 훈련 단계 횟수와 오차 제곱 합을 보고한다.\n\n## Step 4: Evaluating model performance ----\n# obtain model results\nmodel_results <- compute(concrete_model, concrete_test[1:8])\n# compute()는 predict()와는 다르게 작동한다.\n # 이 함수는 두 개의 구성 요소로 된 리스트를 반환한다.\n # $neurons는 네트워크의 계층별로 뉴런을 저장하며,\n # $net.result는 에측 값을 저장한다.\n\n# obtain predicted strength values\npredicted_strength <- model_results$net.result\n# 지금은 분류 문제가 아닌 수치 예측 문제이기 때문에, 모델의 정확도를 검토할 때에 혼동 행렬 사용 불가.\n# 대신 예측된 콘트리트 강도와 실제 값의 상관관계를 측정해야 한다.\n\n# examine the correlation between predicted and actual values\ncor(predicted_strength, concrete_test$strength)\n\n## Step 5: Improving model performance ----\n# a more complex neural network topology with 5 hidden neurons\nset.seed(13123313) # to guarantee repeatable results\nconcrete_model2 <- neuralnet(strength ~ cement + slag +\n ash + water + superplastic + \n coarseagg + fineagg + age,\n data = concrete_train, hidden = 5)\n\n# plot the network\nplot(concrete_model2)\n\n# evaluate the results as we did before\nmodel_results2 <- compute(concrete_model2, concrete_test[1:8])\npredicted_strength2 <- model_results2$net.result\ncor(predicted_strength2, concrete_test$strength)\n\n##### Part 2: Support Vector Machines -------------------\n# 다차원 공간에 표시되는 점들 사이에 경계를 만드는 표면.\n# 분류, 수치 예측을 포함한 거의 도든 유형의 학습 작업에 이용 가능.\n# SVM은 점이 선형적으로 분리되지 않는 문제에도 확장될 수 있다.\n# 서포트 벡터란 각 클래스에서 최대 마진 초평면(MMH)에 가장 가까운 점들이다.\n # 서포트 벡터만을 이용해서 MMH를 정의할 수 있다.\n # 특징의 개수가 엄청나게 많더라도, 서포트 벡터는 분류 모델을 저장하기 위한 아주 간결한 방법을 제공한다.\n # 서포트 벡터를 식별하는 알고리즘은 벡터 기하학에 의존한다. 하지만 과정의 기본 원리는 간단하다.\n# 선형적으로 분리가 불가능한 경우\n # 슬랙 항을 추가해 비선형 데이터에 대해 훈련\n # 커널 트릭을 이용해 문제를 고차원 공간으로 매핑. 그렇게 하면 비선형적 관계가 선형적 관계로 바뀐다.\n # 커널 트릭은 측정된 특성 간의 수학적 관계를 표현하는 새로운 특징의 구성 과정을 포함한다.\n# 장단점\n # 장점\n # 분류 또는 수치 예측 문제에 사용 가능\n # 잡음에 거의 영향을 받지 않음. 과적합도 쉽게 일어나지 않음.\n # 신경망을 사용하는 것보다 쉬움. 잘 지원되는 SVM 알고리즘들이 이미 존재\n # 정확도가 높은 편\n # 단점\n # 최고의 모델을 찾기 위해 커널과 모델 파라미터의 다양한 조합을 테스트해야 한다.\n # 훈련이 느릴 수 있으며, 특히 입력 데이터셋이 아주 많은 특징이나 예시를 갖는 경우 느리다.\n # 해석하기 어려울 수 있다.\n# 커널\n # 일반적인 커널 함수는 특징 벡터 xi,xj에 변환을 적용하고, 내적으로 둘을 결합한다.\n # 이 때 내적은 두 벡터를 받아 하나의 숫자를 반환한다.\n # 선형 커널 : 데이터를 전혀 변환하지 않는다 -> 특징의 내적으로 간단히 표현 가능.\n # d차원 다항 커널 : 간단한 데이터의 비선형 변환을 더한다.\n # 시그모이드 커널 : 시그모이드 활성 함수를 사용한 신경망과 다소 유사한 SVM 모델을 만든다.\n # 가우시안 RBF 커널 : RBF 신경망과 유사하다. 많은 유형의 데이터에서 잘 작동한다.\n# 커널을 특정 학습 작업에 연결해주는 신뢰할 만한 규칙은 없다.\n # 커널의 적합 여부는 훈련 데이터의 양, 특징, 그 관계, 그리고 학습될 개념에 크게 의존한다.\n# 검증 데이터셋에 대해 몇 개의 SVM을 훈련하고 평가하는 식의 시행착오가 필요하다.\n\n## Example: Optical Character Recognition ----\n\n## Step 2: Exploring and preparing the data ----\n# read in data and examine structure\nletters <- read.csv(\"letterdata.csv\")\nstr(letters)\n# SVM 학습자는 모든 특징이 수치여야 하고, 게다가 각 특징이 아주 작은 구간으로 값이 조정되어야 한다.\n# str을 해 보니 데이터의 정규화 또는 표준화가 필요하다는 것을 알 수 있다.\n # 모델을 적합시키기 위해 사용할 R 패키지가 자동으로 재조정을 실행한다.\n\n\n# divide into training and test data\n# 데이터는 이미 무작위로 나뉘어져 있다.\nletters_train <- letters[1:16000, ]\nletters_test <- letters[16001:20000, ]\n\n## Step 3: Training a model on the data ----\n# begin by training a simple linear SVM\n# 뛰어난 패키지들이 많다.\n # e1071 패키지는 LIBSVM 라이브러리의 R 인터페이스를 제공한다.(C++로 작성됨)\n # klaR 패키지는 SVM 구현을 R에서 직접 수행하는 함수를 제공한다.\n # kernlab 패키지는 caret 패키지와 함께 사용할 수 있어서, 다양한 자동화 방법(11장)으로 훈련 및 평가 가능.\n\ninstall.packages(\"kernlab\")\nlibrary(kernlab)\n# ksvm() 함수는 디폴트로 가우시안 RBF 커널을 사용하지만, 다양한 옵션도 제공한다.\n# SVM의 성능 측정 기준선을 마련하기 위해, 단순한 선형 SVM 분류기의 훈련으로 시작해보자.\nletter_classifier <- ksvm(letter ~ ., data = letters_train,\n kernel = \"vanilladot\") # vanilladot 옵션으로 선형 커널을 명시.\n\n# look at basic information about the model\n# 명령어를 동작시켜도, 실제 얼마나 잘 실행될 것인지에 대해서는 알려주지 않는다.\nletter_classifier\n# 모델이 범용 기능을 가지는지 알려면, 테스트 데이터 셋에 대한 성능을 검토해보자.\n\n## Step 4: Evaluating model performance ----\n# predictions on testing dataset 함수 predict() 이용\nletter_predictions <- predict(letter_classifier, letters_test)\n# type 파라미터를 지정하지 않았기 때문에, type =\"response\" 디폴트가 사용되었다. \n\nhead(letter_predictions)\n# 예측된 문자와 테스트 데이터셋에 있는 실제 문자 비교\ntable(letter_predictions, letters_test$letter)\n\n# look only at agreement vs. non-agreement(전체적인 정확도만 평가)\n# construct a vector of TRUE/FALSE indicating correct/incorrect predictions\nagreement <- letter_predictions == letters_test$letter\ntable(agreement)\nprop.table(table(agreement)) # 정확도 약 84%\n\n## Step 5: Improving model performance ----\n# 선형 커널 함수보다 더 복잡한 커널 함수를 사용해, 데이터를 더 높은 차원으로 매핑하여 더 나은 모델 적합 얻기 가능.\nset.seed(13123313)\n\nletter_classifier_rbf <- ksvm(letter ~ ., data = letters_train, kernel = \"rbfdot\")\nletter_predictions_rbf <- predict(letter_classifier_rbf, letters_test)\n\nagreement_rbf <- letter_predictions_rbf == letters_test$letter\ntable(agreement_rbf)\nprop.table(table(agreement_rbf)) # 정확도 93%로 증가\n", "meta": {"hexsha": "ac602c2ab1b149779150890b18760f268b02e6e9", "size": 7982, "ext": "r", "lang": "R", "max_stars_repo_path": "MLwR/Chapter 07/MLwR_v2_07(NN,SVM).r", "max_stars_repo_name": "BeginnerJay/R_STUDYING", "max_stars_repo_head_hexsha": "4dcca5a781cf550c8c40edc636c247357c95a296", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "MLwR/Chapter 07/MLwR_v2_07(NN,SVM).r", "max_issues_repo_name": "BeginnerJay/R_STUDYING", "max_issues_repo_head_hexsha": "4dcca5a781cf550c8c40edc636c247357c95a296", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "MLwR/Chapter 07/MLwR_v2_07(NN,SVM).r", "max_forks_repo_name": "BeginnerJay/R_STUDYING", "max_forks_repo_head_hexsha": "4dcca5a781cf550c8c40edc636c247357c95a296", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 36.6146788991, "max_line_length": 82, "alphanum_fraction": 0.6835379604, "num_tokens": 4585, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9566342037088041, "lm_q2_score": 0.822189123986562, "lm_q1q2_score": 0.786534237922924}} {"text": "## Author: Sergio García Prado\n## Title: Exercises with Solutions 1\n\nrm(list = ls())\n\n\nQ <- matrix(c(-1/3, 1/3, 0,\n 1/20, -1/4, 1/5,\n 1/2, 0, -1/2),\n 3, 3, byrow = TRUE)\n\n(A <- cbind(Q[, 1:(nrow(Q) - 1)], rep(1, nrow(Q))))\n# -0.3333333\t 0.3333333\t1\n# 0.0500000\t-0.2500000\t1\n# 0.5000000\t 0.0000000\t1\n\n(stationary <- solve(A)[nrow(A), ])\n# 0.348837209302326 0.465116279069767 0.186046511627907\n\nR <- Q[1:2, 1:2]\n(between.rainy <- (- solve(R) %*% rep(1, nrow(R)))[1])\n# 8.75\n\nr <- - Q / diag(Q)\n(a <- cbind(r[, 1:(nrow(r) - 1)], rep(1, nrow(r))))\n# -1.0\t 1\t1\n# 0.2\t-1\t1\n# 1.0 \t 0\t1\n\nsolve(a)[nrow(a), ]\n# 0.357142857142857 0.357142857142857 0.285714285714286\n", "meta": {"hexsha": "cc0461abaf7ca81ffd061d180909ff7d5e94f25b", "size": 706, "ext": "r", "lang": "R", "max_stars_repo_path": "stochastic-processes/proposed-exercises/continuous-1.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "stochastic-processes/proposed-exercises/continuous-1.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "stochastic-processes/proposed-exercises/continuous-1.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.0625, "max_line_length": 55, "alphanum_fraction": 0.5325779037, "num_tokens": 346, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9362849986365571, "lm_q2_score": 0.8397339656668287, "lm_q1q2_score": 0.7862303148994374}} {"text": "# Simulación de Variables Aleatorias\n\n# 5.5.1 Método de inversión\n#\n\n# --------------------------------------------------------------------------------\n# Eg\n\n# F(x) = 1-exp(-\\lambda x), x>= 0\n# u = F^-1 (x) ==> x = F^-1(u) = - frac{log(1-5)}{\\lambda}\n\nn <- 1000\nset.seed(1)\nu <- runif(n)\nlambda <- 0.5\nx <- -log(u) / lambda\nx[1:10]\n\n# Comprobamos que es una exponencial con lambda 0.5\nhist(x,\n freq = FALSE, breaks = \"FD\", main = \"Método de inversión (Exponencial)\",\n ylim = c(0, 0.5)\n)\nlines(density(x), col = \"blue\")\ncurve(dexp(x, rate = lambda), add = TRUE, col = 2)\n\n# Comprobamos con Kolmogorov - Smirnov:\nks.test(x, pexp, rate = lambda)\n\n# --------------------------------------------------------------------------------\n# Eg\n# Generamos desde una doble exp/de Cauchy\n# f(x) = \\l/2exp(-\\|x|) ==>\n# F(x) = \\{\n# x<0 -> exp(\\l/x)/2\n# x>0 -> 1-exp(\\l/x)/2\n# }\nddexp <- function(x, lambda) lambda * exp(-lambda * abs(x)) / 2\nrddexp <- function(n, lambda) {\n u <- runif(n)\n x <- ifelse(u < 0.5,\n log(2 * u) / lambda,\n -log(2 * (1 - u)) / lambda # este ifelse es la F^-1(u)\n )\n return(x)\n}\n\nn <- 1000\nset.seed(1)\nlambda <- 1\nx <- rddexp(n, lambda)\nx[1:10]\n\nhist(x,\n freq = FALSE, breaks = \"FD\", ylim = c(0, 0.6),\n main = \"Método de inversión (Doble exponencial)\"\n)\nlines(density(x), col = \"blue\")\ncurve(ddexp(x, lambda), add = TRUE, col = 2)\n\n# la función de distribución de la doble exponencial\npddexp <- function(x, lambda) {\n x <- ifelse(x < 0,\n exp(lambda * x) / 2,\n 1 - exp(-lambda * x) / 2\n )\n return(x)\n}\n# pasamos la función como argumento a ks.test()\nks.test(x, pddexp, lambda = lambda)\n\n# --------------------------------------------------------------------------------\n# EG Weibull\n# F(x) = 1-exp(l(\\l/x)^\\alpha)\n\nf <- function(x, lambda, alpha) {\n alpha * lambda^alpha * x^(alpha - 1) * exp(-(lambda * x)^alpha)\n}\n\nrweib <- function(n, lambda, alpha) {\n u <- runif(n)\n x <- (-log(1 - u))^(1 / alpha) / lambda\n return(x)\n}\n\nn <- 1000\nset.seed(1)\nlambda <- 0.5\nalpha <- 2\nx <- rweib(n, lambda, alpha)\nx[1:10]\n\nhist(x,\n freq = FALSE, breaks = \"FD\", ylim = c(0, 0.5),\n main = \"Método de inversión (Weibull)\"\n)\nlines(density(x), col = \"blue\")\ncurve(ddexp(x, lambda), add = TRUE, col = 2)\n\nks.test(x, pweibull, shape = alpha, scale = 1 / lambda)\n\n# Problema: y si la inversa es difícil de calcular? Numéricamente? Alternativa:\n\n# Método de aceptación-rechazo\n\n# 2 pasos:\n# Generamos un valor candidato para la variable aleatoria.\n# Aceptamos el valor generado sólo si veri\u001cca una condición particular.\n# Alg:\n# Generas U\n# Generas candidato Y desde g(y)\n# Comprobación:\n# U < 1/M * f(Y)/g(Y) ==> X = Y se acepta como valor simulado de f\n# Si no, se rechaza el valor\n\n# EG Beta desde Uniforme\na <- 2.7\nb <- 6.3\n# auxiliar? la uniforme basta. g(y) = unif\n# Necesitamos calcular la M\n\nres <- optimize(\n f = function(x) dbeta(x, shape1 = a, shape2 = b),\n maximum = TRUE, interval = c(0, 1)\n)\nres\nM <- res$objective\n\na <- 2.7\nb <- 6.3\ncurve(dbeta(x, shape1 = a, shape2 = b), 0, 1)\ncurve(M * dunif(x), 0, 1, add = TRUE, col = 2, lty = 2)\nlegend(\"right\",\n legend = c(\n \"f(x): Beta (a=2.7, b=6.3)\",\n \"g(x)*M\"\n ),\n col = c(1, 2), lty = c(1, 2), bty = \"n\"\n)\n\nn <- 1000\nx <- double(n)\nf <- function(x) dbeta(x, shape1 = a, shape2 = b)\ng <- function(x) 1\n# Generación de los n valores a través del algoritmo\nset.seed(1)\ncontador <- 0\nfor (i in 1:n) {\n repeat {\n u <- runif(1)\n y <- runif(1)\n contador <- contador + 1\n if (u <= f(y) / (M * g(y))) {\n break\n }\n }\n x[i] <- y\n}\n\n# Número de simulaciones total que han sido necesarias\ncontador\n# Veremos después que el número esperado\nn * M\n\n# Comprobamos que la secuencia generada procede de la distribución deseada\nhist(x, freq = FALSE, breaks = \"FD\", main = \"Método de aceptación-rechazo (Beta)\")\nlines(density(x), col = \"blue\")\ncurve(dbeta(x, shape1 = a, shape2 = b), add = TRUE, col = 2)\nks.test(x, pbeta, shape1 = a, shape2 = b)\n\n# Nota: eficiencia del algoritmo, elección de g\n# Cuanto más cerca esté M de 1, más eficiente será (M=1 ==> f = g, no tiene sentido)\n# En alguna familia paramétrica,\n# M_opt = min theta max x f(x)/g_theta(x)\n\n# EG Tomamos una doble exponencial como aux:\n\n# Densidad de la doble exponencial:\nddexp <- function(x, lambda) lambda * exp(-lambda * abs(x)) / 2\n# Construimos una función que dado lambda nos da el M óptimo\nM.lambda <- function(lambda) {\n optimize(\n f = function(x) dnorm(x) / ddexp(x, lambda), maximum = TRUE,\n interval = c(0, 2)\n )$objective\n}\n# Minimizamos la función anterior en lambda para obtener el óptimo\n# y el correspondiente M\nres <- optimize(M.lambda, interval = c(0.5, 2))\nres\n\nlambda.opt <- res$minimum\nM <- res$objective\n\ncurve(dnorm(x), -3, 3, ylim = c(0, 0.7))\ncurve(M * ddexp(x, lambda.opt), add = TRUE, col = 2, lty = 2)\nlegend(\"topright\",\n legend = c(\"f(x): N(0,1)\", \"g(x)*M\"),\n col = c(1, 2), lty = c(1, 2), bty = \"n\"\n)\n\n# Función para simular de la doble exponencial (método de inversión)\nrddexp <- function(n, lambda) {\n u <- runif(n)\n x <- ifelse(u < 0.5, log(2 * u) / lambda, -log(2 * (1 - u)) / lambda)\n return(x)\n}\n# Método de aceptación-rechazo para simular la normal\nn <- 1000\nx <- double(n)\nf <- function(x) dnorm(x)\ng <- function(x) ddexp(x, lambda = lambda.opt)\n# Generación de los n valores a través del algoritmo\nset.seed(1)\ncontador <- 0\nfor (i in 1:n) {\n u <- runif(1)\n y <- rddexp(1, lambda.opt)\n contador <- contador + 1\n while (u > f(y) / (M * g(y))) {\n u <- runif(1)\n y <- rddexp(1, lambda.opt)\n contador <- contador + 1\n }\n x[i] <- y\n}\n# Número de simulaciones total que han sido necesarias\ncontador\n# El número esperado es\nn * M\n# Comprobamos que la secuencia generada procede de la distribución deseada\nhist(x, freq = FALSE, breaks = \"FD\", main = \"Método de aceptación-rechazo (Normal)\")\nlines(density(x), col = \"blue\")\ncurve(dnorm(x), add = TRUE, col = 2)\n# Confirmamos con el test de Kolmogorov-Smirnov\nks.test(x, pnorm)\n\n1 / M # tasa de aceptación\n\n# --------------------------------------------------------------------------------\n# modif a A-R\n\n# --------------------------------------------------------------------------------\n# Otros métodos\n\n# Composición\n# Si la densidad objetivo es una mixtura discreta de densidades\n# eso es, es la suma (discreta ie no integral) de funciones de densidad\n# -> escoges j.\n# -> generas X desde f_j\n\n# Box Muller\n# Para generar normales independientes\n# E <- Exp(1); U <- Unif\n# ==> X1 = sqrt(2E) cos(2piU) es normal\n# ==> X2 = sqrt(2E) sin(2piU) es normal\n# y son indep\n\n# Aplicaciones\n# aproximar la distribución de estimadores\n\n# EG 1\nmu <- 10\nsigma <- 1\nn <- 10 # tamaño de la muestra\nnsim <- 1000 # número de simulaciones\n# simulamos nsim=1000 muestras de tamaño n=10\n# y las almacenamos por filas en una matriz (nsim*n)\nset.seed(1)\nmuestras <- matrix(rnorm(nsim * n, mean = mu, sd = sigma), ncol = n, nrow = nsim)\n# A partir de cada muestra calculamos la media muestral\nmedias <- rowMeans(muestras)\n# medias contiene los nsim=1000 valores simulados de la media muestral\n# un histograma de estos valores nos da una aproximación de la distribución muestral\nhist(medias, breaks = 20, freq = FALSE, main = \"Distribución muestral de la media\")\n# superponemos la densidad suavizada\nlines(density(medias), col = \"blue\")\n# ahora la distribución exacta (N(mu, sigma/sqrt(n)))\ncurve(dnorm(x, mean = mu, sd = sigma / sqrt(n)), col = 2, add = TRUE)\n\n\n\n# Ej Comprobar TCL\n# 1.\n# 2.\n# 3.\n\n\n# Eg 2 mediana\n\nmu <- 10\nsigma <- 1\nn <- 10 # tamaño de la muestra\nnsim <- 1000 # número de simulaciones\n# simulamos nsim=1000 muestras de tamaño n=10\n# y las almacenamos por filas en una matriz (nsim*n)\nset.seed(1)\nmuestras <- matrix(rnorm(nsim * n, mean = mu, sd = sigma), ncol = n, nrow = nsim)\n# A partir de cada muestra calculamos la medianal\nmedianas <- apply(muestras, 1, median)\n# medianas contiene los nsim=1000 valores simulados de la media muestral\n# un histograma de estos valores nos da una aproximación de la distribución muestral\nhist(medianas, breaks = 20, xlim = c(9, 11), freq = FALSE, main = \"Distribución muestral de la mediana\")\n# superponemos la densidad suavizada\nlines(density(medianas), col = \"blue\")\n\n\n# Comparación de estimadores\n\n# Sea f una f densidad de una N(0,1) contaminada por una N(3,3) con frecuencias 0.95, 0.05 respectivamente.\n# Con el método de composición:\nn <- 100\nset.seed(1)\nj <- rbinom(n, 1, 0.05) # 1's y 0's indicando si es f2 o f1, respectivamente\nx <- rnorm(n, 3 * j, 1 + 2 * j) # esto genera n valores de f1 o f2 dependiendo de j\n# representamos un histograma de la muestra generada\nhist(x, breaks = \"FD\", freq = FALSE, main = \"Muestra contaminada\")\n# superponemos la densidad desde la que se generó\ncurve(0.95 * dnorm(x, 0, 1) + 0.05 * dnorm(x, 3, 3), add = TRUE, col = 2)\n# Con datos anómalos\nmean(x)\nmedian(x)\n# Dan resultados similares\n\nn <- 100\nset.seed(1)\nj <- rbinom(n * nsim, 1, 0.05)\nmuestras <- matrix(rnorm(n * nsim, 3 * j, 1 + 2 * j), nrow = nsim, ncol = n)\n# cada fila de la matriz 'muestras' es una muestra de tamaño n\n# calculamos los estimadores\nmedias <- apply(muestras, 1, mean)\nmedianas <- apply(muestras, 1, median)\n# comparamos la distribución muestral usando un boxplot\nboxplot(medias, medianas, names = c(\"Media\", \"Mediana\"))\n# una línea horizontal indicando el valor a estimar (mu=0)\nabline(h = 0, col = 2)\n# La media se ve bastante afectada por valores anómalos\n\n# Estimamos los errores cuadráticos medios E[(theta_gorro - theta)^2]\necm.media <- mean((medias - 0)^2)\necm.media\necm.mediana <- mean((medianas - 0)^2)\necm.mediana\n# boxplot de las desviaciones al cuadrado\nboxplot(medias^2, medianas^2,\n ylab = \"Errores cuadráticos\",\n names = c(\"Media\", \"Mediana\")\n)", "meta": {"hexsha": "3d66f5accc84d8d032d4a9abd29624a9ec4ee721", "size": 9854, "ext": "r", "lang": "R", "max_stars_repo_path": "clases/Clase 2022-05-24.r", "max_stars_repo_name": "LucasFA/EC", "max_stars_repo_head_hexsha": "a3822b94fc1c97f3096c9fd40cd3140ee85a5ac8", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "clases/Clase 2022-05-24.r", "max_issues_repo_name": "LucasFA/EC", "max_issues_repo_head_hexsha": "a3822b94fc1c97f3096c9fd40cd3140ee85a5ac8", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "clases/Clase 2022-05-24.r", "max_forks_repo_name": "LucasFA/EC", "max_forks_repo_head_hexsha": "a3822b94fc1c97f3096c9fd40cd3140ee85a5ac8", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 28.316091954, "max_line_length": 107, "alphanum_fraction": 0.6111223868, "num_tokens": 3327, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9086179043564153, "lm_q2_score": 0.8652240877899775, "lm_q1q2_score": 0.7861580974464205}} {"text": "## Author: Sergio García Prado\n\nrm(list = ls())\n\ny <- c(1997, 904, 906)\nk <- length(y) + 1\nn <- 3839\n\n\n## a)\n####\n\nLogLikelihood <- function(p, y, n) {\n sum(y * log(p)) + (n - sum(y)) * log(1 - sum(p))\n}\n\nNegativeLogLikelihood <- function(...) {\n - LogLikelihood(...)\n}\n\nopt <- optim(rep(1 / k, k - 1), NegativeLogLikelihood, y = y, n = n,\n hessian = TRUE)\np.hat <- opt$par\np.hat.var <- solve(opt$hessian)\n\ng.function <- function(p) {\n c(4 * p[1] + 4 * p[2] - 3,\n p[2] - p[3])\n}\n\ng.derivative <- function(p) {\n matrix(c(4, 4, 0,\n 0, 1, -1),\n 2, 3, byrow = TRUE)\n}\n\ng.zero <- rep(0, 2)\n\n## Sandwitch Estimator.\n(W <- (g.function(p.hat) - g.zero) %*% g.derivative(p.hat) %*% p.hat.var %*% t(g.derivative(p.hat)) %*% (g.function(p.hat) - g.zero))\n# 3.809448e-07\n\n(W.pvalue <- 1 - pchisq(W, df = 2))\n# 0.9999998\n\n## b)\n####\n\nLogLikelihoodH0 <- function(theta, y, n) {\n LogLikelihood(c((2 + theta) / 4, (1 - theta) / 4,\n (1 - theta) / 4), y, n)\n}\n\nNegativeLogLikelihoodH0 <- function(...) {\n - LogLikelihoodH0(...)\n}\n\nopt.hzero <- optim(runif(1), NegativeLogLikelihoodH0, y = y, n = n,\n hessian = TRUE)\n(theta.hat <- opt.hzero$par)\n# 0.0357236506373738\n\n(theta.hat.var <- solve(opt.hzero$hessian)[1])\n# 3.63072505048225e-05\n\n(LRT <- 2 * (LogLikelihood(p.hat, y, n) - LogLikelihoodH0(theta.hat, y, n)))\n# 2.01858568600073\n\n(LRT.pvalue <- 1 - pchisq(LRT, df = 2))\n# 0.364476630661476\n\n## c)\n####\n\n# Done in (b).\n\n\n## d)\n####\n\nalpha <- 0.05\n\n## Classic Wald Confidence Interval.\ntheta.hat + c(-1, 1) * qnorm(1 - alpha / 2) * sqrt(theta.hat.var)\n# 0.0238929671430484 0.0474947392364342\n\n\n## Likelihood Ratio Confidence Interval.\n## We'll look for the intersection between LogLikelihood function and Chisq critic value.\n\nf <- function(theta, p, y, n, alpha, df) {\n 2 * (LogLikelihood(p, y, n) - LogLikelihoodH0(theta, y, n)) - qchisq(1 - alpha / 2, df = df)\n}\n\nc(uniroot(f, c(0, theta.hat), p.hat, y, n, alpha, df=2)$root,\n uniroot(f, c(theta.hat, 1), p.hat, y, n, alpha, df=2)$root)\n# 0.0234000324864232 0.0513203185453315\n", "meta": {"hexsha": "0dd2023e5e91628b74cd0778c16eb469f0808670", "size": 2094, "ext": "r", "lang": "R", "max_stars_repo_path": "statistical-inference/likelihood/exercise-09.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "statistical-inference/likelihood/exercise-09.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "statistical-inference/likelihood/exercise-09.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 21.3673469388, "max_line_length": 133, "alphanum_fraction": 0.5778414518, "num_tokens": 809, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9381240090865197, "lm_q2_score": 0.8376199673867852, "lm_q1q2_score": 0.7857914018958109}} {"text": "# ************************************************\n### simon munzert\n### logit and probit\n# ************************************************\n\nsource(\"packages.r\")\nsource(\"functions.r\")\n\n\n### Running a logit model -----------------------\n\ndata(\"turnout\") # example dataset from the Zeliig package\n?turnout\ntabyl(turnout$vote)\n\n# estimation with glm function\nlogit_out <- glm(vote ~ age + educate + income,\n family = binomial, data = turnout)\nsummary(logit_out)\n\n# estimation with manually programmed logit likelihood function\n# see also http://www.stat.cmu.edu/~cshalizi/uADA/12/lectures/ch12.pdf\nlogit_loglik <- function(theta, y, X){\n b <- theta\n logl <- sum(-y*log(1+exp(- X %*% b)) # for y = 1\n - (1-y)*log(1+exp(X %*% b))) # for y = 0\n return(-logl)\n}\t\n\nlogit_out_manual <- optim(rep(1,4), logit_loglik, y = turnout$vote, X = as.matrix(cbind(1,(turnout[,c(\"age\", \"educate\", \"income\")]))), method = \"BFGS\") \nlogit_out_manual \n\n\n### Running a probit model ---------------------\n\n# estimation with glm function\nprobit_out <- glm(vote ~ age + educate + income,\n family = binomial(link = \"probit\"), data = turnout)\nsummary(probit_out) # careful - the coefficients are not directly comparable with those from the logit model! (Divide logit coefficients by approximately 1.6 to arrive at probit coefficients; see http://andrewgelman.com/2006/06/06/take_logit_coef/)\n\n# again, a little simulation\nn <- 100\nx <- rnorm (n) \na <- 1.5 \nb <- 1 \ny <- rbinom (n, 1, invlogit(a + b*x)) \nM1 <- glm (y ~ x, family=binomial(link=\"logit\")) \nsummary (M1)\nM2 <- glm(y ~ x, family=binomial(link=\"probit\")) \nsummary (M2)\n\n\n\n\n### Goodness of fit ----------------------------\n\n# Log-Likelihood\nLogLik <- logLik(logit_out)\nLogLik\n\n# McFadden's Pseudo-R^2 \nlogit_out_empty <- glm(vote ~ 1, family = binomial, data = turnout) # estimate empty model \nPseudo_R2 <- 1 - (as.numeric(logLik(logit_out)))/(as.numeric(logLik(logit_out_empty)))\nPseudo_R2\n\n# Likelihood ratio Chi-squared\nchi2_test_stat <- 2*(as.numeric(logLik(logit_out)) - as.numeric(logLik(logit_out_empty)))\nlr_test <- 1 - pchisq(chi2_test_stat, 1)\nchi2_test_stat\nlr_test\n \n# BIC\n# see J. Scott Long and Jeremy Freese 2000. Stata Technical Bulletin STB-56:34-40\nD.M.mod <- as.numeric(-2*LogLik)\nN <- length(logit_out$y)\nk <- length(logit_out$coef)\ndf.mod <- N - k\nBIC.mod <- D.M.mod - df.mod*log(N)\nBIC.mod\n\n\n### Precision and recall -----------------------\n\nturnout$vote_pred_link <- predict(logit_out, type = \"link\")\nturnout$vote_pred_prob <- predict(logit_out, type = \"response\")\nturnout$vote_pred <- ifelse(turnout$vote_pred_prob > .5, 1, 0)\n\nplot(turnout$vote_pred_link, turnout$vote_pred_prob) # links versus response\n\ntab <- table(turnout$vote, turnout$vote_pred)\ncolnames(tab) <- c(\"pred vote NO\", \"pred vote YES\")\nrownames(tab) <- c(\"rep vote NO\", \"rep vote YES\")\ntab\n\n# precision:\nsum(turnout$vote_pred == 1 & turnout$vote == 1) / sum(turnout$vote_pred == 1)\n\n# recall:\nsum(turnout$vote_pred == 1 & turnout$vote == 1) / sum(turnout$vote == 1)\n\n\n\n### From log odds to odds ratios and probabilities ---\n\nsummary(logit_out)\ncbind(log_odds <- round(coef(logit_out), 4),\n odds_ratios <- round(exp(coef(logit_out)), 4),\n probabilities <- round(1/(1+exp(-coef(logit_out))), 4))\n\n# look at an empty model again to understand how the log odds and the probability are related\nlogit_out_empty <- glm(vote ~ 1,\n family = binomial, data = turnout)\nsummary(logit_out_empty)\nsummary(turnout$vote)\n1/(1+exp(-coef(logit_out_empty)))\n\n\n# here's a little logit to probability function\nlogit2prob <- function(logit){\n odds <- exp(logit)\n prob <- odds / (1 + odds)\n return(prob)\n}\nlogit2prob(.5)\nlogit2prob(-.5)\n\n\n### Predict marginal effects with the margins package ---\n\nlibrary(margins)\nsummary(logit_out)\nmargins(logit_out, type = \"link\") # this equals the log odds\n\nmargins(logit_out, type = \"response\") # this equals marginal probabilities\n\nmargins(logit_out, at = list(age = c(25, 60),\n educate = c(10, 10),\n income = c(3, 3)))\n\nmarginal_effects(logit_out) # unit-specific marginal effects with respect to all variables \n\n\n### Visualize probabilities - graphical solution ---\n\ndf <- data.frame(age = min(turnout$age):max(turnout$age), educate = 10, income = 4) \nmodel_preds <- predict(logit_out, newdata = df, type = 'response', se.fit = TRUE)\ndf$prediction <- model_preds$fit \ndf$lower <- model_preds$fit - 1.96 * model_preds$se.fit \ndf$upper <- model_preds$fit + 1.96 * model_preds$se.fit\n\n# graph predicted probabilities\nggplot(df) + geom_line(aes(x = age, y = prediction)) + theme_bw() + geom_ribbon(aes(ymin = lower, ymax = upper, x = age), alpha = .3)\n\n# alternatively, use cplot() command from the margins package\ncplot(logit_out, \"age\")\n\n# graph marginal effects\ncplot(logit_out, \"age\", what = \"effect\")\n\n\n\n\n## Interactions in logit models -------------\n\nlogit_out_int <- glm(vote ~ educate + income*age,\n family = binomial, data = turnout)\nsummary(logit_out_int)\n\nhist(turnout$income)\n\ndf <- data.frame(educate = 12, age = rep(min(turnout$age):max(turnout$age), 10), income = rep(1:10, each = diff(range(turnout$age))+1))\nmodel_preds <- predict(logit_out, newdata = df, type = 'response', se.fit = TRUE)\ndf$prediction <- model_preds$fit \n\nplot(df$age, df$prediction, cex = 0)\nincome_values <- unique(df$income)\nfor(i in income_values) { \n with(filter(df, income == income_values[i]), lines(age, prediction))\n }\n#plot(df$income, df$prediction)\n\n# also see \nbrowseURL(\"https://cran.r-project.org/web/packages/margins/vignettes/Introduction.html\") \n# --> section \"Interactions in Logit\"\n\n\n## Credit Default data -------------\n\n?Default\ndat <- Default\ndat$def <- ifelse(as.numeric(dat$default) == 2, 1, 0)\ntable(dat$def)\n\npdf(file=\"../output/logit-viz-1.pdf\", height=4, width=6, family=\"URWTimes\")\npar(oma=c(0,0,0,0))\npar(mar=c(4,4,1.2,.5))\nplot(dat$balance, dat$def, col = \"blue\", xlab = \"Balance\", ylab = \"Credit default (No/Yes)\")\nabline(h=0:1, lty = 3)\nabline(h=.5, lty = 3)\ndev.off()\n\npdf(file=\"../output/logit-viz-2.pdf\", height=4, width=6, family=\"URWTimes\")\npar(oma=c(0,0,0,0))\npar(mar=c(4,4,1.2,.5))\nplot(dat$balance, dat$def, col = \"blue\", xlab = \"Balance\", ylab = \"Credit default (No/Yes)\")\nabline(h=0:1, lty = 3)\nabline(h=.5, lty = 3)\nabline(lm(def~balance, data = dat), col = \"red\", lwd = 2)\ndev.off()\n\npdf(file=\"../output/logit-viz-3.pdf\", height=4, width=6, family=\"URWTimes\")\npar(oma=c(0,0,0,0))\npar(mar=c(4,4,1.2,.5))\nplot(dat$balance, dat$def, col = \"blue\", xlab = \"Balance\", ylab = \"Credit default (No/Yes)\")\nabline(h=0:1, lty = 3)\nabline(h=.5, lty = 3)\n# logit fit\nfit = glm(def ~ balance, data=dat, family = binomial)\nnewdat <- data.frame(balance = seq(min(dat$balance), max(dat$balance),len=100))\nnewdat$vs = predict(fit, newdata=newdat, type=\"response\")\nlines(vs ~ balance, newdat, col=\"red\", lwd=2)\ndev.off()\n\npdf(file=\"../output/logit-viz-4.pdf\", height=4, width=6, family=\"URWTimes\")\npar(oma=c(0,0,0,0))\npar(mar=c(4,4,1.2,.5))\nplot(dat$balance, dat$def, col = \"blue\", xlab = \"Balance\", ylab = \"Credit default (No/Yes)\")\nabline(h=0:1, lty = 3)\nabline(h=.5, lty = 3)\n# logit fit\nfit = glm(def ~ balance, data=dat, family = binomial)\nnewdat <- data.frame(balance = seq(min(dat$balance), max(dat$balance),len=100))\nnewdat$vs = predict(fit, newdata=newdat, type=\"response\")\nlines(vs ~ balance, newdat, col=\"red\", lwd=2)\nabline(v=c(500, 1000), col = \"black\", lwd = 3)\narrows(500, .3, 1000, .3, lwd = 3)\ndev.off()\n\npdf(file=\"../output/logit-viz-5.pdf\", height=4, width=6, family=\"URWTimes\")\npar(oma=c(0,0,0,0))\npar(mar=c(4,4,1.2,.5))\nplot(dat$balance, dat$def, col = \"blue\", xlab = \"Balance\", ylab = \"Credit default (No/Yes)\")\nabline(h=0:1, lty = 3)\nabline(h=.5, lty = 3)\n# logit fit\nfit = glm(def ~ balance, data=dat, family = binomial)\nnewdat <- data.frame(balance = seq(min(dat$balance), max(dat$balance),len=100))\nnewdat$vs = predict(fit, newdata=newdat, type=\"response\")\nlines(vs ~ balance, newdat, col=\"red\", lwd=2)\nabline(v=c(1500, 2000), col = \"black\", lwd = 3)\narrows(1500, .3, 2000, .3, lwd = 3)\ndev.off()\n\n\n## Probability and cumulative density functions --------------\n\n# probability and cumulative density functions of the logistic distribution\nz_scores <- seq(-5, 5, by = .1)\ndlogistic_values <- dlogis(z_scores, 0, 1)\nplot(z_scores, dlogistic_values, type = \"l\", main = \"pdf of the Logistic\", xlab= \"Z score\", ylab=\"Probability Density\", col = \"blue\") \n\ndlogistic_values <- plogis(z_scores, 0, 1)\nplot(z_scores, dlogistic_values, type = \"l\", main = \"cdf of the Logistic\", xlab= \"Z score\", ylab=\"Probability Density\", col = \"blue\") \n# playing with the scale parameter\nlines(z_scores, plogis(z_scores, 0, 2), col = \"red\") \nlines(z_scores, plogis(z_scores, 0, .5), col = \"red\")\n# playing with the location parameter\nlines(z_scores, plogis(z_scores, -2, 1), col = \"green\")\nlines(z_scores, plogis(z_scores, 2, 1), col = \"green\")\n\n# probability and cumulative density functions of the standard normal distribution\nz_scores <- seq(-5, 5, by = .1)\ndnorm_values <- dnorm(z_scores, 0, 1)\nplot(z_scores, dnorm_values, type = \"l\", main = \"pdf of the Standard Normal\", xlab= \"Z score\", ylab=\"Probability Density\", col = \"blue\") \n\ndnorm_values <- pnorm(z_scores, 0, 1)\nplot(z_scores, dnorm_values, type = \"l\", main = \"cdf of the Standard Normal\", xlab= \"Z score\", ylab=\"Probability Density\", col = \"blue\") \n\n\n", "meta": {"hexsha": "6a66d638e3b6759ca284ef90e0e88b9a2b2aca88", "size": 9489, "ext": "r", "lang": "R", "max_stars_repo_path": "code/08-logit-probit.r", "max_stars_repo_name": "simonmunzert/stats-II-hertie-2017", "max_stars_repo_head_hexsha": "f577db8b0b5f2599e7896907233ef6871d793253", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "code/08-logit-probit.r", "max_issues_repo_name": "simonmunzert/stats-II-hertie-2017", "max_issues_repo_head_hexsha": "f577db8b0b5f2599e7896907233ef6871d793253", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "code/08-logit-probit.r", "max_forks_repo_name": "simonmunzert/stats-II-hertie-2017", "max_forks_repo_head_hexsha": "f577db8b0b5f2599e7896907233ef6871d793253", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2017-09-18T08:04:57.000Z", "max_forks_repo_forks_event_max_datetime": "2018-03-22T08:28:12.000Z", "avg_line_length": 33.8892857143, "max_line_length": 248, "alphanum_fraction": 0.6538096744, "num_tokens": 2984, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9263037343628703, "lm_q2_score": 0.8479677526147223, "lm_q1q2_score": 0.7854756958663078}} {"text": "### 線形回帰分析(重回帰)の例\n### - New York Air Quality Measurements\n\n## パッケージの読み込み\nrequire(tidyverse) \nrequire(ggfortify)\nrequire(GGally)\n\n## データの読み込み (\"datasets::airquality\"を用いる)\ndata(airquality) # データの読み込み\nhelp(airquality) # 内容の詳細を表示\nstr(airquality) # データの構造を表示\n\n## データの内容を表示\nhead(airquality,n=10) # 最初のnデータを表示\ntail(airquality,n=10) # 最後のnデータを表示\n## print(airquality) では表示が長すぎる\n\n## データのプロット (pairs plot)\nmydat <- airquality %>%\n mutate(Level=ifelse(Ozone>60,\"high\",ifelse(Ozone<20,\"low\",\"mid\"))) \nmydensity <- function(data, mapping, ...) {\n ggplot(data = data, mapping = mapping) +\n geom_point(...,colour=\"gray50\",size=1) +\n geom_density_2d(alpha=.8)\n}\nggpairs(na.omit(mydat), columns=1:4,\n upper=list(continuous=mydensity),\n lower=list(continuous=wrap(\"smooth_loess\"),\n mapping=aes(colour=Level))) +\n theme(axis.title.x=element_text(size=10),\n axis.title.y=element_text(size=10)) # 文字の大きさを調整\n\n## データの素性を確認\nis.data.frame(airquality) # データフレームかどうか確認\nnames(airquality) # 各列の名称を調べる\ndim(airquality) # データフレームのサイズを調べる\n\n## 回帰分析 (Ozoneを目的変数，Solar.R, Wind, Tempを説明変数)\nmodel <- lm(Ozone ~ Solar.R + Wind + Temp, data=airquality)\nsummary(model) # 分析のまとめ\n\n## モデルの計算結果を表示する関数群\ncoef(model) # または coefficients(model): モデルの係数 \nresid(model) # または residuals(model): 各データの残差\nfitted(model) # または fitted.values(model): 各データの予測値\n## これ以外にも以下が用意されている\n## effects(model) \n## deviance(model)\n## df.residual(model)\n## anova(model)\n## モデルが保持している情報の要素名を調べるには\n## names(model) \n## 各要素の表示を行うには\n## model$coefficients, model$residuals, model$fitted.values\n## などとすればよい\n\n## 当て嵌り具合を表示\nmydat <- airquality %>%\n mutate(Date=as.Date(paste(Month,Day,\"73\",sep=\"/\"),\"%m/%d/%y\"),\n Pred=predict(model, newdata=airquality))\nggplot(mydat, aes(Date)) +\n geom_line(aes(y=Ozone,colour=\"true\"), size=1) +\n geom_line(aes(y=Pred, colour=\"predict\"), size=1) +\n scale_colour_manual(values=c(predict=\"blue\",true=\"red\")) + # lineの色を指定\n theme(legend.position=c(.9,.9)) # 凡例の位置を指定\n\n## 診断プロット (いろいろと問題の多いモデルであることがわかる)\nautoplot(model)\n\n## モデルの指定方法 \n## 風量(Wind) と 温度(Temp) で回帰\nsummary(lm(Ozone ~ Wind + Temp, data=airquality))\n## 切片を0として Wind と Temp で回帰\nsummary(lm(Ozone ~ Wind + Temp - 1, data=airquality))\n## Wind と Temp の積の効果まで入れて回帰\nsummary(lm(Ozone ~ Wind * Temp, data=airquality))\n## Wind と Temp の積と Wind で回帰\nsummary(lm(Ozone ~ Wind * Temp - Temp, data=airquality))\n## Wind の2次多項式で回帰\nsummary(lm(Ozone ~ Wind + I(Wind^2), data=airquality))\n## Wind の2次直交多項式で回帰\nsummary(lm(Ozone ~ poly(Wind,2), data=airquality))\n\n## 関数 update によるモデルの更新方法\n## Wind のみで回帰\nsummary(model <- lm(Ozone ~ Wind, data=airquality))\n## Solar.R を加える\nsummary(model <- update(model, . ~ . + Solar.R, data=airquality))\n## Solar.R の積の効果を加える\nsummary(model <- update(model, . ~ . * Solar.R, data=airquality))\n## 切片を 0 にする\nsummary(model <- update(model, . ~ . -1 , data=airquality))\n\n## AICによる最適なモデルの自動探索\n## 初期モデルの設定 (ここでは全ての相互作用を含むモデルを用いる)\nsummary(model <- lm(Ozone ~ Solar.R * Wind * Temp, data=airquality))\n## AICの意味で最適なモデルを探索\nsummary(opt <- step(model))\n\n## 当て嵌り具合を表示\nmydat <- airquality %>%\n mutate(Date=as.Date(paste(Month,Day,\"73\",sep=\"/\"),\"%m/%d/%y\"),\n Pred=predict(model, newdata=airquality))\nggplot(mydat, aes(Date)) +\n geom_line(aes(y=Ozone,colour=\"true\"), size=1) +\n geom_line(aes(y=Pred, colour=\"predict\"), size=1) +\n scale_colour_manual(values=c(predict=\"blue\",true=\"red\")) + # lineの色を指定\n theme(legend.position=c(.9,.9)) # 凡例の位置を指定\n\n## 診断プロット (前モデルよりは改善されていることがわかる)\nautoplot(model) \n\n## 回帰式による予測\n## 8月までのデータで回帰式を推定\nsummary(model <- lm(formula(opt), # 上で探索されたモデルを利用\n data=airquality, subset=(Month<9)))\n## 9月のデータを予測\nidx <- with(airquality,Month==9) # 9月のデータのindexを取得\npred <- predict(model,newdata=airquality[idx,], # 9月分を予測\n interval=\"prediction\",level=0.7)\nmydat <- data.frame(airquality[idx,], pred) # 9月のデータとその予測\nggplot(mydat, aes(Day)) +\n geom_ribbon(aes(ymin=lwr,ymax=upr), fill=\"red\", alpha=0.2)+\n geom_line(aes(y=Ozone,colour=\"true\"), size=1) +\n geom_line(aes(y=fit, colour=\"predict\"), size=1) +\n theme(legend.position=c(.9,.9)) + # 凡例の位置を指定\n labs(title=\"Ozone Level Prediction (September; 70% pred. int.)\",x=\"Day\",y=\"Ozone\")\n", "meta": {"hexsha": "2b069b6f704c677388b366bc78869195b6d4e2bf", "size": 4207, "ext": "r", "lang": "R", "max_stars_repo_path": "docs/code/r-airquality.r", "max_stars_repo_name": "noboru-murata/multivariate-analysis", "max_stars_repo_head_hexsha": "645bff23d3868e5d7c245ef4af7d0ff9fe98e017", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "docs/code/r-airquality.r", "max_issues_repo_name": "noboru-murata/multivariate-analysis", "max_issues_repo_head_hexsha": "645bff23d3868e5d7c245ef4af7d0ff9fe98e017", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "docs/code/r-airquality.r", "max_forks_repo_name": "noboru-murata/multivariate-analysis", "max_forks_repo_head_hexsha": "645bff23d3868e5d7c245ef4af7d0ff9fe98e017", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 32.6124031008, "max_line_length": 86, "alphanum_fraction": 0.6802947469, "num_tokens": 1822, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.930458251637412, "lm_q2_score": 0.8438950947024555, "lm_q1q2_score": 0.785209154382235}} {"text": "rm(list=ls())\nset.seed(34)\n\n# sample size\nN = 50\n\n\n# explanatory variables\nmake_x = function(n=N, xmin=0, xmax=100){\n return (runif(n, xmin, xmax))\n}\n\n# define true model\nb0 = 15\nb1 = 0.5\nf = function(x){\n return (b0 + b1 * x)\n}\n\n# generate disturbances\nsd_e = 4\nmake_epsilon = function(n=N, mean=0, sd=sd_e){\n return (rnorm(n, mean, sd)) \n}\n\n# make data generating process\ndgp = function(){\n x = make_x()\n y = f(x)+make_epsilon()\n return (data.frame(x=x,y=y))\n}\n\n# estime by ols once and show results\ndf = dgp()\n\npng('C:/Users/Евгений/Documents/GitHub/multiple-regression-revisited/ols_true_model.png')\n\nplot(df$x,df$y, xlab = \"x\", ylab=\"y\", main=\"Observations and true model y=15+.5x+e\")\nabline(a=b0,b=b1,col=\"green\")\n\ndev.off()\n\n\n# TODO: make plot for distrubance term\n# plot(make_x(), make_epsilon())\n\nlm1 <- lm(y~x, data = df)\nabline(lm1, col=\"red\")\nsummary(lm1)\n\n\nextract_b0 = function(lm_){\n return (coef(lm_)[1])\n}\n\nextract_b1 = function(lm_){\n return (coef(lm_)[2])\n}\n\n# repeat estimation \nget_b1 = function(){extract_b1(lm(y~x, data = dgp()))}\n\nn_experiments = 1000\nb1_list = replicate(n_experiments, get_b1())\n\n\n# plot estimator desities \nb1_avg = mean(b1_list)\nb1_sd = sd(b1_list)\n\npng('C:/Users/Евгений/Documents/GitHub/multiple-regression-revisited/ols_b1.png')\n\nh = hist(b1_list, breaks=40, freq=FALSE, \n main=paste(\"Distribution of b1 on\", n_experiments,\"experiments\"),\n sub=paste(\"True value:\", b1, \" \",\n \"Mean: \", round(b1_avg,4), \" \",\n \"SD: \", round(b1_sd,4)),\n xlab=\"b1\",\n col=\"lightblue\")\n#curve(dnorm(x, mean=b1_avg, sd=b1_sd), add=TRUE, col=\"darkblue\", lwd=2) \nlines(density(b1_list), col=\"darkblue\", lwd=2) \nabline(v=b1, col =\"green\")\nabline(v=b1_avg, col =\"red\")\ndev.off()\n", "meta": {"hexsha": "21e4de6851ae3e74b09ff8630bbd272b46a7e694", "size": 1783, "ext": "r", "lang": "R", "max_stars_repo_path": "r/ols.r", "max_stars_repo_name": "epogrebnyak/multiple-regression-revisited", "max_stars_repo_head_hexsha": "8881d5a8cab31693d3ca652b3e96c6fbbaf318b0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 3, "max_stars_repo_stars_event_min_datetime": "2018-11-26T17:11:56.000Z", "max_stars_repo_stars_event_max_datetime": "2019-07-02T07:06:56.000Z", "max_issues_repo_path": "r/ols.r", "max_issues_repo_name": "epogrebnyak/multiple-regression-revisited", "max_issues_repo_head_hexsha": "8881d5a8cab31693d3ca652b3e96c6fbbaf318b0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "r/ols.r", "max_forks_repo_name": "epogrebnyak/multiple-regression-revisited", "max_forks_repo_head_hexsha": "8881d5a8cab31693d3ca652b3e96c6fbbaf318b0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2019-07-02T07:06:57.000Z", "max_forks_repo_forks_event_max_datetime": "2019-07-02T07:06:57.000Z", "avg_line_length": 20.9764705882, "max_line_length": 89, "alphanum_fraction": 0.6382501402, "num_tokens": 599, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9173026663679976, "lm_q2_score": 0.8558511524823263, "lm_q1q2_score": 0.7850745441861616}} {"text": "1+1\r\nx <- c(1,3,4,5,6)\r\nx\r\nprint(x)\r\nx*3\r\nx+6\r\nx/2\r\nx^4\r\ny <- seq(1:length(x))\r\nx%*%y\r\ndrop(x%*%y)\r\nz <- runif(100)\r\nstr(z) \r\nhead(z)\r\ntail(z) \r\nZ <- matrix(z, nrow=5, byrow=FALSE)\r\ndim(Z) \r\nstr(Z) \r\nx%*%Z\r\ndrop(x%*%Z)\r\nx[2:3]\r\nx[c(2:3,5)]\r\nZ[,1]\r\nZ[,2:3]\r\nZ[1:2,2:4]\r\nps <- function(x, a=1) a*x^2\r\nps(2)\r\nps(5)\r\nps(4, 3)\r\nps <- function(x, a=1) {\r\n z <- a*x^2 \r\n return(z)\r\n}\r\nps(5)\r\nps(4, 3)\r\nps <- function(x, a=1) { z <- a*x^2; z }\r\nps(x=x, a=3)\r\nps(x=3, a=x) \r\nps <- function(x, a=1) {\r\n if (a >= 0) {\r\n z <- a*x^2\r\n } else {\r\n z <- a*x^3\r\n }\r\n return(z)\r\n}\r\nps(4, 2)\r\nps(4, -2)\r\nps <- function(x, a=1) {\r\n z <- ifelse (a >= 0, a*x^2, a*x^3)\r\n return(z)\r\n}\r\nps(x, a=-2)\r\nps(x, a=2) \r\nps(x, a=c(-2, 2)) \r\n\r\ngenere <- sample(c(\"M\", \"F\"), size=170, replace=TRUE)\r\nstr(genere)\r\naltezza <- rnorm(170, 170, 1)\r\nstr(altezza)\r\nhist(altezza)\r\nhist(altezza, xlab=\"Altezza (cm)\", ylab=\"Frequenza\", main=\"La vostra altezza\") \r\nboxplot(altezza) \r\ntable(genere)\r\nboxplot(split(altezza, genere))\r\n \r\n ", "meta": {"hexsha": "eeba544cbc0fc09c9722c70d109722ad1446b5a0", "size": 1053, "ext": "r", "lang": "R", "max_stars_repo_path": "code/Intro.r", "max_stars_repo_name": "mfranzil/PSUniTN", "max_stars_repo_head_hexsha": "c4baecf5b01fb7cc2cfc66f4881ae47451475dac", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "code/Intro.r", "max_issues_repo_name": "mfranzil/PSUniTN", "max_issues_repo_head_hexsha": "c4baecf5b01fb7cc2cfc66f4881ae47451475dac", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "code/Intro.r", "max_forks_repo_name": "mfranzil/PSUniTN", "max_forks_repo_head_hexsha": "c4baecf5b01fb7cc2cfc66f4881ae47451475dac", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 15.7164179104, "max_line_length": 81, "alphanum_fraction": 0.4700854701, "num_tokens": 473, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9073122113355091, "lm_q2_score": 0.8652240686758841, "lm_q1q2_score": 0.7850283630510227}} {"text": "\r\n# Function to combine binned data based on the mean and standard deviation of the bins and their sample sizes.\r\n# Based on: \"Combining Multiple binmeand Data Points And Their Errors\" by Ken Tatebe (http://docplayer.net/33088897-Combining-multiple-binmeand-data-points-and-their-errors.html)\r\n# And: \"Data Analyis Toolkit #12\" by James Kirchner (http://seismo.berkeley.edu/~kirchner/Toolkits/Toolkit_12.pdf)\r\n# Approach for combining more than two bins while weighting uncertainty and means by sample size and variance within the bin\r\n# Worked out by Barbara Goudsmit (see SI document)\r\n\r\nbinmeans <- function(x, x_sd = NA, n = NA, verbose = FALSE, output = \"All\"){\r\n if(is.na(n)){\r\n n = rep(1, length(x)) # If no N are given, the bins are assumed to have equal sample sizes\r\n }\r\n if(is.na(x_sd)){\r\n x_sd = rep(1, length(x)) # If no SDs of the bins are given, the bins are assumed to have equal variance\r\n }\r\n if(length(n) == 1){\r\n N = n[1] # In case only one entry is provided, the mean and SD of the one entry are returned as the mean and SD of the result\r\n binmean = x[1]\r\n SD_bin = x_sd[1]\r\n }else{\r\n N <- sum(n) # Calculate total sample size\r\n binmean <- sum(x * n * x_sd ^ -2) / sum(n * x_sd ^ -2) # Calculate weighted binmean (equation 16 in SI document)\r\n SD_bin <- sqrt(sum(n) / (sum(n) - 1) * sum((n - 1) + x_sd ^ -2 * n * (x - binmean) ^ 2) / sum(n * x_sd ^ -2)) # Calculate weighted standard deviation (equation 17 in SI document)\r\n }\r\n resultvec <- c(binmean, SD_bin, N)\r\n names(resultvec) <- c(\"binmean\", \"sd\", \"N\")\r\n if(output == \"SD\"){\r\n return(resultvec[2])\r\n }else if(output == \"mean\"){\r\n return(resultvec[1])\r\n }else if(output == \"All\"){\r\n return(resultvec)\r\n }else{\r\n return(\"Error: output string not recognized\")\r\n }\r\n}\r\n", "meta": {"hexsha": "568a22b80d2016f0751795c78f3e188c1ed28299", "size": 1870, "ext": "r", "lang": "R", "max_stars_repo_path": "03_Average_error_propagation.r", "max_stars_repo_name": "nielsjdewinter/Aragonite_clumped", "max_stars_repo_head_hexsha": "bb45ac98cddfc879b7b943a9166a9bb158352aa9", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2022-01-27T09:11:14.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-27T09:11:14.000Z", "max_issues_repo_path": "03_Average_error_propagation.r", "max_issues_repo_name": "nielsjdewinter/Aragonite_clumped", "max_issues_repo_head_hexsha": "bb45ac98cddfc879b7b943a9166a9bb158352aa9", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2022-01-27T11:17:53.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-27T11:17:53.000Z", "max_forks_repo_path": "03_Average_error_propagation.r", "max_forks_repo_name": "nielsjdewinter/Aragonite_clumped", "max_forks_repo_head_hexsha": "bb45ac98cddfc879b7b943a9166a9bb158352aa9", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2022-01-27T09:24:23.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-27T09:24:23.000Z", "avg_line_length": 51.9444444444, "max_line_length": 187, "alphanum_fraction": 0.6278074866, "num_tokens": 522, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9546474246069458, "lm_q2_score": 0.8221891370573386, "lm_q1q2_score": 0.7849007422315956}} {"text": "library(ggplot2)\n\n\nm = 1 #rotation order\n\n\nphi = seq(0,2*pi,length.out = 100)\nr = seq(0,1,length.out = 50)\n\nreal_filter = function(r,phi,m)exp(-r^2)*cos(phi*m)\nimg_filter = function(r,phi,m)exp(-r^2)*sin(phi*m)\n\n\n\ndf = expand.grid(phi = phi, r = r)\ndf$real_filter = real_filter(df$r,df$phi,m)\ndf$img_filter = img_filter(df$r,df$phi,m)\n\n\n\ndf$input = 0\ndf$input[df$phi > 0 & df$phi < pi/6 & df$r>0.48 & df$r<0.52] = 1\ndf$input[df$phi > pi/12-0.01 & df$phi < pi/12+0.01 & df$r>0.3 & df$r<0.7] = 1\n\np_in <- ggplot(df) + geom_tile(aes(phi,r,fill=input))+ coord_polar(direction = -1,start=3*pi/2)\n\n# plot the original image on the polar coordinates\nplot(p_in)\n\n\n\ndf$input_rotate = 0\ndf$input_rotate[df$phi > 0+pi/2 & df$phi < pi/6+pi/2 & df$r>0.48 & df$r<0.52] = 1\ndf$input_rotate[df$phi > pi/12+pi/2-0.01 & df$phi < pi/12+0.01+pi/2 & df$r>0.3 & df$r<0.7] = 1\np_in_rotate <- ggplot(df) + geom_tile(aes(phi,r,fill=input_rotate))+ coord_polar(direction = -1,start=3*pi/2)\n\n\n# plot the rotated image on the polar coordinates (pi/2, counter-clockwise)\nplot(p_in_rotate)\n\n\n# kernel weights\np_real <- ggplot(df) + geom_tile(aes(phi,r,fill=real_filter))+ coord_polar(direction = -1,start=3*pi/2)\np_img <- ggplot(df) + geom_tile(aes(phi,r,fill=img_filter))+ coord_polar(direction = -1,start=3*pi/2)\n\n\n# Real and imaginary part of the convolution operation, which resulted in a complex number\nout_real = sum(df$input*df$real_filter)\nout_img = sum(df$input*df$img_filter)\n\nout_real_rotate = sum(df$input_rotate*df$real_filter)\nout_img_rotate = sum(df$input_rotate*df$img_filter)\n\n\nplot(0,0,type='n',xlim = c(-100,100),ylim = c(-100,100))\nabline(h=0,lty = 2)\nabline(v=0,lty = 2)\nlines(c(0,out_real),c(0,out_img),col=2)\nlines(c(0,out_real_rotate),c(0,out_img_rotate),col=3)\n\n\n", "meta": {"hexsha": "9f1f6ec4122f1bb9c84ee809c29675dc0e1c6b5a", "size": 1758, "ext": "r", "lang": "R", "max_stars_repo_path": "project/proof-of-concept/harmonic_filters.r", "max_stars_repo_name": "amorehead/Equivariant-GNNs", "max_stars_repo_head_hexsha": "4e81136242a4c8905b0e5fc39be5f704a42cc5e1", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2021-10-07T12:53:51.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-04T19:26:08.000Z", "max_issues_repo_path": "project/proof-of-concept/harmonic_filters.r", "max_issues_repo_name": "amorehead/Equivariant-GNNs", "max_issues_repo_head_hexsha": "4e81136242a4c8905b0e5fc39be5f704a42cc5e1", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "project/proof-of-concept/harmonic_filters.r", "max_forks_repo_name": "amorehead/Equivariant-GNNs", "max_forks_repo_head_hexsha": "4e81136242a4c8905b0e5fc39be5f704a42cc5e1", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 28.3548387097, "max_line_length": 109, "alphanum_fraction": 0.6854379977, "num_tokens": 633, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9489172659321806, "lm_q2_score": 0.826711787666479, "lm_q1q2_score": 0.7844810892663807}} {"text": "n = c(50,59,161,88,20,40,56,52,188,4,3,5,2,66,6)\r\nE=c(67.5,67.5,135,37,37,74,74,74,148,3,3,6,18.5,18.5,37)\r\n# test statistic\r\nXsquare = 0\r\ni=1\r\nwhile(i<=length( n)){\r\n Xsquare=Xsquare+(((n[i]-E[i])^2)/E[i])\r\n i=i+1\r\n}\r\nprint(Xsquare)\r\n# critical value\r\nalpha = 0.001\r\nX.alpha=qchisq(1-alpha,df=8)\r\n# The computed value of xsquare is greater than x.alpha, so we reject the null hypothes\r\n\r\n", "meta": {"hexsha": "bea185843dbfaa7361aba6d9e4fdc40120992656", "size": 391, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH10/EX10.14/Ex10_14.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH10/EX10.14/Ex10_14.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH10/EX10.14/Ex10_14.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 24.4375, "max_line_length": 88, "alphanum_fraction": 0.6342710997, "num_tokens": 172, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9314624993576759, "lm_q2_score": 0.8418256412990657, "lm_q1q2_score": 0.784129015867806}} {"text": "# computing probabilties and quantiles in R\r\n\r\n# computing T quantile for one d.f. \r\n# arguments are probability, d.f.\r\n\r\nqt(0.975, 10)\r\n\r\n# can also provide many d.f. or probabilities\r\n\r\nqt(0.975, c(10,20))\r\n\r\n# going backward: computing probability from T value\r\n# arguments are value, d.f.\r\n\r\npt(2, 10)\r\n\r\n# and can apply to many \r\n\r\npt(2, c(10,20))\r\n\r\n# same for Chi-square: only one indicated\r\n\r\nqchisq(0.975,10)\r\npchisq(38.2,20)\r\n\r\n# often want upper tail prob. (default is lower)\r\npchisq(38.2,20,lower=F)\r\n\r\n# which is same as 1-pchisq(38.2,20)\r\n", "meta": {"hexsha": "dd8099398cfb69adfcb0f1469563df44940a26b2", "size": 553, "ext": "r", "lang": "R", "max_stars_repo_path": "RFrontEndSolution/Tests Repo/Rscripts All (163 files)/pq.r", "max_stars_repo_name": "AlexandrosPlessias/CompilerFrontEndForRLanguage", "max_stars_repo_head_hexsha": "71e3e60476f6f83b05cc97c625265edbde086341", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "RFrontEndSolution/Tests Repo/Rscripts All (163 files)/pq.r", "max_issues_repo_name": "AlexandrosPlessias/CompilerFrontEndForRLanguage", "max_issues_repo_head_hexsha": "71e3e60476f6f83b05cc97c625265edbde086341", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "RFrontEndSolution/Tests Repo/Rscripts All (163 files)/pq.r", "max_forks_repo_name": "AlexandrosPlessias/CompilerFrontEndForRLanguage", "max_forks_repo_head_hexsha": "71e3e60476f6f83b05cc97c625265edbde086341", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 18.4333333333, "max_line_length": 53, "alphanum_fraction": 0.6618444846, "num_tokens": 179, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9559813513911654, "lm_q2_score": 0.8198933381139645, "lm_q1q2_score": 0.7838027413668014}} {"text": "N <- 1000\ngamma <- 0.9\nalpha <- 1\nFinalState <- 6\n\nRMatrix <- matrix(c(-1,50,1,-1,-1,-1,\n -1,-1,-1,1,50,-1,\n -1,-1,-1,1,-1,-1,\n -1,-1,-1,-1,-1,100,\n -1,-1,-1,50,-1,-1,\n -1,-1,-1,-1,-1,100),nrow=6,byrow = TRUE)\n\nprint(RMatrix)\n\nQMatrix <- matrix(rep(0,length(RMatrix)), nrow=nrow(RMatrix))\n\nfor (i in 1:N) {\n \n CurrentState <- sample(1:nrow(RMatrix), 1)\n \n repeat {\n \n AllNS <- which(RMatrix[CurrentState,] > -1)\n if (length(AllNS)==1)\n NextState <- AllNS\n else\n NextState <- sample(AllNS,1)\n \n QMatrix[CurrentState,NextState] <- QMatrix[CurrentState,NextState] + alpha*(RMatrix[CurrentState,NextState] + gamma*max(QMatrix[NextState, which(RMatrix[NextState,] > -1)]) - QMatrix[CurrentState,NextState])\n \n if (NextState == FinalState) break\n CurrentState <- NextState\n }\n}\n\nprint(QMatrix)\n\nRowMaxPos<-apply(QMatrix, 1, which.max)\nShPath <- list(1)\ni=1\nwhile (i!=6) {\n IndRow<- RowMaxPos[i]\n ShPath<-append(ShPath,IndRow)\n i= RowMaxPos[i]\n}\n\nprint(ShPath)\n\n", "meta": {"hexsha": "29453a71edfe214ea8d219ee9b96b3c320d913d1", "size": 1101, "ext": "r", "lang": "R", "max_stars_repo_path": "Chapter07/ShortPathQLearn.r", "max_stars_repo_name": "CiaburroGiuseppe/Hands-On-Reinforcement-Learning-with-R", "max_stars_repo_head_hexsha": "5966656378792ea3d65a62e283e2bf3c74467ffc", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 6, "max_stars_repo_stars_event_min_datetime": "2020-01-19T06:32:15.000Z", "max_stars_repo_stars_event_max_datetime": "2021-10-04T06:37:07.000Z", "max_issues_repo_path": "Chapter07/ShortPathQLearn.r", "max_issues_repo_name": "CiaburroGiuseppe/Hands-On-Reinforcement-Learning-with-R", "max_issues_repo_head_hexsha": "5966656378792ea3d65a62e283e2bf3c74467ffc", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Chapter07/ShortPathQLearn.r", "max_forks_repo_name": "CiaburroGiuseppe/Hands-On-Reinforcement-Learning-with-R", "max_forks_repo_head_hexsha": "5966656378792ea3d65a62e283e2bf3c74467ffc", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 7, "max_forks_repo_forks_event_min_datetime": "2019-12-25T17:17:42.000Z", "max_forks_repo_forks_event_max_datetime": "2021-07-30T13:19:18.000Z", "avg_line_length": 22.4693877551, "max_line_length": 211, "alphanum_fraction": 0.5622161671, "num_tokens": 375, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9381240108164657, "lm_q2_score": 0.8354835371034368, "lm_q1q2_score": 0.7837871667986036}} {"text": "#!/usr/bin/Rscript\n\n# Copyright © 2016 Martin Ueding \n# Licensed under the MIT license.\n\nmyprint = function(varname, var) {\n cat(paste0(varname, ':', '\\n'))\n print(var)\n cat('\\n')\n}\n\nnumber_of_generations = function() {\n iterations = 0\n repeat {\n u = runif(1, min=-1, max=1)\n v = runif(1, min=-1, max=1)\n\n iterations = iterations + 1\n\n r_sq = u^2 + v^2\n\n if (r_sq <= 1) {\n break;\n }\n }\n\n return(iterations)\n}\n\nnumbers = replicate(10000, number_of_generations())\nmyprint('numbers', numbers)\n\naverage_number = mean(numbers)\nmyprint('average_number', average_number)\n\n# Define the function again, this time it returns an actual data type\nbox_muller_alternative_1 = function() {\n repeat {\n u = runif(1, min=-1, max=1)\n v = runif(1, min=-1, max=1)\n\n s = u^2 + v^2\n\n if (s <= 1) {\n break;\n }\n }\n\n z = sqrt(- 2 * log(s) / s)\n x1 = z * u\n x2 = z * v\n\n return(c(x1, x2))\n}\n\n# Draw a bunch of samples\nsamples = matrix(replicate(10000, box_muller_alternative_1()), nrow=1)\n\n# Make a quantile-quantile plot which the actual against the theoretical\n# quantiles. That should quickly tell whether the resulting numbers are sampled\n# from a normal distribution.\nqqnorm(samples)\nlines(c(-4, 4), c(-4, 4))\ngrid()\n", "meta": {"hexsha": "8e28b987a0618e17d2a6f16e859730a41481f2b4", "size": 1355, "ext": "r", "lang": "R", "max_stars_repo_path": "02/R/accept-reject.r", "max_stars_repo_name": "martin-ueding/exercides-2016", "max_stars_repo_head_hexsha": "a16a5a8bd9b0acd5f84ef5156e0a220c7ceb27e7", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "02/R/accept-reject.r", "max_issues_repo_name": "martin-ueding/exercides-2016", "max_issues_repo_head_hexsha": "a16a5a8bd9b0acd5f84ef5156e0a220c7ceb27e7", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "02/R/accept-reject.r", "max_forks_repo_name": "martin-ueding/exercides-2016", "max_forks_repo_head_hexsha": "a16a5a8bd9b0acd5f84ef5156e0a220c7ceb27e7", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 20.8461538462, "max_line_length": 79, "alphanum_fraction": 0.5977859779, "num_tokens": 408, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9263037241905732, "lm_q2_score": 0.8459424450764199, "lm_q1q2_score": 0.7835996373251671}} {"text": "rm(list = ls()) #cleaning up\nlibrary(utils)\nlibrary(tidyverse)\n\ndata <- as.tibble(read.csv(\"demo.csv\"))\nmodel <- lm(GDP ~ FHouse, data=data)\n\nggplot(data, aes(x = FHouse, y = GDP)) +\n geom_point()+\n geom_smooth(method='lm')\n\npredict(model, data.frame(FHouse=c(3)))\nsummary(model)\n\n##### conditional expectations: E[GDP|FHouse=fh] ####\ncond_exp <- c()\nfor(fh in c(sort(unique(data$FHouse)))){\n cond_exp <- c(cond_exp, mean(data$GDP[data$FHouse==fh]) )\n}\ncond_exp\n\n#### plotting them\nfh <- sort(unique(data$FHouse))\nmeans <- data.frame(fh, cond_exp)\nggplot(data, aes(x = FHouse, y = GDP)) +\n geom_point()+\n geom_smooth(method='lm')+\n geom_point(data=means, aes(x=fh, y=cond_exp), color=\"green\")\n\n#### Change the model\n\nmodel2 <- lm(GDP ~ FHouse + I(FHouse^2), data=data)\n\nggplot(data, aes(x = FHouse, y = GDP)) +\n geom_point()+\n geom_smooth(method='lm', formula= y ~ x + I(x^2))+\n geom_point(data=means, aes(x=fh, y=cond_exp), color=\"green\")\n\npredict(model2, data.frame(FHouse=c(3)))\nsummary(model2)\n\n### differences\nfh1 <- predict(model2, data.frame(FHouse=c(1)))\nfh3 <- predict(model2, data.frame(FHouse=c(3)))\n\ndiff_fh_3_1 <- fh3 - fh1\n\nfh4 <- predict(model2, data.frame(FHouse=c(4)))\nfh6 <- predict(model2, data.frame(FHouse=c(6)))\n\ndiff_fh_6_4 <- fh6 - fh4\n", "meta": {"hexsha": "6988c78cc0408bc3ed8c921a433d865fb3b9870c", "size": 1269, "ext": "r", "lang": "R", "max_stars_repo_path": "exam3.r", "max_stars_repo_name": "samuxiii/r-projects", "max_stars_repo_head_hexsha": "13a17bdf5a3db2efcf785c4810bb55c86459bfb3", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "exam3.r", "max_issues_repo_name": "samuxiii/r-projects", "max_issues_repo_head_hexsha": "13a17bdf5a3db2efcf785c4810bb55c86459bfb3", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "exam3.r", "max_forks_repo_name": "samuxiii/r-projects", "max_forks_repo_head_hexsha": "13a17bdf5a3db2efcf785c4810bb55c86459bfb3", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 5, "max_forks_repo_forks_event_min_datetime": "2019-06-24T17:18:38.000Z", "max_forks_repo_forks_event_max_datetime": "2020-07-22T03:39:37.000Z", "avg_line_length": 24.4038461538, "max_line_length": 62, "alphanum_fraction": 0.6627265563, "num_tokens": 399, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9425067195846919, "lm_q2_score": 0.8311430520409023, "lm_q1q2_score": 0.7833579114846797}} {"text": "# Perceptron\r\nPLA <- function(x, y, maxit = 1000, plotLn = FALSE, traceFlg = FALSE) {\r\n # Add in bias?\r\n x <- cbind(x, bias = rep(1, nrow(x)))\r\n # Initialize\r\n iter <- 0\r\n Cost <- 100\r\n w <- matrix(rep(0, ncol(x)), ncol=ncol(x))\r\n \r\n while(Cost > 0 & iter < maxit) {\r\n iter <- iter + 1\r\n # Predict\r\n h <- sign(x %*% t(w))\r\n \r\n misclassified <- which(h != y)\r\n Cost <- length(misclassified)\r\n \r\n if (Cost > 0) {\r\n # Update\r\n # hkReeves pointed out that sample(c(10),1) will give a random number between 1 and 10\r\n pickOne <- ifelse(Cost == 1, misclassified, sample(misclassified, 1))\r\n # Update weight vector\r\n # w <- w + t(y[pickOne]) %*% x[pickOne,]\r\n w <- w + y[pickOne] * x[pickOne,]\r\n }\r\n if(plotLn) abline(w[2], w[1], col = iter)\r\n if(traceFlg) print(paste(\"At iter\", iter, \"Cost \", Cost))\r\n }\r\n return(list(iter = iter, w = w))\r\n}\r\n\r\n# Pick which side of the line this should be on\r\nchooseSide <- function(f, x) {\r\n m <- matrix(c(f[2,1] - f[1,1], x[1] - f[1,1], \r\n f[2,2] - f[1,2], x[2] - f[1,2]), \r\n byrow=TRUE, nrow=2)\r\n sign(det(m))\r\n}\r\n\r\n\r\n# Run many simulations\r\nN <- 10\r\niterations = list()\r\nfor (runs in seq(1000)) {\r\n # Create linearly separable data\r\n # Choose a line in X^2 {-1, 1}\r\n f <- matrix(c(runif(2, min = -1, max = 1), -1, 1),\r\n nrow = 2)\r\n # Get uniformly distributed points in {-1, 1}\r\n x <- matrix(runif(2 * N, min=-1, max=1), ncol=2)\r\n # Figure out which side of our line they are on\r\n y <- apply(x, 1, function(z) chooseSide(f, z))\r\n \r\n # Fit perceptron model\r\n fit <- PLA(x, y, maxit=10000, plotLn=FALSE)\r\n iter <- fit$iter\r\n w <- fit$w\r\n iterations <- c(iterations, iter)\r\n}\r\n\r\n# Distribution of trials\r\nsummary(unlist(iterations))\r\n\r\n\r\n# Test one\r\nplot(x[,1], x[,2], pch = y+2, col = y+2)\r\nlines(f, lwd = 3)\r\n\r\nfit <- PLA(x, y, maxit=100, plotLn=FALSE, traceFlg=TRUE)\r\n\r\n# Plot perceptron\r\nabline(fit$w[2], fit$w[1], lty= 3)\r\ntitle(paste(\"Perceptron at step\", fit$iter))\r\n\r\n\r\n# mydf <- as.data.frame(cbind(y, x))\r\n# colnames(mydf) <- c(\"y\", \"x1\", \"x2\")\r\n# \r\n# library(ggplot2)\r\n# qplot(x1, x2, data = mydf, color=factor(y)) + \r\n# geom_abline(aes(intercept = w[2], slope = w[1]))\r\n\r\n", "meta": {"hexsha": "e079f11939dbf1e9ec4838c1d26f6530fa9b2449", "size": 2245, "ext": "r", "lang": "R", "max_stars_repo_path": "Homework_1/Rcode/perceptron_hw1_by_sanealytics.r", "max_stars_repo_name": "freeernest/edX-Learning-From-Data-Solutions", "max_stars_repo_head_hexsha": "5cbcf0885b5fdb00c3658d230fc7bb7e20b5cf44", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 79, "max_stars_repo_stars_event_min_datetime": "2015-01-27T11:09:24.000Z", "max_stars_repo_stars_event_max_datetime": "2022-02-05T12:01:35.000Z", "max_issues_repo_path": "Homework_1/Rcode/perceptron_hw1_by_sanealytics.r", "max_issues_repo_name": "freeernest/edX-Learning-From-Data-Solutions", "max_issues_repo_head_hexsha": "5cbcf0885b5fdb00c3658d230fc7bb7e20b5cf44", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2018-08-25T05:45:11.000Z", "max_issues_repo_issues_event_max_datetime": "2018-12-04T14:44:32.000Z", "max_forks_repo_path": "Homework_1/Rcode/perceptron_hw1_by_sanealytics.r", "max_forks_repo_name": "freeernest/edX-Learning-From-Data-Solutions", "max_forks_repo_head_hexsha": "5cbcf0885b5fdb00c3658d230fc7bb7e20b5cf44", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": 40, "max_forks_repo_forks_event_min_datetime": "2015-04-06T18:43:34.000Z", "max_forks_repo_forks_event_max_datetime": "2021-03-28T18:08:40.000Z", "avg_line_length": 27.0481927711, "max_line_length": 93, "alphanum_fraction": 0.5478841871, "num_tokens": 798, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9449947148047777, "lm_q2_score": 0.8289388125473628, "lm_q1q2_score": 0.7833427967538061}} {"text": "log1pexp <- function(x)\n{\n ## taken from https://github.com/mfasiolo/qgam/blob/3bff42449b865a12c264c5b61438def5d74fdc70/R/log1pexp.R\n indx <- .bincode(x, \n c(-Inf, -37, 18, 33.3, Inf), \n right = TRUE, \n include.lowest = TRUE)\n \n kk <- which(indx==1)\n if( length(kk) ){ x[kk] <- exp(x[kk]) }\n \n kk <- which(indx==2)\n if( length(kk) ){ x[kk] <- log1p( exp(x[kk]) ) }\n \n kk <- which(indx==3)\n if( length(kk) ){ x[kk] <- x[kk] + exp(-x[kk]) }\n \n return(x)\n}\n####\n\nlogPr <- function(x, n, rho0){\n -log1pexp(\n log1p(-rho0)-log(rho0) +\n n * log(2) + \n lbeta(x + 1, n -x +1)\n )\n}\n\nf_rho <- function(rho){\n exp(logPr(x = 5, n = 10, rho0 = rho))\n}\nf_rho <- Vectorize(f_rho)\n\ncurve(f_rho, xlab = expression(rho), ylab = \"Posterior probability\",\n main = \"x = 5, n = 10\")\n\nf_x <- function(x){\n exp(logPr(x = x, n = 10, rho0 = 1/2))\n}\nf_x <- Vectorize(f_x)\n\ncurve(f_x, 0, 10,\n xlab = expression(rho), ylab = \"Posterior probability\",\n main = \"x = 5, n = 10\")", "meta": {"hexsha": "330ae1daed39e26ee82e4045510348778bbbb413", "size": 1046, "ext": "r", "lang": "R", "max_stars_repo_path": "code/example_5.2.7.r", "max_stars_repo_name": "lucasmoschen/BayesianStatisticsCourse", "max_stars_repo_head_hexsha": "79fe17dd71fa9638ae4865c8e75eeb0f814d2ccb", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 6, "max_stars_repo_stars_event_min_datetime": "2021-03-17T17:39:29.000Z", "max_stars_repo_stars_event_max_datetime": "2022-02-15T23:40:56.000Z", "max_issues_repo_path": "code/example_5.2.7.r", "max_issues_repo_name": "anhnguyendepocen/BayesianStatisticsCourse", "max_issues_repo_head_hexsha": "79fe17dd71fa9638ae4865c8e75eeb0f814d2ccb", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 6, "max_issues_repo_issues_event_min_datetime": "2021-03-24T01:28:22.000Z", "max_issues_repo_issues_event_max_datetime": "2022-02-16T20:49:10.000Z", "max_forks_repo_path": "code/example_5.2.7.r", "max_forks_repo_name": "anhnguyendepocen/BayesianStatisticsCourse", "max_forks_repo_head_hexsha": "79fe17dd71fa9638ae4865c8e75eeb0f814d2ccb", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2021-05-26T16:28:02.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-23T12:33:26.000Z", "avg_line_length": 23.2444444444, "max_line_length": 107, "alphanum_fraction": 0.5219885277, "num_tokens": 406, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9173026528034426, "lm_q2_score": 0.8539127566694177, "lm_q1q2_score": 0.7832964369555574}} {"text": "# Example : 4 Chapter : 8.3 Page No: 437\n# Linear Algebra in Economy\nA<-matrix(c(0.2,0.4,0.5,0.3,0.4,0.1,0.4,0.1,0.3),ncol=3)\nlambda<-eigen(A)$values\nprint(\"Lambda max is \")\nprint(lambda[1])\nI<-matrix(c(1,0,0,0,1,0,0,0,1),ncol=3)\nA1<-solve(I-A)\nprint(A1)\n#The answers may vary due to rounding off values\n", "meta": {"hexsha": "f94b4967c57d33ddd2f62c13833bae2b7832841d", "size": 310, "ext": "r", "lang": "R", "max_stars_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.4/Ex8.3_4.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.4/Ex8.3_4.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.4/Ex8.3_4.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 28.1818181818, "max_line_length": 56, "alphanum_fraction": 0.6516129032, "num_tokens": 140, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9304582497090321, "lm_q2_score": 0.8418256551882382, "lm_q1q2_score": 0.7832836256866073}} {"text": "# y has a normal distribution with mean = 160 and sd = 20.\r\n# the probability that a single blood pressure measurement will fail to detect that the patient has high blood pressure is <150\r\npnorm(150,mean =160,sd=20)\r\n# If five blood pressure measurements are taken at various times during the day\r\nsd <-20/sqrt(5)\r\n # the probability that the average of the five measurements will be less than 150\r\npnorm(150,160,sd=8.94)\r\n# measurements would be required in a given day so that there\r\n#is at most 1% probability of failing to detect that the patient has high blood pressure\r\nstandard_deviation=20\r\nn=((-2.326*standard_deviation)/(150-160))^2\r\nprint(n)\r\n# It would require at least 22 measurements in order to achieve\r\n# the goal of at most a 1% chance of failing to detect high blood pressure.\r\n\r\n\r\n\r\n", "meta": {"hexsha": "e6d04a241a04c51345071e3655b228dac6156c3c", "size": 807, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH4/EX4.24/Ex4_24.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH4/EX4.24/Ex4_24.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH4/EX4.24/Ex4_24.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 44.8333333333, "max_line_length": 129, "alphanum_fraction": 0.7484510533, "num_tokens": 205, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9693241974031599, "lm_q2_score": 0.8080672066194945, "lm_q1q2_score": 0.7832790965042549}} {"text": "\nAuto = read.csv(\"../../../data/Auto.csv\", header = T, na.strings = \"?\")\nAuto = na.omit(Auto)\nsummary(Auto)\n\nlm.fit1 = lm(mpg ~ horsepower, data = Auto)\nsummary(lm.fit1)\n\npredict(lm.fit1, data.frame(horsepower=c(98)), interval=\"confidence\")\n\npredict(lm.fit1, data.frame(horsepower=c(98)), interval=\"prediction\")\n\nplot(Auto$horsepower, Auto$mpg, main = \"Scatterplot of mpg vs. horsepower\", xlab = \"horsepower\", ylab = \"mpg\", col = \"blue\")\nabline(lm.fit1, col = \"red\")\n\npar(mfrow = c(2, 2))\nplot(lm.fit1)\n\npairs(Auto)\n\ncor(subset(Auto, select = -name))\n\nlm.fit2 = lm(mpg ~ . - name, data = Auto)\nsummary(lm.fit2)\n\npar(mfrow = c(2, 2))\nplot(lm.fit2)\n\nlm.fit3 = lm(mpg ~ .*., data = Auto[, 1:8])\nsummary(lm.fit3)\n\npar(mfrow = c(2, 2))\nplot(log(Auto$horsepower), Auto$mpg)\nplot(sqrt(Auto$horsepower), Auto$mpg)\nplot((Auto$horsepower)^2, Auto$mpg)\n\nCarseats = read.csv(\"../../../data/Carseats.csv\", header=T, na.strings=\"?\")\n\nsummary(Carseats)\n\nattach(Carseats)\nlm.fit4 = lm(Sales ~ Price + Urban + US)\nsummary(lm.fit4)\n\nlm.fit5 = lm(Sales ~ Price + US)\nsummary(lm.fit5)\n\nconfint(lm.fit5)\n\nplot(predict(lm.fit5), rstudent(lm.fit5))\n\npar(mfrow = c(2, 2))\nplot(lm.fit5)\n\nset.seed(1)\nx = rnorm(100)\ny = 2 * x + rnorm(100)\n\nlm.fit6 = lm(y ~ x + 0)\nsummary(lm.fit6)\n\nlm.fit7 = lm(x ~ y + 0)\nsummary(lm.fit7)\n\nn = length(x)\nt = sqrt(n - 1)*(x %*% y)/sqrt(sum(x^2) * sum(y^2) - (x %*% y)^2)\nas.numeric(t)\n\nlm.fit8 = lm(y ~ x)\nsummary(lm.fit8)\n\nlm.fit9 = lm(x ~ y)\nsummary(lm.fit9)\n\nset.seed(1)\nx = 1:100\ny = 2 * x + rnorm(100, sd = 0.1)\nlm.fit10 = lm(y ~ x + 0)\nsummary(lm.fit10)\n\nlm.fit11 = lm(x ~ y + 0)\nsummary(lm.fit11)\n\nx = 1:100\ny = 100:1\nlm.fit12 = lm(y ~ x + 0)\nsummary(lm.fit12)\n\nlm.fit13 = lm(x ~ y + 0)\nsummary(lm.fit13)\n\nset.seed(1)\nx = rnorm(100)\n\neps = rnorm(100, sd = 0.25)\n\ny = -1 + 0.5 * x + eps\nlength(y)\n\nplot(x, y)\n\nlm.fit14 = lm(y ~ x)\nsummary(lm.fit14)\n\nplot(x, y)\nabline(lm.fit14, col = \"red\")\nabline(-1, 0.5, col = \"blue\")\nlegend(\"topleft\", c(\"Least square\", \"Regression\"), col = c(\"red\", \"blue\"), lty = c(1, 1))\n\nlm.fit15 = lm(y ~ x + I(x^2))\nsummary(lm.fit15)\n\nset.seed(1)\nx = rnorm(100)\neps = rnorm(100, sd = 0.0025)\ny = -1 + 0.5 * x + eps\nplot(x, y)\n\nlm.fit16 = lm(y ~ x)\nsummary(lm.fit16)\n\nabline(lm.fit16, col = \"red\")\nabline(-1, 0.5, col = \"blue\")\nlegend(\"topleft\", c(\"Least square\", \"Regression\"), col = c(\"red\", \"blue\"), lty = c(1, 1))\n\nset.seed(1)\nx = rnorm(100)\neps = rnorm(100, sd = 2.5)\ny = -1 + 0.5 * x + eps\nplot(x, y)\n\nlm.fit17 = lm(y ~ x)\nsummary(lm.fit17)\n\nabline(lm.fit17, col = \"red\")\nabline(-1, 0.5, col = \"blue\")\nlegend(\"topleft\", c(\"Least square\", \"Regression\"), col = c(\"red\", \"blue\"), lty = c(1, 1))\n\nconfint(lm.fit14)\n\nconfint(lm.fit16)\n\nconfint(lm.fit17)\n\nset.seed(1)\nx1 = runif(100)\nx2 = 0.5 * x1 + rnorm(100)/10\ny = 2 + 2*x1 + 0.3*x2 + rnorm(100)\n\ncor(x1, x2)\n\nplot(x1, x2)\n\nlm.fit18 <- lm(y ~ x1 + x2)\nsummary(lm.fit18)\n\nlm.fit19 <- lm(y ~ x1)\nsummary(lm.fit19)\n\nlm.fit20 <- lm(y ~ x2)\nsummary(lm.fit20)\n\nx1 = c(x1, 0.1)\nx2 = c(x2, 0.8)\ny = c(y, 6)\n\nlm.fit21 = lm(y ~ x1 + x2)\nsummary(lm.fit21)\n\nlm.fit22 = lm(y ~ x1)\nsummary(lm.fit22)\n\nlm.fit23 = lm(y ~ x2)\nsummary(lm.fit23)\n\npar(mfrow=c(2,2))\nplot(lm.fit21)\n\npar(mfrow=c(2,2))\nplot(lm.fit22)\n\npar(mfrow=c(2,2))\nplot(lm.fit23)\n\nBoston = read.csv(\"../../../data/Boston.csv\", header=T, na.strings=\"?\")\nBoston$chas <- factor(Boston$chas, labels = c(\"N\",\"Y\"))\nsummary(Boston)\n\nattach(Boston)\nlm.zn = lm(crim~zn)\nsummary(lm.zn) # yes\n\nlm.indus = lm(crim~indus)\nsummary(lm.indus) # yes\n\nlm.chas = lm(crim~chas) \nsummary(lm.chas) # no\n\nlm.nox = lm(crim~nox)\nsummary(lm.nox) # yes\n\nlm.rm = lm(crim~rm)\nsummary(lm.rm) # yes\n\nlm.age = lm(crim~age)\nsummary(lm.age) # yes\n\nlm.dis = lm(crim~dis)\nsummary(lm.dis) # yes\n\nlm.rad = lm(crim~rad)\nsummary(lm.rad) # yes\n\nlm.tax = lm(crim~tax)\nsummary(lm.tax) # yes\n\nlm.ptratio = lm(crim~ptratio)\nsummary(lm.ptratio) # yes\n\nlm.black = lm(crim~black)\nsummary(lm.black) # yes\n\nlm.lstat = lm(crim~lstat)\nsummary(lm.lstat) # yes\n\nlm.medv = lm(crim~medv)\nsummary(lm.medv) # yes\n\nlm.all = lm(crim ~ ., data = Boston)\nsummary(lm.all)\n\n# Simple regresion\nx = c(coefficients(lm.zn)[2],\n coefficients(lm.indus)[2],\n coefficients(lm.chas)[2],\n coefficients(lm.nox)[2],\n coefficients(lm.rm)[2],\n coefficients(lm.age)[2],\n coefficients(lm.dis)[2],\n coefficients(lm.rad)[2],\n coefficients(lm.tax)[2],\n coefficients(lm.ptratio)[2],\n coefficients(lm.black)[2],\n coefficients(lm.lstat)[2],\n coefficients(lm.medv)[2])\n\n# Multiple regresion\ny = coefficients(lm.all)[2:14]\n\nplot(x, y)\n\ncor(Boston[-c(1, 4)])\n\nlm.zn = lm(crim ~ poly(zn, 3))\nsummary(lm.zn) # 1, 2\n\nlm.indus = lm(crim ~ poly(indus, 3))\nsummary(lm.indus) # 1, 2, 3\n\nlm.nox = lm(crim ~ poly(nox, 3))\nsummary(lm.nox) # 1, 2, 3\n\nlm.rm = lm(crim ~ poly(rm, 3))\nsummary(lm.rm) # 1, 2\n\nlm.age = lm(crim ~ poly(age, 3))\nsummary(lm.age) # 1, 2, 3\n\nlm.dis = lm(crim ~ poly(dis, 3))\nsummary(lm.dis) # 1, 2, 3\n\nlm.rad = lm(crim ~ poly(rad, 3))\nsummary(lm.rad) # 1, 2\n\nlm.tax = lm(crim ~ poly(tax, 3))\nsummary(lm.tax) # 1, 2\n\nlm.ptratio = lm(crim ~ poly(ptratio, 3))\nsummary(lm.ptratio) # 1, 2, 3\n\nlm.black = lm(crim ~ poly(black, 3))\nsummary(lm.black) # 1\n\nlm.lstat = lm(crim ~ poly(lstat, 3))\nsummary(lm.lstat) # 1, 2\n\nlm.medv = lm(crim ~ poly(medv, 3))\nsummary(lm.medv) # 1, 2, 3\n", "meta": {"hexsha": "8359ca85a0ac595a9bf5a8aeaf54d8eb65361608", "size": 5296, "ext": "r", "lang": "R", "max_stars_repo_path": "notebooks/R/3 Linear Regression/3.7 Exercises.r", "max_stars_repo_name": "jagin/isl-notebooks", "max_stars_repo_head_hexsha": "ef6ca2ebc80efd8103859f4cd6a36e43b01687d6", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 5, "max_stars_repo_stars_event_min_datetime": "2018-05-14T08:05:28.000Z", "max_stars_repo_stars_event_max_datetime": "2020-10-31T07:52:26.000Z", "max_issues_repo_path": "notebooks/R/3 Linear Regression/3.7 Exercises.r", "max_issues_repo_name": "jagin/isl-notebooks", "max_issues_repo_head_hexsha": "ef6ca2ebc80efd8103859f4cd6a36e43b01687d6", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "notebooks/R/3 Linear Regression/3.7 Exercises.r", "max_forks_repo_name": "jagin/isl-notebooks", "max_forks_repo_head_hexsha": "ef6ca2ebc80efd8103859f4cd6a36e43b01687d6", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 18.3252595156, "max_line_length": 124, "alphanum_fraction": 0.6095166163, "num_tokens": 2105, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8976952811593495, "lm_q2_score": 0.8723473730188543, "lm_q1q2_score": 0.7831021202907804}} {"text": "# OLS conditions violations: Heterscedasticity\n# Based on:\n# https://stats.stackexchange.com/questions/33028/measures-of-residuals-heteroscedasticity\n# See also:\n# https://stats.stackexchange.com/questions/258485/simulate-linear-regression-with-heteroscedasticity\n\nset.seed(17)\nn <- 500\n\nmake_x = function(){return (rgamma(n, shape=6, scale=1/2))}\nmake_e = function(x){return (rnorm(length(x), sd=abs(sin(x))))}\nb = 2\nf = function(x){return (b*x)}\ndgp = function(){\n x <- make_x() \n y = f(x)+make_e(x)\n return (data.frame(x=x,y=y))\n}\n\n# single run\nx <- make_x() \ne <- make_e(x) \ny_true = f(x) \ny <- y_true + e\nfit <- lm(y ~ x + 0)\n\n\n# regression \npng(\"C:/Users/Евгений/Documents/GitHub/multiple-regression-revisited/hsc1.png\")\nplot(x,y, main=\"Observations with heteroscedаsticity\")\nabline(0, b, col=\"green\")\nabline(fit, col=\"red\")\ndev.off()\n\n\n# repeat estimation \nextract_b0 = function(lm_){return (coef(lm_)[1])}\nget_b = function(){coef(lm(y~x+0, data = dgp()))}\nn_experiments = 1000\nbs = replicate(n_experiments, get_b())\n\n\n# plot estimator desities \n\npng(\"C:/Users/Евгений/Documents/GitHub/multiple-regression-revisited/hsc2.png\")\n\nb_avg = mean(bs)\nb_sd = sd(bs)\nh = hist(bs, breaks=40, freq=FALSE, \n main=paste(\"Distribution of b on\", n_experiments,\"experiments\"),\n sub=paste(\"True value:\", b, \" \",\n \"Mean: \", round(b_avg,4), \" \",\n \"SD: \", round(b_sd,4)),\n xlab=\"b\",\n col=\"lightblue\")\n# curve(dnorm(x, mean=b_avg, sd=b_sd), add=TRUE, col=\"darkblue\", lwd=2) \nlines(density(bs), col=\"darkblue\", lwd=2) \nabline(v=b, col =\"green\")\nabline(v=b_avg, col =\"red\")\n\n\n# from https://stackoverflow.com/questions/6973579/plotting-probability-density-mass-function-of-dataset-in-r\n# hist(energy,probability=TRUE)\n# lines(density(bs), col=\"darkblue\", lwd=2) \n\ndev.off()\n\n", "meta": {"hexsha": "452f49ff315f78b7e9ba5afae6234ccf84eb2bb4", "size": 1838, "ext": "r", "lang": "R", "max_stars_repo_path": "r/heteroscedasticity.r", "max_stars_repo_name": "epogrebnyak/multiple-regression-revisited", "max_stars_repo_head_hexsha": "8881d5a8cab31693d3ca652b3e96c6fbbaf318b0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 3, "max_stars_repo_stars_event_min_datetime": "2018-11-26T17:11:56.000Z", "max_stars_repo_stars_event_max_datetime": "2019-07-02T07:06:56.000Z", "max_issues_repo_path": "r/heteroscedasticity.r", "max_issues_repo_name": "epogrebnyak/multiple-regression-revisited", "max_issues_repo_head_hexsha": "8881d5a8cab31693d3ca652b3e96c6fbbaf318b0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "r/heteroscedasticity.r", "max_forks_repo_name": "epogrebnyak/multiple-regression-revisited", "max_forks_repo_head_hexsha": "8881d5a8cab31693d3ca652b3e96c6fbbaf318b0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2019-07-02T07:06:57.000Z", "max_forks_repo_forks_event_max_datetime": "2019-07-02T07:06:57.000Z", "avg_line_length": 27.0294117647, "max_line_length": 109, "alphanum_fraction": 0.6599564744, "num_tokens": 582, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9086178919837705, "lm_q2_score": 0.8615382076534743, "lm_q1q2_score": 0.7828090301015758}} {"text": "hist_nw <- function(x, alpha=0.01, pvalue=0.99, breaks=NULL, suppress='no') {\r\n ## plot histogram, normal distribution, and Weibull distribution\r\n ## add lines for upper tolerance limits for given alpha and pvalue\r\n ## alpha = 1 - confidence\r\n ## pvalue = coverage (tolerance interval only)\r\n\r\n ## normal distribution calculations\r\n tol_out <- normtol.int(x, alpha = alpha, P=pvalue, side=1)\r\n upper_tolerance_limit_norm <- tol_out$'1-sided.upper'\r\n\r\n ## Weibull distribution calculations\r\n tol_out <- exttol.int(x, alpha=alpha, P=pvalue, side=1, dist=\"Weibull\")\r\n shape <- tol_out$'shape.1'\r\n scale <- tol_out$'shape.2'\r\n upper_tolerance_limit_weib <- tol_out$'1-sided.upper'\r\n\r\n ## create vectors with density distributions\r\n xmin <- min(x)\r\n xmax <- max(x,upper_tolerance_limit_norm,upper_tolerance_limit_weib)\r\n chuncks <- (xmax-xmin)/1000\r\n xrange <- seq(xmin,xmax,by=chuncks)\r\n xmean <- mean(x)\r\n xsd <- sd(x)\r\n xdensity_norm <- dnorm(xrange,xmean,xsd) \r\n xdensity_weib <- dweibull(xrange,shape=shape,scale=scale)\r\n maxdensity <- max(xdensity_norm, xdensity_weib)\r\n\r\n ## make histogram\r\n ## warning: xlim range can mess up x-axis\r\n ## obtain histogram parameters but suppress plot\r\n out <- hist(x, plot=FALSE)\r\n if (is.null(breaks)) breaks <- length(out$breaks)\r\n ymax <- max(out$density, maxdensity)\r\n ## create plot\r\n hist(x, breaks=breaks,\r\n xlim=c(xmin,xmax+(xmax-xmin)/breaks), \r\n ylim=c(0,maxdensity),\r\n freq=FALSE)\r\n\r\n ## add distributions\r\n lines(x=xrange, y=xdensity_norm, col='red', lty=1)\r\n lines(x=xrange, y=xdensity_weib, col='blue', lty=1)\r\n\r\n ## add lines for mean and upper 1-sided 99/99 tolerance limits\r\n abline(v=xmean,col=\"red\")\r\n abline(v=upper_tolerance_limit_norm,col=\"red\",lty=2)\r\n abline(v=upper_tolerance_limit_weib,col=\"blue\",lty=2)\r\n\r\n ## print to screen\r\n if (suppress == 'no') {\r\n cat(\"Tolerance limit input parameters:\\n\")\r\n cat(\" upper, 1-sided,\", pvalue*100,\"/\",(1-alpha)*100,\"\\n\")\r\n cat(\"\\n\")\r\n cat(\"Normal distribution (red):\\n\")\r\n cat(\" mean =\",xmean,\"\\n\")\r\n cat(\" standard deviation =\",xsd,\"\\n\")\r\n cat(\" tolerance limit =\",upper_tolerance_limit_norm,\"\\n\")\r\n cat(\"\\n\")\r\n cat(\"Weibull distribution (blue):\\n\")\r\n cat(\" shape =\",shape,\"\\n\")\r\n cat(\" scale =\",scale,\"\\n\")\r\n cat(\" tolerance limit =\",upper_tolerance_limit_weib,\"\\n\")\r\n } \r\n}\r\n## hist_nw(mtcars$mpg)\r\n", "meta": {"hexsha": "3c5bd52575f5a0d4ab2b7406862ae70f755a8a72", "size": 2615, "ext": "r", "lang": "R", "max_stars_repo_path": "modules/hist_nw.r", "max_stars_repo_name": "TECComputing/R-setup", "max_stars_repo_head_hexsha": "f4b5e45c6e2e55fcc6f58f804bb50cea3a697fe0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "modules/hist_nw.r", "max_issues_repo_name": "TECComputing/R-setup", "max_issues_repo_head_hexsha": "f4b5e45c6e2e55fcc6f58f804bb50cea3a697fe0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "modules/hist_nw.r", "max_forks_repo_name": "TECComputing/R-setup", "max_forks_repo_head_hexsha": "f4b5e45c6e2e55fcc6f58f804bb50cea3a697fe0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 39.6212121212, "max_line_length": 78, "alphanum_fraction": 0.6011472275, "num_tokens": 717, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9518632316144273, "lm_q2_score": 0.8221891305219504, "lm_q1q2_score": 0.7826116027768799}} {"text": "# Example : 2 Chapter : 2.5 Pageno : 82\n# Inverse of an Elimination Matrix\nE<-matrix(c(1,-5,0,0,1,0,0,0,1),ncol=3)\nE1<-solve(E)\nprint(\"The inverse of the given elimination matrix is\")\nprint(E1)", "meta": {"hexsha": "672d518be5cdb1576e0cddbb1766be8b004800ff", "size": 197, "ext": "r", "lang": "R", "max_stars_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH2/EX2.5.2/Ex2.5_2.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH2/EX2.5.2/Ex2.5_2.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH2/EX2.5.2/Ex2.5_2.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 32.8333333333, "max_line_length": 55, "alphanum_fraction": 0.6802030457, "num_tokens": 78, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9362849986365572, "lm_q2_score": 0.8354835330070838, "lm_q1q2_score": 0.7822506985624035}} {"text": "## Author: Sergio García Prado\n\nrm(list = ls())\n\n\n## a)\n####\n\n## Asymptotic distibution of (p1.hat, p2.hat) as parameters p1 of Bin(n, p1) and\n## p2 of Bin(n, p2) independent of each other.\n##\n## (p1.hat, p2.hat) ~ N_2( (p1, p2) , [p1 * (1 - p1) / n, 0;\n## 0, p2 * (1 - p2) / n] )\n##\n\n\n## b)\n####\nn1 <- 50\ny1 <- 35\n\nn2 <- 50\ny2 <- 40\n\nn <- c(n1, n2)\ny <- c(y1, y2)\n\nalpha <- 0.05\n\nLogLikelihood <- function(p, y, n) {\n sum(y * log(p) + (n - y) * log(1 - p))\n}\n\nNegativeLogLikelihood <- function(...) {\n - LogLikelihood(...)\n}\n\nopt <- optim(runif(2), NegativeLogLikelihood, y = y, n = n, hessian = TRUE,\n lower = rep(10e-3, 2), upper = rep(1 - 10e-3, 2), method = \"L-BFGS-B\")\n\n(p.hat <- opt$par)\n# 0.69999745777599 0.799999683303738\n\n(p.hat.var <- solve(opt$hessian))\n# 0.004199941\t0.000000000\n# 0.000000000\t0.003199902\n\ng.transform <- c(-2, 1)\n\n(g.hat <- (g.transform %*% p.hat)[1])\n# -0.59999999367853\n\n(g.hat.var <- (g.transform %*% p.hat.var %*% g.transform)[1])\n# 0.0199995879878169\n\n## Wald's Confidence Interval at (1 - alpha)% level.\ng.hat + c(-1, 1) * qnorm(1 - alpha / 2) * sqrt(g.hat.var)\n# -0.87717790348746 -0.3228220838696\n\n\n## b)\n####\ng.zero <- 0\n\n(W <- (g.hat - g.zero) ^ 2 / g.hat.var)\n# 18.0003059668258\n\n(W.pvalue <- 1 - pchisq(W, df = 1))\n# 2.20869627943765e-05\n\n## b)\n####\n\nLogLikelihoodHZero <- function(pp, ...) {\n LogLikelihood(c(2 * pp, pp), ...)\n}\n\nNegativeLogLikelihoodHZero <- function(...) {\n - LogLikelihoodHZero(...)\n}\n\nopt.hzero <- optim(runif(1), NegativeLogLikelihoodHZero, y = y, n = n,\n lower = 10e-3, upper = 0.5 - 10e-3, method = \"L-BFGS-B\" )\n\n(LRT <- 2 * (LogLikelihood(p.hat, y, n) - LogLikelihoodHZero(opt.hzero$par, y, n)))\n# 36.089146035026\n\n(LRT.pvalue <- 1 - pchisq(LRT, df = 1))\n# 1.88493831654313e-09\n", "meta": {"hexsha": "97d973cbd7ae778c5aa967e84009ec463adff300", "size": 1818, "ext": "r", "lang": "R", "max_stars_repo_path": "statistical-inference/likelihood/exercise-03.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "statistical-inference/likelihood/exercise-03.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "statistical-inference/likelihood/exercise-03.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 20.2, "max_line_length": 84, "alphanum_fraction": 0.5621562156, "num_tokens": 739, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9314625050654264, "lm_q2_score": 0.8397339616560072, "lm_q1q2_score": 0.7821806995126191}} {"text": "#break-even multiple products\n\n# computing a value-weighted average\n\n# product A, CM of $10\n# product B, CM of $6\n\n# for each 1 unit of A, 2 units of B are sold\nvolumes <- c(1, 2)\n# contribution margins\nCMs <- c(10, 6)\n\n#make the volumes relative\nvol_weights <- volumes / sum(volumes)\nvol_weights\n#[1] 0.3333333 0.6666667\n\n# weighted CM\nCM_weighted <- weighted.mean( CMs, vol_weights )\nCM_weighted\n#[1] 7.333333\n\n#if fixed costs are $10,000 then break-even is\nbeUnits <- 10000/CM_weighted\nbeUnits\n#1363.636\n\n#volumes\nbeUnits * vol_weights\n#[1] 454.5455 909.0909\n#454.5 units of A, 909 units of B (adds up to beUnits)\n", "meta": {"hexsha": "96236dfcc1c673c8093790288bf3e425bcd4767c", "size": 618, "ext": "r", "lang": "R", "max_stars_repo_path": "chapter15/breakeven-multipe_products.r", "max_stars_repo_name": "JoostUF/introR", "max_stars_repo_head_hexsha": "7a4d152ec8e78e47aef9a6460b6e7e819fb3ce35", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "chapter15/breakeven-multipe_products.r", "max_issues_repo_name": "JoostUF/introR", "max_issues_repo_head_hexsha": "7a4d152ec8e78e47aef9a6460b6e7e819fb3ce35", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "chapter15/breakeven-multipe_products.r", "max_forks_repo_name": "JoostUF/introR", "max_forks_repo_head_hexsha": "7a4d152ec8e78e47aef9a6460b6e7e819fb3ce35", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 19.3125, "max_line_length": 54, "alphanum_fraction": 0.716828479, "num_tokens": 215, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9566342024724487, "lm_q2_score": 0.8175744828610095, "lm_q1q2_score": 0.7821197133735666}} {"text": "\ntwostreaks=function(song){\n# song is a vector of 0's and 1's that represents the hits (0) and \n# misses (1) of the notes in order \n\n temp = diff(c(0,which(song == 1),length(song)+1))-1\n top2 = -sort.int(-temp,partial=1:min(2,length(temp)))[1:2]\n len_top2 = sum(top2,na.rm = T)\n\n # About these commands:\n # which(song == 1) returns a vector indicating which on which notes (indices) a miss occurs\n # this is important for you because it will indicate the end of a streak\n # c(0,which(song == 1),length(song)+1) creates a vector starting with 0 (indicates the beginning of the song),\n # then the locations of misses, and then the length of the song + 1 (indicates when the song has ended)\n # By doing a partial sort of the above vector we can quickly find to longest streaks. However, since the sort.int function \n # doesn't sort in decreasing order you need to first negate the vector of hit streaks so an \n # increasing sort finds the correct streaks, then negate the results to obtain the actual values.\n # While other methods could be used to obtain the same information (possibly by sorting the entire \"temp\" vector)\n # this provides a nice illustration of how to use some of the more computationally efficient tools in R that may \n # otherwise go unnoticed. \n #\n # The combination of min(2,length(temp)) and the na.rm = T in the sum are needed when only one hit streak occurs.\n \n return(len_top2)\n}\n\n# Hypothesis test based on the twostreaks method\ntwostreaks_test = function(song,B=1000){\n # song is a vector of 0's and 1's that represents the hits (0) \n\t# and misses (1) of the notes in order\n\t# B is the number of new samples to generate\n\t\n\ttest_stat = twostreaks(song)\n\tn = length(song)\n\ttstar_b = numeric(B)\n\tfor(b in 1:B){\n\t\tsong_tmp = sample(song) # for permutation test\n#\t\tsong_tmp = sample(song,replace=T) # for non-parametric bootstrap\n#\t\tsong_tmp = rbinom(n,1,mean(song)) # for parametric bootstrap\n\t\ttstar_b[b] = twostreaks(song_tmp)\n\t}\n\t\n\t# calculate the two-sided p-value from the sampling distribution\n\tpval = 2*min(sum(tstar_b >= test_stat),sum(tstar_b <= test_stat))/B\n\t\t# calculate a one sided p-value\n#\tpval = sum(tstar_b >= test_stat)/B\n\treturn(pval)\n}\n \n# Examples using Songs A and B from Table 1\n\nsongA = c(1,0,0,0,0,0,1,0,1,0,0,1,0,0,0,0,1,0,0,0)\ntwostreaks(songA)\ntwostreaks_test(songA,5000)\n\n\nsongB = c(0,0,0,1,0,0,0,0,0,0,0,1,1,1,1,0,0)\ntwostreaks(songB)\ntwostreaks_test(songB,5000)\n", "meta": {"hexsha": "67eb74e6785bae2f5f23e791586a835682de67e1", "size": 2480, "ext": "r", "lang": "R", "max_stars_repo_path": "GHSupplementaryFiles/AppendixC/top2streaks.r", "max_stars_repo_name": "iramler/guitar_hero_jse", "max_stars_repo_head_hexsha": "daaa66120705cd66d517bd35a66d4151683f9480", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "GHSupplementaryFiles/AppendixC/top2streaks.r", "max_issues_repo_name": "iramler/guitar_hero_jse", "max_issues_repo_head_hexsha": "daaa66120705cd66d517bd35a66d4151683f9480", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "GHSupplementaryFiles/AppendixC/top2streaks.r", "max_forks_repo_name": "iramler/guitar_hero_jse", "max_forks_repo_head_hexsha": "daaa66120705cd66d517bd35a66d4151683f9480", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 41.3333333333, "max_line_length": 125, "alphanum_fraction": 0.7032258065, "num_tokens": 751, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9019206659843131, "lm_q2_score": 0.8670357615200475, "lm_q1q2_score": 0.7819974714623773}} {"text": "### 主成分分析の例\n### - 県別の生活環境に関するデータ\n\n## パッケージの読み込み\nrequire(MASS) \nrequire(tidyverse) \nrequire(ggfortify)\nrequire(GGally)\n\n## データの読み込み (\"jpamenity.csv\"を用いる)\nraw <- read.csv(file=\"data/jpamenity.csv\") # データの読み込み\nscan(file=\"data/jpamenity.txt\",what=character(),sep=\";\") # 説明の表示\n\n## データの整形\nmydata <- raw[-1,-c(1,2)] # 不要な行・列を削除\nnames(mydata) <- names(read.csv(\"data/jpamenityitem.csv\")) # 変数名の略記\nrownames(mydata) <- raw[-1,1] # 各行の名前を県名\nareaname <- c(\"北海道\",\"東北\",\"関東\",\"中部\",\"近畿\",\"中国\",\"四国\",\"九州\")\narea <- rep(areaname,c(1,6,7,9,7,5,4,8))\n\n## データの内容を表示\n## print(mydata) # 全データの表示\nhead(mydata) # 最初の6個を表示\n## tail(mydata) # 最後の6個を表示\n\n## データの散布図 (一部項目のみ): 図(a)\nitem <- c(1,7,8,18,19,20)\n## print(names(mydata)[item])\nggscatmat(data.frame(mydata,area),\n columns=item, color=\"area\", alpha=.5) +\n theme(text=element_text(family=\"HiraMaruProN-W4\"))\n## ## ggparis を用いる場合 (legendが付かない)\n## ggpairs(data.frame(mydata,area),\n## columns=item, mapping=aes(colour=area)) +\n## theme(text=element_text(family=\"HiraMaruProN-W4\"))\n\n## 主成分分析\nmodel <-princomp(mydata,cor=TRUE)\n## model <-prcomp(mydata,scale.=TRUE) # prcompを使う場合\n\n## 分析結果を表示\nprint(model) \n## 寄与率 (正規化あり): 図(b)\nplot(model)\n\n## 主成分得点 (scale=1) [既定値]: 図(c)\nautoplot(model, data=mydata, shape=FALSE,\n label=TRUE, label.family=\"HiraMaruProN-W4\", label.size=3, \n loadings=TRUE, loadings.colour=\"blue\",\n loadings.label=TRUE, loadings.label.family=\"HiraMaruProN-W4\",\n loadings.label.size=4, loadings.label.colour=\"blue\",\n main=\"県別の生活環境\") +\n theme(text=element_text(family=\"HiraMaruProN-W4\"))\n\n## 中心部の拡大表示: 図(d)\nautoplot(model, data=mydata, shape=FALSE,\n xlim=c(-.3,.3), ylim=c(-.3,.3),\n label=TRUE, label.family=\"HiraMaruProN-W4\", label.size=3, \n loadings=TRUE, loadings.colour=\"blue\",\n loadings.label=TRUE, loadings.label.family=\"HiraMaruProN-W4\",\n loadings.label.size=4, loadings.label.colour=\"blue\",\n main=\"県別の生活環境 (中心を拡大)\") +\n theme(text=element_text(family=\"HiraMaruProN-W4\"))\n\n## 主成分得点 (scale=0): 図(e)\nautoplot(model, data=mydata, scale=0, shape=FALSE,\n label=TRUE, label.family=\"HiraMaruProN-W4\", label.size=3, \n loadings=TRUE, loadings.colour=\"blue\",\n loadings.label=TRUE, loadings.label.family=\"HiraMaruProN-W4\",\n loadings.label.size=4, loadings.label.colour=\"blue\",\n main=\"scale=0での表示\") +\n theme(text=element_text(family=\"HiraMaruProN-W4\"))\n\n## 主成分得点 (scale=1/2): 図(f)\nautoplot(model, data=mydata, scale=1/2, shape=FALSE,\n label=TRUE, label.family=\"HiraMaruProN-W4\", label.size=3, \n loadings=TRUE, loadings.colour=\"blue\",\n loadings.label=TRUE, loadings.label.family=\"HiraMaruProN-W4\",\n loadings.label.size=4, loadings.label.colour=\"blue\",\n main=\"scale=1/2での表示\") +\n theme(text=element_text(family=\"HiraMaruProN-W4\"))\n", "meta": {"hexsha": "158825320ce908e1d430bf0a185cdaebfe86fe58", "size": 2859, "ext": "r", "lang": "R", "max_stars_repo_path": "docs/code/p-jpamenity.r", "max_stars_repo_name": "noboru-murata/multivariate-analysis", "max_stars_repo_head_hexsha": "645bff23d3868e5d7c245ef4af7d0ff9fe98e017", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "docs/code/p-jpamenity.r", "max_issues_repo_name": "noboru-murata/multivariate-analysis", "max_issues_repo_head_hexsha": "645bff23d3868e5d7c245ef4af7d0ff9fe98e017", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "docs/code/p-jpamenity.r", "max_forks_repo_name": "noboru-murata/multivariate-analysis", "max_forks_repo_head_hexsha": "645bff23d3868e5d7c245ef4af7d0ff9fe98e017", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 34.8658536585, "max_line_length": 70, "alphanum_fraction": 0.6547743966, "num_tokens": 1132, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9407897492587141, "lm_q2_score": 0.831143054132195, "lm_q1q2_score": 0.7819308654951496}} {"text": "'''\nA fast food franchise is test marketing 3 new \nmenu items. To find out if they have the same \npopularity, 6 franchisee restaurants are\nrandomly chosen for participation in the study.\nIn accordance with the randomized block design,\neach restaurant will be test marketing all \n3 new menu items. Furthermore, a restaurant \nwill test market only one menu item per week,\nand it takes 3 weeks to test market all menu \nitems. The testing order of the menu items \nfor each restaurant is randomly assigned as\nwell.\n\nSuppose each row in the following table represents \nthe sales figures of the 3 new menu in a restaurant \nafter a week of test marketing. At .05 level of significance, \ntest whether the mean sales volume for the 3 new menu items\nare all equal.\n'''\n\nlibrary(readr)\ndataset <- read_csv('fastfood-2.csv')\nView(dataset)\n\n#creamos un vector\nr = c(t(as.matrix(df2)))\n\nf = c(\"Item1\", \"Item2\", \"Item3\") \n\nk = 3\nn = 6\n\n#treatment factors\ntm = gl(k, 1, n*k, factor(f)) \n\n#blocking factors\nblk = gl(n, k, k*n) \n\nav = aov(r ~ tm +blk)\n\nsummary(av)\n\n'''\n Df Sum Sq Mean Sq F value Pr(>F) \ntm 2 539 269 4.96 0.032 * \nblk 5 560 112 2.06 0.155 \nResiduals 10 543 54\n\nComo el p-value 0.032 es menor a la significancia .05, rechazamos la hipotesis\n'''\n\n", "meta": {"hexsha": "5d9871fb23d2e262dfc32ad8a6e858066ddb8086", "size": 1306, "ext": "r", "lang": "R", "max_stars_repo_path": "Parcial/4. ANOVA/RandomizedBlockDesign.r", "max_stars_repo_name": "jchudb93/Exp-Numerica", "max_stars_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Parcial/4. ANOVA/RandomizedBlockDesign.r", "max_issues_repo_name": "jchudb93/Exp-Numerica", "max_issues_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Parcial/4. ANOVA/RandomizedBlockDesign.r", "max_forks_repo_name": "jchudb93/Exp-Numerica", "max_forks_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 24.641509434, "max_line_length": 78, "alphanum_fraction": 0.691424196, "num_tokens": 374, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9334308184368928, "lm_q2_score": 0.837619959279793, "lm_q1q2_score": 0.7818602841296141}} {"text": "\nnstreaks=function(song)\n{\n# song is a vector of 0's and 1's that represents the hits (0) and \n# misses (1) of the notes in order \n\n# determine the total number of hit streaks\n streaks = sum(diff(c(song,1)) == 1)\n\n # About these commands:\n # diff(c(song,1) calculates the difference between consecutive entries in this vector; we don't actually care about \n #\t\t\t the locations of the misses but how many hits occur between misses; we start the process of finding this \n #\t\t\t by finding the difference between consecutive indices in the vector. The end of hit streaks are indicated\n # \t\t by this difference being 1 (i.e., going from a hit of 0 to a miss of 1). Attaching an additional 1 at\n # \t\t the end of the song will ensure that if the song ends in a steak of hits it is included in the total.\n # sum( above vector == 1) counts the number of hit streaks\n\n return(streaks)\n}\n\n# Hypothesis test based on the nstreaks test method\nnstreaks_test = function(song,B=1000){\n # song is a vector of 0's and 1's that represents the hits (0) \n\t# and misses (1) of the notes in order\n\t# B is the number of new samples to generate\n\t\n\ttest_stat = nstreaks(song)\n\tn = length(song)\n\ttstar_b = numeric(B)\n\tfor(b in 1:B){\n\t\tsong_tmp = sample(song) # for permutation test\n#\t\tsong_tmp = sample(song,replace=T) # for non-parametric bootstrap\n#\t\tsong_tmp = rbinom(n,1,mean(song)) # for parametric bootstrap\n\t\ttstar_b[b] = nstreaks(song_tmp)\n\t}\n\t\n\t# calculate the two-sided p-value from the sampling distribution\n\tpval = 2*min(sum(tstar_b >= test_stat),sum(tstar_b <= test_stat))/B\n\t\t# calculate a one sided p-value\n#\tpval = sum(tstar_b >= test_stat)/B\n\treturn(pval)\n}\n\n# Examples using Songs A and B from Table 1\n\nsongA = c(1,0,0,0,0,0,1,0,1,0,0,1,0,0,0,0,1,0,0,0)\nnstreaks(songA)\nnstreaks_test(songA,5000)\n\n\nsongB = c(0,0,0,1,0,0,0,0,0,0,0,1,1,1,1,0,0)\nnstreaks(songB)\nnstreaks_test(songB,5000)", "meta": {"hexsha": "547f96f98da41f8382839c58a7eea3a59a941c52", "size": 1891, "ext": "r", "lang": "R", "max_stars_repo_path": "GHSupplementaryFiles/AppendixC/num_streaks.r", "max_stars_repo_name": "iramler/guitar_hero_jse", "max_stars_repo_head_hexsha": "daaa66120705cd66d517bd35a66d4151683f9480", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "GHSupplementaryFiles/AppendixC/num_streaks.r", "max_issues_repo_name": "iramler/guitar_hero_jse", "max_issues_repo_head_hexsha": "daaa66120705cd66d517bd35a66d4151683f9480", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "GHSupplementaryFiles/AppendixC/num_streaks.r", "max_forks_repo_name": "iramler/guitar_hero_jse", "max_forks_repo_head_hexsha": "daaa66120705cd66d517bd35a66d4151683f9480", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 35.679245283, "max_line_length": 118, "alphanum_fraction": 0.7070333157, "num_tokens": 602, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9219218284193597, "lm_q2_score": 0.8479677583778258, "lm_q1q2_score": 0.781759986244351}} {"text": "#задание 2\nprint (\"task 2\")\nA <- matrix (c(-11,8,-7,0,14,-7,-1,-6,8,2,-3,8,-4,10,6,7,-4,-2,6,3,6,-4,-2,-5,10,-5,-14,9,7,9,2,-3,-8,-6,2,-9),6,6)\nA\n#определитель\ndet(A) # Определитель A\n\n#задание 4\nprint (\"task 4\")\nA <- matrix (c(-6,6,0,7,9,7,-9,-9,-9,-4,9,-5,6,-3,-7,-8,7,5,-1,3,3,9,-7,3,-3,-1,8,1,0,0,7,-8,2,-2,1,0),6,6)\nA\nB <- matrix (c(4,8,4,-5,9,-7,9,-8,-7,-7,5,3,-8,5,-1,7,-7,-10,11,7,-9,4,6,-7,1,-11,-1,0,-9,-9,-1,-6,-11,-4,-10,2),6,6)\nB\nx <- solve(A,B)\nprint (\"x равен\")\nx\n#проверка\ny <- A%*%x\ny\n\n#задание 5\nprint (\"5 task\")\na <- c(3,3,-2,1,2,3,-4,0,-1,2,3,3)\nb <- c(-2,3,3,1,1,1,0,-1,2,4,-4,2)\np <- c(4,2,2,2,5,1,3,3,0,-3,-2,-1)\n\nfir <- ((3)*a)+(4*b)\nprint (\"first answer\")\nfir\nsec <- ((2)*as.numeric(a%*%b))*p+2*(norm(p, type=\"2\"))*a\nprint (\"second answer\")\nsec\nthr <- 1*as.numeric(a%*%p)*b-2*as.numeric(b%*%p)*a-2*(norm(p, type=\"2\"))*p\nprint (\"third answer\")\nthr\n\n#6 задание\nprint (\"sixth task\")\ninstall.packages(\"lpSolveAPI\") # Загружаем библиотеку\nlibrary(lpSolveAPI) # Активируем библиотеку линейного программирования\nM <- make.lp(ncol= 2) # Объявляем количество неотрицательных переменных в M\nname.lp(M, \"Example\") # Объявляем название \"Example\"для задачи(модели) М\ncolnames(M) <- c(\"X1\", \"X2\") # Объявляем названия переменных в модели М\nlp.control(M, sense = \"min\")$sense# Объявляем задачу на минимум модели М\nset.objfn(M, c(10,5)) # Задаем целевую функцию:\nadd.constraint(M, c(2,4), \">=\", 4) # Задаем ограничение:\nadd.constraint(M, c(4, 1), \">=\",1) #\nadd.constraint(M, c(2, -3), \"<=\",6) #\n\n\n\nrownames(M) <- c(\"A\", \"B\",\"C\") # Называем ограничения в модели М\nM # Выводим модель M на экран\nsolve.lpExtPtr(M)\nget.variables(M) # Оптимальный план\nget.objective(M) # Достигнутый min\nX1.opt<- get.variables(M)[1]; X1.opt # Оптимальное значение для X1\nX2.opt<- get.variables(M)[2]; X2.opt # Оптимальное значение для X2\nf.max<- get.objective(M); f.max# Значение целевой функции на оптимальном решении\n", "meta": {"hexsha": "68358b42b028d10d216b352e66c2d2e67f696963", "size": 1906, "ext": "r", "lang": "R", "max_stars_repo_path": "Tasks/Task 5/solution.r", "max_stars_repo_name": "Master-sniffer/Doing-some-tasks-with-R", "max_stars_repo_head_hexsha": "629e7add02437ea22c079ecd7a4279e46028b69c", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Tasks/Task 5/solution.r", "max_issues_repo_name": "Master-sniffer/Doing-some-tasks-with-R", "max_issues_repo_head_hexsha": "629e7add02437ea22c079ecd7a4279e46028b69c", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Tasks/Task 5/solution.r", "max_forks_repo_name": "Master-sniffer/Doing-some-tasks-with-R", "max_forks_repo_head_hexsha": "629e7add02437ea22c079ecd7a4279e46028b69c", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 31.7666666667, "max_line_length": 117, "alphanum_fraction": 0.6185729276, "num_tokens": 931, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9481545392102523, "lm_q2_score": 0.8244619306896955, "lm_q1q2_score": 0.7817173219894832}} {"text": "# Your friend investigates the three observations above 700 grams and discovers that she had ordered \n# the incorrect meal on those dates. \n# She removes these observations from the data set and proceeds with the analysis using n=27.\n# \n# She assumes a normal likelihood for the data with unknown mean μ and unknown variance σ2. \n# She uses the model presented in Lesson 10.2 where, conditional on σ2, \n# the prior for μ is normal with mean mmm and variance σ2/w. \n\n# Next, the marginal prior for σ2 is Inverse-Gamma(a,b).\n# \n# Your friend's prior guess on the mean dish weight is 500 grams, \n# so we set m=500. She is not very confident with this guess, \n# so we set the prior effective sample size w=0.1. Finally, she sets a=3 and b=200.\n# \n# We can learn more about this inverse-gamma prior by simulating draws from it. If a random variable \n# X follows a Gamma(a,b) distribution, then 1/X follows an Inverse-Gamma(a,b) distribution. \n# Hence, we can simulate draws from a gamma distribution and take their reciprocals, \n# which will be draws from an inverse-gamma.\n\n\n# Simulate a large number of draws (at least 300) from the prior for σ2\n# and report your approximate prior mean from these draws. It does not need to be exact.\n\nm = 500\nw = .1\nalpha = 3\nbeta = 200\n\nn = 27\n\nx_mean = 609.7\nx_var = 401.8\n\nalpha_prim = 16.5\nbeta_prim = 6022.9\nm_prim = 609.3\n\n\nprior_var_1 = 1 / rgamma(10000, alpha, beta)\n\nposterior_var_1 = 1 / rgamma(10000, alpha_prim, beta_prim)\n\nposterior_mean_1 = rnorm(10000, m_prim, sqrt((posterior_var_1 / (w + n))))\n\nquantile(posterior_mean_1, c(.025, .975))\n\n# You complete your experiment at Restaurant A with n=30 data points, \n# which appear to be normally distributed. \n# You calculate the sample mean y¯= 622.8 and sample variance s2 = 403.1.\n\n# Repeat the analysis from Question 9 using the same priors and draw samples from the \n# posterior distribution of sigma_A^2 and μA (where the A denotes that these parameters are for Restaurant A).\n\n# Treating the data from Restaurant A as independent from Restaurant B, \n# we can now attempt to answer your friend's original question: \n# is restaurant A more generous? \n\n# To do so, we can compute posterior probabilities of hypotheses \n# like μA > μB. \n# This is a simple task if we have simulated draws for μA and μB. \n# For i=1,…,N (the number of simulations drawn for each parameter), \n# make the comparison μA > μB using the i-th draw for μA and μB. \n# Then count how many of these return a TRUE value and divide by N, the total number of simulations.\n\nn_A = 30\n\nx_mean_A = 622.8\nx_var_A = 403.1\n\nalpha_prim_A = alpha + (n_A / 2)\nbeta_prim_A = beta + ((n_A - 1) / 2) * x_var_A + ((w * n_A) / (2 * (w + n_A))) * (x_mean_A - m)**2\nm_prim_A = (n_A * x_mean_A + w * m) / (w + n_A)\n\n\nprior_var_A = 1 / rgamma(10000, alpha, beta)\n\nposterior_var_A = 1 / rgamma(10000, alpha_prim_A, beta_prim_A)\n\nposterior_mean_A = rnorm(10000, m_prim_A, sqrt((posterior_var_A / (w + n_A))))\n\n\nsum(posterior_mean_A > posterior_mean_1) / 10000\n", "meta": {"hexsha": "9869495cb2a37bf7fb04db16bfcf1b55344281c9", "size": 3017, "ext": "r", "lang": "R", "max_stars_repo_path": "bayesian-notes-santa-cruz/ex_2.r", "max_stars_repo_name": "AlxndrMlk/bayesian-stuff", "max_stars_repo_head_hexsha": "86a45f4a2835d512093813faa27775c2dddc25e2", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "bayesian-notes-santa-cruz/ex_2.r", "max_issues_repo_name": "AlxndrMlk/bayesian-stuff", "max_issues_repo_head_hexsha": "86a45f4a2835d512093813faa27775c2dddc25e2", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "bayesian-notes-santa-cruz/ex_2.r", "max_forks_repo_name": "AlxndrMlk/bayesian-stuff", "max_forks_repo_head_hexsha": "86a45f4a2835d512093813faa27775c2dddc25e2", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 36.3493975904, "max_line_length": 110, "alphanum_fraction": 0.7235664567, "num_tokens": 892, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9532750400464604, "lm_q2_score": 0.8198933381139645, "lm_q1q2_score": 0.7815838547244155}} {"text": "## 1. Probability In Terms of Sets ##\n\ncoin_toss_omega <- length(c('HH', 'TT', 'HT', 'TH'))\n\n## 2. Venn Diagrams ##\n\np_c <- 3/6\np_d <- 3/6\np_c_or_d <- 4/6\np_c_and_d <- 2/6\n\n## 3. Unions and Intersections of Sets ##\n\noperation_1 <- FALSE\noperation_2 <- TRUE\noperation_3 <- FALSE\noperation_4 <- TRUE\n\n## 4. Mutually Exclusive Events ##\n\nmutual_exclusive_1 <- TRUE\nmutual_exclusive_2 <- TRUE\nmutual_exclusive_3 <- FALSE\n\n## 5. The Addition Rule ##\n\np_heart_or_diamonds <- 13/52 + 13/52\np_face_card <- 3/52 + 3/52 + 3/52 + 3/52\n\n## 6. A More General Addition Rule ##\n\np_f_or_t <- 0.26 + 0.11 - 0.03", "meta": {"hexsha": "8c271c8aa72586bfb5deba1cdcf747b245dab2a4", "size": 594, "ext": "r", "lang": "R", "max_stars_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/3. Probability Fundamentals in R/2. Probability Rules.r", "max_stars_repo_name": "MyArist/Dataquest", "max_stars_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 8, "max_stars_repo_stars_event_min_datetime": "2020-07-27T12:04:54.000Z", "max_stars_repo_stars_event_max_datetime": "2021-03-01T04:39:33.000Z", "max_issues_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/3. Probability Fundamentals in R/2. Probability Rules.r", "max_issues_repo_name": "myarist/Dataquest", "max_issues_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/3. Probability Fundamentals in R/2. Probability Rules.r", "max_forks_repo_name": "myarist/Dataquest", "max_forks_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 15, "max_forks_repo_forks_event_min_datetime": "2021-03-30T06:45:19.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-17T03:55:02.000Z", "avg_line_length": 18.5625, "max_line_length": 52, "alphanum_fraction": 0.6548821549, "num_tokens": 232, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9585377249197138, "lm_q2_score": 0.8152324826183822, "lm_q1q2_score": 0.7814310891696742}} {"text": "## Loss/cost functions and their gradients\n\n## the least squares cost function - matrix operations\nls_cost_fn<-function(actual,prediction){\n n<-nrow(actual)\n (1/n)*t(prediction-actual)%*%(prediction-actual)\n}\n\n## least squares gradient - matrix operations\nls_gradient_fn<-function(w,X,y){\n if(is.null(dim(X)[2])){ \n #single obs case - for stochastic alg\n X*(X%*%w-y)\n }else{ \n #complete cases\n t(X)%*%(X%*%w-y)\n } \n}\n\n## Log loss function\nll_cost_fn<-function(actual, prediction) {\n epsilon <- .000000000000001\n yhat <- pmin(pmax(prediction, epsilon), 1-epsilon)\n logloss <- -mean(actual*log(yhat)\n + (1-actual)*log(1 - yhat))\n return(logloss)\n}\n\n## -gradient of the log loss function\nll_gradient_fn<-function(w,X,y){\n n<-nrow(X)\n if(is.null(n)){\n n<-1\n }\n cost<-0\n for(i in 1:n){\n cost<-cost+(-(y*X*(1/(1+exp(X%*%w))) - \n (1-y)*X*(1/(1+exp(-X%*%w)))))\n }\n cost/n\n}\n", "meta": {"hexsha": "9ce32bbb42b6b13007780c95968465f6bdc2d9ee", "size": 941, "ext": "r", "lang": "R", "max_stars_repo_path": "cost_functions.r", "max_stars_repo_name": "saq7/ml_toolset", "max_stars_repo_head_hexsha": "a8b12966e9d47fa8f7955129f28e6064279f4807", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "cost_functions.r", "max_issues_repo_name": "saq7/ml_toolset", "max_issues_repo_head_hexsha": "a8b12966e9d47fa8f7955129f28e6064279f4807", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "cost_functions.r", "max_forks_repo_name": "saq7/ml_toolset", "max_forks_repo_head_hexsha": "a8b12966e9d47fa8f7955129f28e6064279f4807", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.4047619048, "max_line_length": 54, "alphanum_fraction": 0.5961742827, "num_tokens": 300, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9669140206578809, "lm_q2_score": 0.8080672204860316, "lm_q1q2_score": 0.7813315251219872}} {"text": "#' Fitting Weibull-log-normal model to wave data\r\n#'\r\n#' @description \r\n#' This function fits a Weibull-log-normal (\\code{wln}) model to the given wave data, such that the wave height\r\n#' \\code{hs} follows a translated (or 3-parameter) Weibull distribution, and the wave period given the wave\r\n#' follows a conditional log-normal distributuion with the location and scale parameters as functions\r\n#' of the corresponding \\code{hs} value.\r\n#' \r\n#' @param data the wave data in the form a \\code{data.table} with wave height \\code{hs} and wave period\r\n#' \\code{tp} as columns.\r\n#' \r\n#' @param npy the number of data points per year, usually estimated by the number of rows in the\r\n#' supplied wave data divided by the total period of data coverage (in years).\r\n#' \r\n#' @param weibull_method the method for fitting the Weibull distribution to the \\code{hs} column in the wave data. Choose\r\n#' between \\code{\"lmom\"} for L-moment or \\code{\"mle\"} for maximum likelihood estimator. The default option\r\n#' is \\code{\"lmom\"}.\r\n#' \r\n#' @details\r\n#' The input \\code{data} must be a \\code{data.table} object with \\code{hs} and \\code{tp} columns. This can be\r\n#' generated by reading a CSV file using function \\code{\\link[data.table]{fread}}.\r\n#' \r\n#' The formulation of the conditional distribution is given by\r\n#' \\deqn{log(tp | hs=h) ~ N(\\mu(h), \\sigma(h)^2)}\r\n#' where the mean and the standard deviation are\r\n#' \\deqn{\\mu(h) = a_0 + a_1 h^a_2 and \\sigma(h) = b_0 + b_1 exp(h * b_2)}\r\n#' \r\n#' A two-step regression-based estimation method is used for fitting the conditional distribution of\r\n#' \\code{tp} given \\code{hs}. The conditonal means and standard deviations are\r\n#' estimated over fixed-width bands of \\code{hs} in the first step, and regressed onto the above\r\n#' functions of \\code{hs} in the second step.\r\n#' \r\n#' @return A joint distribution object of class \\code{wln} containing the key information of a fitted\r\n#' Weibull-log-normal model, including the three parameters of the Weibull distribution for \\code{hs} (as a named\r\n#' numeric vector) and the six parameters of the conditional log-normal distribution for \\code{tp} given \\code{hs}\r\n#' (as an unamed numeric vector, in the order of \\eqn{{a_0, a_1, a_2, b_0, b_1, b_2}}).\r\n#'\r\n#' It is possible to replace one or multiple \\code{hs} or \\code{tp} parameters in an existing \\code{wln} object\r\n#' (see the examples provided below). The current version of the package does not automatically check the\r\n#' validity of these user-input parameters. Therefore users are advised to perform the check independently.\r\n#' \r\n#' @examples\r\n#' # Load data\r\n#' data(ww3_pk)\r\n#' \r\n#' # Fit Weibull-log-normal distribution \r\n#' wln1 = fit_wln(data = ww3_pk, npy = nrow(ww3_pk)/10, weibull_method = \"mle\")\r\n#' \r\n#' # Fit Weibull-log-normal distribution using the alternative method\r\n#' wln2 = fit_wln(data = ww3_pk, npy = nrow(ww3_pk)/10, weibull_method = \"lmom\")\r\n#' \r\n#' # Update the hs parameters for object wln1\r\n#' wln3 = copy(wln1)\r\n#' wln3$hs$par[[\"loc\"]] = 0.66\r\n#' wln3$hs$par[[\"scale\"]] = 2.2\r\n#' wln3$hs$par[[\"shape\"]] = 1.8\r\n#' \r\n#' @references \r\n#' Haver, Sverre & Winterstein, Steven. (2009). Environmental Contour Lines: A Method for Estimating Long\r\n#' Term Extremes by a Short Term Analysis. Transactions - Society of Naval Architects and Marine Engineers. 116. \r\n#' \r\n#' @seealso \\code{\\link{fit_ht}}, \\code{\\link{sample_jdistr}}\r\n#' \r\n#' @export\r\nfit_wln = function(data, npy, weibull_method=\"lmom\"){\r\n \r\n res = list()\r\n class(res) = \"wln\"\r\n res$npy = npy\r\n res$hs = .fit_weibull(data = data$hs, weibull_method = weibull_method)\r\n res$tp = .fit_iform_lnorm(hs = data$hs, tp = data$tp)\r\n return(res)\r\n}\r\n\r\n\r\n# Conditional log-normal used for IFROM -----------------------------------\r\n\r\n.fit_iform_lnorm = function(hs, tp){\r\n \r\n input_data = data.table(hs, tp)[sort.list(-hs)]\r\n mod_data = input_data[, .(log_mean=mean(log(tp)), log_sd=sd(log(tp))), .(hs=round(hs/.hs_res)*.hs_res)]\r\n \r\n mod_mean = nls(\r\n formula = log_mean~.cond_norm_mean(hs, a0, a1, a2), data = mod_data, \r\n start = list(a0=1, a1=1, a2=.1), algorithm = \"port\", control = list(maxiter = 1e3, warnOnly=T))\r\n \r\n mod_sd = nls(\r\n formula = log_sd~.cond_norm_sd(hs, b0, b1, b2), data = mod_data, lower = c(0, 0, -Inf),\r\n start = list(b0=0.25, b1=0.1, b2=-0.1), algorithm = \"port\", control = list(maxiter = 1e3, warnOnly=T))\r\n \r\n res = list(par = c(coef(mod_mean), coef(mod_sd)))\r\n class(res) = \"iform_lnorm\"\r\n return(res)\r\n}\r\n\r\n.cond_norm_mean = function(hs, a0, a1, a2){\r\n a0+a1*hs^a2\r\n}\r\n.cond_norm_sd = function(hs, b0, b1, b2){\r\n b0+b1*exp(b2*hs)\r\n}\r\n\r\n\r\n# Weibull fit ----------------------------------------------------\r\n\r\n.fit_weibull = function(data, weibull_method){\r\n res = list()\r\n \r\n if(weibull_method==\"lmom\"){\r\n out = as.numeric(lmom::pelwei(lmom::samlmu(data)))\r\n res$par = c(loc=out[1], scale=out[2], shape=out[3])\r\n res$conv = NA\r\n }else if(weibull_method==\"mle\"){\r\n theta0 = c(min(data-min(data))/2, sd(data), 1)\r\n op = nlminb(\r\n start = theta0,\r\n objective = .nll_weibull3, data = data,\r\n lower = c(.limit_zero, .limit_zero, .limit_zero),\r\n upper = c(min(data)-.limit_zero, .limit_inf, .limit_inf))\r\n res$par = c(loc=op$par[1], scale=op$par[2], shape=op$par[3])\r\n res$conv = op$convergence\r\n }else{\r\n stop(\"Only \\\"lmom\\\" and \\\"mle\\\" are supported.\")\r\n }\r\n \r\n class(res) = \"weibull\"\r\n return(res)\r\n}\r\n\r\n.nll_weibull3 = function(theta, data) {\r\n if(theta[1]>=min(data) || theta[2]<=0 || theta[3]<=0){\r\n res = .limit_inf\r\n }else{\r\n nll = dweibull(data-theta[1], scale=theta[2], shape=theta[3], log = TRUE)\r\n res = -sum(nll)\r\n }\r\n return(res)\r\n}", "meta": {"hexsha": "aaa91bff4a5f32215c9f7f2aea4fc9cb0022f554", "size": 5684, "ext": "r", "lang": "R", "max_stars_repo_path": "ecsades/R/fit_wln.r", "max_stars_repo_name": "ECSADES/ecsades-r", "max_stars_repo_head_hexsha": "47ea50385c48030729d8227031a8ca73ab6a30b6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 4, "max_stars_repo_stars_event_min_datetime": "2020-09-17T00:06:29.000Z", "max_stars_repo_stars_event_max_datetime": "2022-02-14T08:13:22.000Z", "max_issues_repo_path": "ecsades/R/fit_wln.r", "max_issues_repo_name": "ECSADES/ecsades-r", "max_issues_repo_head_hexsha": "47ea50385c48030729d8227031a8ca73ab6a30b6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 17, "max_issues_repo_issues_event_min_datetime": "2019-01-22T13:00:29.000Z", "max_issues_repo_issues_event_max_datetime": "2019-11-04T16:45:59.000Z", "max_forks_repo_path": "ecsades/R/fit_wln.r", "max_forks_repo_name": "ECSADES/ecsades-r", "max_forks_repo_head_hexsha": "47ea50385c48030729d8227031a8ca73ab6a30b6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 41.1884057971, "max_line_length": 122, "alphanum_fraction": 0.6502463054, "num_tokens": 1741, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9399133515091156, "lm_q2_score": 0.8311430415844384, "lm_q1q2_score": 0.7812024417991097}} {"text": "# ***************************** Neural Network ***************************\r\nsigmoid <- function(z) {\r\n return(1/(1 + exp(-z)))\r\n}\r\n\r\n## Loss Function (Cross Entropy)\r\nforward <- function(theta, X, y, lambda) {\r\n m <- length(y)\r\n return(1/m * sum(-y * log(sigmoid(X %*% theta)) - (1 - y) *\r\n log(1 - sigmoid(X %*% theta))) + lambda/2/m * sum(theta[-1]^2))\r\n}\r\n\r\n\r\n## Gradient\r\ngradient <- function(theta, X, y, lambda) {\r\n m <- length(y)\r\n return(1/m * t(X) %*% (sigmoid(X %*% theta) - y) + lambda/m *\r\n c(0, theta[-1]))\r\n}\r\n\r\n# expand 2-dimension to N dimensions: N = (degree + 1) * (degree + 2) / 2\r\nmapFeature <- function(X1, X2, degree) {\r\n out <- rep(1, length(X1)) #for bias\r\n for (i in 1:degree) {\r\n for (j in 0:i) {\r\n out <- cbind(out, (X1^(i - j)) * (X2^j))\r\n }\r\n }\r\n return(out)\r\n}\r\n\r\n# ***************************** Parameter Optimizer ***************************\r\n\r\nlambda <- 1\r\nlearningRate <- 1e-1\r\nmaxIteration <- 10000\r\ntolerance <- 1e-6\r\n\r\nmu <- 0.9\r\nv <- NA\r\nm <- NA\r\ncache <- NA\r\ndecayRate <- 0.99\r\nbeta1 <- 0.9\r\nbeta2 <- 0.995\r\n\r\ntrain <- function(dt, y, method){\r\n nPara <- ncol(dt)\r\n initialTheta <- rep(0, nPara)\r\n v <<- rep(0, nPara)\r\n m <<- rep(0, nPara)\r\n cache <<- rep(0, nPara)\r\n \r\n #sampling data from all train data: mini-batch\r\n #here, give all data (full batch)\r\n res <- paraOptim(dt, y, initialTheta, method)\r\n}\r\n\r\nTRACE_MODE <- TRUE\r\ntrace.log <- NULL\r\ntrace.level <- 10\r\n\r\nparaOptim <- function(dt, y, theta, method){\r\n trace.df <- NULL\r\n \r\n #pre_loss <- NaN\r\n for(i in 0:maxIteration){\r\n loss <- forward(theta, dt, y, lambda)\r\n dx <- gradient(theta, dt, y, lambda)\r\n \r\n if(TRACE_MODE && (i %% trace.level == 0) ){\r\n trace.row <- c(epoch=i, loss=loss, theta=theta)\r\n trace.df <- rbind(trace.df, trace.row)\r\n }\r\n \r\n delta <- paraUpdate(method, dx, i+1)\r\n theta <- theta + delta\r\n \r\n if(sqrt(sum(delta ^ 2)) < tolerance) break\r\n #if((!is.nan(pre_loss)) && abs(pre_loss - loss) < tolerance) break\r\n #pre_loss <- loss\r\n }\r\n \r\n if(i %% maxIteration != 0){\r\n trace.row <- c(epoch=i, loss=loss, theta=theta)\r\n trace.df <- rbind(trace.df, trace.row)\r\n }\r\n \r\n converged <- if(i >= maxIteration) FALSE else TRUE\r\n trace.log <<- rbind(trace.log, list(method=method, final.loss=loss, final.iteration=i, converged=converged, trace=trace.df))\r\n \r\n print(theta)\r\n print(i)\r\n print(loss)\r\n \r\n return(list(theta=theta,loss=loss,iteration=i))\r\n}\r\n\r\nparaUpdate <- function(method, dx, t){\r\n if(method == \"SGD\"){ #Stochastic Gradient Descent\r\n delta <- -learningRate * dx\r\n }\r\n else if(method == \"momentum\"){\r\n v <<- mu * v - learningRate * dx\r\n delta <- v\r\n }\r\n else if(method == \"NAG\"){ #Nesterov Accelerated Gradient\r\n v_prev <- v\r\n v <<- mu * v - learningRate * dx\r\n delta <- -mu * v_prev + (1 + mu) * v\r\n }\r\n else if(method == \"AdaGrad\"){ #Duchi et al., 2011\r\n cache <<- cache + dx ^ 2\r\n delta <- -learningRate * dx / (sqrt(cache) + 1e-7)\r\n }\r\n else if(method == \"RmsProp\"){ #Geoff Hinton’s Coursera, 2012\r\n cache <<- cache * decayRate + dx ^ 2 * (1 - decayRate)\r\n delta <- -learningRate * dx / (sqrt(cache) + 1e-7)\r\n }\r\n else if(method == \"Adam\"){ #Kingma and Ba, 2014\r\n m <<- beta1 * m + (1-beta1) * dx\r\n v <<- beta2 * v + (1-beta2) * (dx ^ 2)\r\n if(t < 10){\r\n mb <- m / (1-beta1^t) \r\n vb <- v / (1-beta2^t) \r\n }\r\n else{\r\n mb <- m\r\n vb <- v\r\n }\r\n delta <- -learningRate * mb / (sqrt(vb) + 1e-7)\r\n }\r\n else{\r\n print(\"Error: No such optimization method!\")\r\n }\r\n \r\n return(delta)\r\n}\r\n\r\n# ***************************** TEST Stage ***************************\r\n\r\ndata <- read.csv(\"ex2data2.txt\", header = F) #from Andrew Ng Course\r\n\r\nsampleSize <- 1000\r\n\r\nrandomSample <- function(sampleSize){\r\n data <- cbind(runif(sampleSize, -1, 1), runif(sampleSize, -1, 1), runif(sampleSize, -1, 1))\r\n data[,3] <- ifelse(data[,3] > 0, 1, 0)\r\n return(data)\r\n}\r\n\r\n#data <- randomSample(sampleSize) #generate random data\r\n\r\nX <- as.matrix(data[,c(1,2)])\r\ny <- data[,3]\r\nX <- mapFeature(X[,1],X[,2], 3)\r\nm <- nrow(X)\r\nn <- ncol(X)\r\n\r\ninitialTheta <- rep(0, n)\r\n#initialTheta <- rnorm(n) / sqrt(n) #Xavier initialization (Glorot et al., 2010)\r\n\r\ntrace.log <- NULL\r\n\r\ntrain(X, y, \"SGD\")\r\ntrain(X, y, \"momentum\")\r\ntrain(X, y, \"NAG\")\r\ntrain(X, y, \"AdaGrad\")\r\ntrain(X, y, \"RmsProp\")\r\ntrain(X, y, \"Adam\")\r\n\r\nplotRes(\"epoch\")\r\nplotRes(\"position\", paraX.ind=2, paraY.ind = 3) #para.ind = 1 is the bias parameter\r\n\r\nres <- optim(initialTheta, forward, gradient, X, y, lambda, method = \"BFGS\", control = list(maxit = maxIteration, trace=3))\r\nres$par\r\nres$value\r\nres$counts\r\nres <- optim(initialTheta, forward, gradient, X, y, lambda, method = \"L-BFGS-B\", control = list(maxit = maxIteration, trace=6))\r\nres$par\r\nres$value\r\nres$counts\r\n\r\n# **************************** Visulization ****************************\r\nmaxEpoch <- 500\r\nplotRes <- function(type, paraX.ind=2, paraY.ind=3) #show loss over paraX when set paraY.ind = 0\r\n{\r\n #color_arr <- NULL;\r\n xrange <- NA\r\n yrange <- NA\r\n labels <- NULL;\r\n for(i in 1:nrow(trace.log)){\r\n col <- rgb(runif(5),runif(5),runif(5))\r\n #color_arr <- cbind(color_arr, col)\r\n \r\n labels <- c(labels, trace.log[[i,1]])\r\n \r\n xx <- trace.log[i,5]\r\n td <- as.data.frame(xx$trace)\r\n if(is.na(xrange)) {\r\n xrange <- c(min(td[,2+paraX.ind]),max(td[,2+paraX.ind]))\r\n } \r\n else{\r\n xrange = c(min(xrange[1], min(td[,2+paraX.ind])),max(xrange[2], max(td[,2+paraX.ind])))\r\n }\r\n \r\n if(is.na(yrange)){\r\n yrange <- c(min(td[,2+paraY.ind]),max(td[,2+paraY.ind]))\r\n }\r\n else{\r\n yrange = c(min(yrange[1], min(td[,2+paraY.ind])),max(yrange[2], max(td[,2+paraY.ind]))) \r\n }\r\n }\r\n \r\n xx <- trace.log[1,5]\r\n td <- as.data.frame(xx$trace)\r\n if(type == \"epoch\"){\r\n px <- td$epoch\r\n py <- td$loss \r\n \r\n plot(x=px, y=py, col=color_arr[1], type=\"l\", main=\"Convergence Performance\", pch=0, xlab=\"epoch\", ylab=\"loss\", lty=1, lwd=2, xlim=c(0,maxEpoch))\r\n }\r\n else{\r\n px <- td[,2+paraX.ind]\r\n py <- td[,2+paraY.ind] \r\n \r\n xrange[2] <- xrange[2] + (xrange[2]-xrange[1])*0.4 #preserve space for legend\r\n plot(x=px, y=py, col=color_arr[1], type=\"l\", main=\"Convergence Performance\", pch=0, xlab=\"para 1\", ylab=\"para2\", lty=1, lwd=2,xlim=xrange,ylim=yrange)\r\n \r\n points(x=px[1], y=py[1], col=\"black\", type='p', lwd=2, lty=1, pch=16, cex=2) #start Point\r\n text(px[1],py[1], labels=\"start\", adj=c(-0.3, 0.2))\r\n }\r\n \r\n for(i in 2:nrow(trace.log)){\r\n xx <- trace.log[i,5]\r\n td <- as.data.frame(xx$trace)\r\n \r\n if(type == \"epoch\"){\r\n px <- td$epoch\r\n py <- td$loss\r\n }\r\n else{\r\n px <- td[,2+paraX.ind]\r\n py <- td[,2+paraY.ind]\r\n }\r\n points(x=px, y=py, col=color_arr[i], type='l', lwd=2, lty=1, pch=0) \r\n \r\n fp <- nrow(td)\r\n points(x=px[fp], y=py[fp], col=\"black\", type='p', lwd=2, lty=1, pch=13,cex=1.5) #final point\r\n }\r\n \r\n legend(\"topright\", legend = labels, col = color_arr, \r\n lty = 1, bg = \"transparent\", lwd=2)\r\n \r\n}\r\n\r\n", "meta": {"hexsha": "9f301879d8432f9675a389edb7928ee1cca1a84e", "size": 7119, "ext": "r", "lang": "R", "max_stars_repo_path": "source/R/parameter_optimizer.r", "max_stars_repo_name": "liu-gmo/DLinside", "max_stars_repo_head_hexsha": "71ee1c81f9dbaa1c8fd87898137b57a5ce403d50", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-06-24T20:37:20.000Z", "max_stars_repo_stars_event_max_datetime": "2017-06-24T20:37:20.000Z", "max_issues_repo_path": "source/R/parameter_optimizer.r", "max_issues_repo_name": "liu-gmo/DLinside", "max_issues_repo_head_hexsha": "71ee1c81f9dbaa1c8fd87898137b57a5ce403d50", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "source/R/parameter_optimizer.r", "max_forks_repo_name": "liu-gmo/DLinside", "max_forks_repo_head_hexsha": "71ee1c81f9dbaa1c8fd87898137b57a5ce403d50", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 27.7003891051, "max_line_length": 155, "alphanum_fraction": 0.5336423655, "num_tokens": 2345, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9372107949104865, "lm_q2_score": 0.8333245891029456, "lm_q1q2_score": 0.7810008005716262}} {"text": "# ************************************************\n### simon munzert\n### ols and multiple regression\n# ************************************************\n\nsource(\"packages.r\")\nsource(\"functions.r\")\n\n\n# ************************************************\n# Implementing interactive relationships ---------\n\ndata(\"wage1\")\n?wage1\n\n# without interaction\nsummary(wage_model <- lm(wage ~ exper + tenure, data = wage1))\n\n# with interaction\nsummary(wage_model <- lm(wage ~ exper + tenure + exper*tenure, data = wage1))\n\n# with interaction, multiplicative variable created manually\nwage1$experXtenure <- wage1$exper * wage1$tenure\nView(select(wage1, wage, exper, tenure, experXtenure))\nsummary(wage_model <- lm(wage ~ exper + tenure + experXtenure, data = wage1))\n\n# with interaction, constitutive variables automatically added\nsummary(wage_model <- lm(wage ~ exper*tenure, data = wage1))\n\n\n\n# ************************************************\n# Discrete constitutive terms --------------------\n\ndata(\"wage1\")\n?wage1\n\n# recode continuous variable to discrete variable\ntable(wage1$edu)\nwage1$educ_cat <- car::recode(wage1$educ, \"0:9='low' ; \n 10:14='medium' ; \n 15:18='high'\",\n as.factor.result = TRUE,\n levels = c(\"low\", \"medium\", \"high\"))\n\n# run model\nsummary(wage_model <- lm(wage ~ educ_cat*female, data = wage1))\nsummary(wage_model <- lm(wage ~ educ_cat, data = wage1))\n\n\n# ************************************************\n# Replicating Brambor et al. Fig. 2 --------------\n\n# simulation setup\nset.seed(123)\nN <- 500\nx <- runif(N, 0, 1) * 3\n\nz <- runif(N, 0, 1)\nz <- ifelse(z >= .5, 1, 0)\nz[z >= .5] <- 1\nz[z < .5] <- 0\n\nz <- rbinom(N, 1, .5)\nb0 <- 2\nb1 <- 0\nb2 <- 2\nb3 <- 2\ne <- rnorm(N, 0, sqrt(.5))\ny <- b0 + b1*x + b2*z + b3*x*z + e\ndat <- as.data.frame(y = y, x = x, z = z)\n# plot points\nplot(x[z==0], y[z==0], pch = 1, ylim = c(0, 10), xlab = \"X\", ylab = \"Y\")\npoints(x[z==1], y[z==1], pch = \"+\")\n# compute models\nmodel_full <- lm(y ~ x*z, data = dat)\nmodel_red <- lm(y ~ x*z - z, data = dat)\n# add lines, full model\nabline(coef = c(coef(model_full)[1], coef(model_full)[2]), lwd = 3)\nabline(coef = c(coef(model_full)[1] + coef(model_full)[3], coef(model_full)[2] + coef(model_full)[4]), lwd = 3)\n# add lines, reduced model\nabline(coef = c(coef(model_red)[1], coef(model_red)[2]), lwd = 3, col = \"red\")\nabline(coef = c(coef(model_red)[1], coef(model_red)[2] + coef(model_red)[3]), lwd = 3, col = \"red\")\n\n\n\n# ************************************************\n# Plotting marginal effects ----------------------\n\n## the interplot packacge\n\n# continuous * continuous setup\nsummary(wage_model <- lm(wage ~ exper*tenure, data = wage1))\n\n# tenure as mediator\ninterplot(m = wage_model, var1 = \"exper\", var2 = \"tenure\", hist = TRUE) +\n xlab('Tenure') +\n ylab('Estimated coefficient for experience') +\n ggtitle('Estimated coefficient of experience\\non wage by tenure') +\n theme(plot.title = element_text(face='bold'))\n\n# experience as mediator\ninterplot(m = wage_model, var1 = \"tenure\", var2 = \"exper\", hist = TRUE) +\n xlab('Experience') +\n ylab('Estimated coefficient for tenure') +\n ggtitle('Estimated coefficient of tenure\\non wage by experience') +\n theme(plot.title = element_text(face='bold'))\n\n# continuous * discrete setup\nwage1$woman <- as.factor(wage1$female)\nsummary(wage_model <- lm(wage ~ exper*woman, data = wage1))\n\n# tenure as mediator\ninterplot(m = wage_model, var1 = \"exper\", var2 = \"woman\") +\n xlab('Woman') +\n ylab('Estimated coefficient for experience') +\n ggtitle('Estimated coefficient of experience\\non wage by gender') +\n theme(plot.title = element_text(face='bold'))\n\n# experience as mediator\ninterplot(m = wage_model, var1 = \"woman\", var2 = \"exper\", hist = TRUE) +\n xlab('Woman') +\n ylab('Estimated Coefficient for gender') +\n ggtitle('Estimated Coefficient of gender\\non wage by experience') +\n theme(plot.title = element_text(face='bold'))\n\n# for more ways to tweak the plots, see\nbrowseURL(\"https://cran.r-project.org/web/packages/interplot/vignettes/interplot-vignette.html\")\n\n\n\n# ************************************************\n# Diagnosing non-linearity and common support ----\n\nlibrary(interflex)\n# Mac users facing installationg problems should check out\n# browseURL(\"http://yiqingxu.org/software/interaction/RGuide.html\")\n# and perform the listed Terminal calls\n\n# again, the model\nsummary(wage_model <- lm(wage ~ exper*tenure, data = wage1))\n\n# raw plots\ninter.raw(Y = \"wage\", D = \"tenure\", X = \"exper\", data = wage1)\ninter.raw(Y = \"wage\", D = \"exper\", X = \"tenure\", data = wage1)\ninter.raw(Y = \"wage\", D = \"female\", X = \"exper\", data = wage1)\n\n\n# plots of Generalized Additive Model (GAM)\ninter.gam(Y = \"wage\", D = \"exper\", X = \"tenure\", data = wage1)\n\n# binning\ninter.binning(Y = \"wage\", D = \"female\", X = \"exper\", Z = c(\"tenure\"), data = wage1)\ninter.binning(Y = \"wage\", D = \"exper\", X = \"tenure\", Z = c(\"female\"), data = wage1, Xdistr = \"density\")\ninter.binning(Y = \"wage\", D = \"exper\", X = \"tenure\", Z = c(\"female\"), data = wage1, cutoffs = (seq(0, 40, 10)))\n\n# kernel estimation\ninter.kernel(Y = \"wage\", D = \"exper\", X = \"tenure\", Z=\"female\", data = wage1, nboots = 200, parallel = TRUE, cores = 3)\n\n\n\n", "meta": {"hexsha": "f9d0a3511a30f11017760a29183f78cecdacdedc", "size": 5318, "ext": "r", "lang": "R", "max_stars_repo_path": "code/03-interactions.r", "max_stars_repo_name": "simonmunzert/stats-II-hertie-2017", "max_stars_repo_head_hexsha": "f577db8b0b5f2599e7896907233ef6871d793253", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "code/03-interactions.r", "max_issues_repo_name": "simonmunzert/stats-II-hertie-2017", "max_issues_repo_head_hexsha": "f577db8b0b5f2599e7896907233ef6871d793253", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "code/03-interactions.r", "max_forks_repo_name": "simonmunzert/stats-II-hertie-2017", "max_forks_repo_head_hexsha": "f577db8b0b5f2599e7896907233ef6871d793253", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2017-09-18T08:04:57.000Z", "max_forks_repo_forks_event_max_datetime": "2018-03-22T08:28:12.000Z", "avg_line_length": 32.8271604938, "max_line_length": 119, "alphanum_fraction": 0.5910116585, "num_tokens": 1546, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9230391558355999, "lm_q2_score": 0.8459424431344437, "lm_q1q2_score": 0.7808379985963219}} {"text": "## 2. Combining Vectors into Matrices ##\n\nharvard <- c(1,1,1,1,3)\nstanford <- c(2,9,3,4,10)\nMIT <- c(3,3,2,2,1)\ncambridge <- c(4,2,6,13,48)\noxford <- c(5,7,12,9,15)\ncolumbia <- c(6,13,13,12,4)\nuni_matrix<-rbind(harvard,stanford,MIT,cambridge,oxford,columbia)\nuni_matrix\n\n## 3. Naming Matrix Rows and Columns ##\n\nuni_matrix <- rbind(harvard, stanford, MIT, cambridge, oxford, columbia)\ncategories <- c(\"world_rank\", \"quality_of_education\", \"influence\", \"broad_impact\" ,\"patents\")\ncolnames(uni_matrix)<-categories\nuni_matrix\n\n## 4. Finding Matrix Dimensions ##\n\ntuition <- c(43280,45000,45016,49350,28450,55161)\ndim(uni_matrix)[1]==length(tuition)\n\n## 5. Adding Columns to Matrices ##\n\ntuition <- c(43280, 45000, 45016, 49350, 28450, 55161)\ncomplete_matrix<-cbind(uni_matrix,tuition)\ncomplete_matrix\n\n## 6. Indexing Matrices By Element ##\n\ncomplete_matrix <- cbind(uni_matrix, tuition)\noxford_influence<-complete_matrix['oxford','influence']\ncam_stan_patents<-complete_matrix[c('cambridge','stanford'),'patents']\ncam_stan_patents\n\n## 7. Subsetting Matrices by Rows and Columns ##\n\noxford_rank<-complete_matrix['oxford',]\ninfluence<-complete_matrix[,'influence']\nharv_mit_rank<-complete_matrix[c('harvard','MIT'),]\ninfluence_patents<-complete_matrix[,c('influence','patents')]\n\n## 8. Ranking Universites ##\n\nworld_rank_rank<-rank(complete_matrix[,'world_rank'])\nquality_of_education_rank<-rank(complete_matrix[,'quality_of_education'])\ninfluence_rank<-rank(complete_matrix[,'influence'])\nbroad_impact_rank<-rank(complete_matrix[,'broad_impact'])\npatents_rank<-rank(complete_matrix[,'patents'])\ntuition_rank<-rank(complete_matrix[,'tuition'])\n\n## 9. Scoring and Ranking Universities ##\n\nranks_matrix <- rbind(world_rank_rank, quality_of_education_rank, influence_rank, broad_impact_rank, patents_rank, tuition_rank)\nsum(ranks_matrix[,('harvard')])\nsum(ranks_matrix[,('stanford')])\nsum(ranks_matrix[,('MIT')]) \nsum(ranks_matrix[,('cambridge')])\nsum(ranks_matrix[,('oxford')])\nsum(ranks_matrix[,('columbia')]) ", "meta": {"hexsha": "5254aa02eaf51355b949a8d9cdb79471bc6a6ffd", "size": 2007, "ext": "r", "lang": "R", "max_stars_repo_path": "Working With Matrices-334.r", "max_stars_repo_name": "saquibmehmood/Data-Projects", "max_stars_repo_head_hexsha": "136fbcd46f728e09c627f690fa1fa6c1d71c3ad2", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2020-11-29T10:41:57.000Z", "max_stars_repo_stars_event_max_datetime": "2020-11-29T10:41:57.000Z", "max_issues_repo_path": "Working With Matrices-334.r", "max_issues_repo_name": "saquib-mehmood/R_basics_to_advanced", "max_issues_repo_head_hexsha": "136fbcd46f728e09c627f690fa1fa6c1d71c3ad2", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Working With Matrices-334.r", "max_forks_repo_name": "saquib-mehmood/R_basics_to_advanced", "max_forks_repo_head_hexsha": "136fbcd46f728e09c627f690fa1fa6c1d71c3ad2", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 32.9016393443, "max_line_length": 128, "alphanum_fraction": 0.7513702043, "num_tokens": 619, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9184802484881361, "lm_q2_score": 0.8499711699569787, "lm_q1q2_score": 0.7806817313898377}} {"text": "# ......................................................................................\n# ........................Exercise 4 - Continuous random variable.......................\n# ......................................................................................\n# ......................................................................................\n\n# If text does not display correctly, set File \\Reopen with Encoding ... to UTF-8 \n# Use CTRL + SHIFT + O to display the contents of the script \n# Use CTRL + ENTER to run commands on a single line \n\n# **The content of this script is only as a supplementary illustration to the exercise,\n# it is not necessary to know at the exam. It is important to be able to calculate\n# manually.**\n# \n# * Numerical integration in R ####\n# \n# R function **integrate**integrate(f, a, b)=$\\int_{a}^{b}f(x)dx$\n# \n# - **f** is a R function(defined by us) which has one input argument - a vector of\n# values in which to return its values\n# \n# - **a** lower integration limit\n# \n# - **b** upper integration limit\n# \n\n\nf = function(x){return(x*x)} # x ^ 2\na = -1\nb = 2\nintegrate(f, a, b)\n\nx = seq(0,10,0.1)\n\ny=x*x/100\nplot(x,y)\n\n(9*50-20^2)/9\n\n# Examples ####\n# \n# * Example 1. ####\n# \n# Random variable X has distribution function$F(x)=\\begin{cases} 0 & x \\leq\n# 0 \\\\ cx^2 & 0 < x \\leq 1 \\\\ 1 & 1 < x \\end{cases}$What values can the\n# constant c take?\n# \n\n\n# derivative of F(x) is the density of density f(x)\n# corresponding probability density at interval<0.1>\nf = function(x){return(2*x)} # f(x)=2x\na = 0\nb = 1\nintegrate(f, a, b)$value\n\n# c=1, so the distribution function looks like this:\nF.dist = function(x){\n res = x*x # x ^ 2\n res[x<=0] = 0 # 0 for x<=0\n res[x>1] = 1 # 1 for x>1\n return(res)\n}\n\nx = seq(from = -1, to = 2, by = 0.01) # points on the x-axis\nFX = F.dist(x) # values of F(x)\nplot(x, FX, type = 'l') # draw as a line\n\n\n# * Example 2. ####\n# \n# The distribution of a random variable X is given by the density$f(x)=\\begin{cases}\n# 2x+2 & x \\in <-1;0> \\\\ 0 & x \\notin <-1;0> \\end{cases}$Specify:\n# \n# ** 2. a) ####\n# \n# $F(x)$,\n# \n\n\nf.dens = function(x){\n res = 2*x + 2 \n # watch out for x<-1 because '<-' is in the assignment line\n res[x < -1] = 0 # 0 for x<=0\n res[x > 0] = 0 # 1 for x>1\n return(res)\n}\n\nx = seq(from = -2, to = 1, by = 0.01) # points on the x-axis\nfx = f.dens(x) # values of f(x)\nplot(x, fx, cex=0.2) # draw dots(cex is the size)\n\n\nF.dist = function(x){\n res = x*x+2*x+1 # x ^ 2 + 2x + 1\n res[x < -1] = 0 # 0 for x<=0\n res[x > 0] = 1 # 1 for x>1\n return(res)\n}\n\nx = seq(from = -2, to = 1, by = 0.01) # points on the x-axis\nFX = F.dist(x) # values of f(x)\nplot(x, FX, type='l') # draw dots(cex is the size)\n\n\n# ** 2. b) ####\n# \n# P(−2 ≤ X ≤ 0.5), P(−2 ≤ X ≤ −1), P(X>0.5), P(X=0.3)\n# \n\n\n# P(−2 ≤ X ≤.50.5)\nintegrate(f.dens, -2, -0.5)$value\nintegrate(f.dens, -1, -0.5)$value\n\n# P(−2 ≤ X − −1)\nintegrate(f.dens, -2, -1)$value\n\n# P(X>0.5)\nintegrate(f.dens, 0.5, 1e16)$value # This will not always work\n\n\n# P(X=0.3)\nintegrate(f.dens, 0.3, 0.3)$value\n# it is clear that this probability is 0\n# corresponds to the integral sa=b, ie with zero size on the x-axis\n\n\n# ** 2. c) ####\n# \n# mean, variance and standard deviation of the random variable X.\n# \n\n\n# E(X)\nx_fx = function(x){\n fx = f.dens(x)\n return(x*fx)\n} \n# we integrate only where we know that f(x) is nonzero\nE_X = integrate(x_fx, -1, 0)$value\nE_X\n-1/3\n\n# E(X ^ 2)\nxx_fx = function(x){\n fx = f.dens(x) \n return(x*x*fx)\n} \n# we integrate only where we know that f(x) is nonzero\nE_XX = integrate(xx_fx, -1, 0)$value\nE_XX\n1/6\n\n# D(X)\nD_X = E_XX - E_X^2\nD_X\n1/18\n\n# sigma(x)\nstd_X = sqrt(D_X)\nstd_X\nsqrt(2)/6\n\n# ** 2. d) ####\n# \n# mode $\\hat{x}$\n# \n\n\n# mode=0\n\n\n# ** 2. e) ####\n# \n# median $x_{0,5}$\n# \n\n\nx = seq(from = -2, to = 1, by = 0.001) # points on the x-axis\nFX = F.dist(x)\nplot(x, FX, type='l')\nlines(c(-2, 1),c(0.5, 0.5))\n\nx[FX >= 0.5][1] # first element zx for which F(x)>=0.5\n(-2+sqrt(2))/2\n\n# * Example 3. ####\n# \n# The random variable Y is defined as: Y=3X + 1, where X is the random variable from the\n# previous example. Specify:\n# \n# ** 3. a) ####\n# \n# $F_Y(y)$\n# \n\n\nFY.dist = function(y){\n # calculated from the relation FY(y)=P(Y 1] = 0 # 1 for x>1\n return(res)\n}\nintegrate(fY.dens,-2,1)$value # total integral check\ny = seq(from = -3, to = 2, by = 0.001) # points on the x-axis\nfY = fY.dens(y)\nplot(y, fY, cex=0.2)\n\n# ** 3. c) ####\n# \n# E(Y), D(Y), σ(Y)\n# \n\n\n# E(Y)\ny_fy = function(y){\n fy = fY.dens(y)\n return(y*fy)\n} \n# we integrate only where we know that f(y) is nonzero\nE_Y = integrate(y_fy, -2, 1)$value\nE_Y\n0\n\n# alternatively\nE_Y = 3*E_X + 1\nE_Y\n\n# E(Y ^ 2)\nyy_fy = function(y){\n fy = fY.dens(y)\n return(y*y*fy)\n} \n# we integrate only where we know that f(y) is nonzero\nE_YY = integrate(yy_fy, -2, 1)$value\nE_YY\n1/2\n\n# D(Y)\nD_Y = E_YY - E_Y^2\nD_Y\n1/2\n\n# alternatively\nD_Y = 3^2*D_X\nD_Y\n\n# sigma(Y)\nsqrt(D_Y)\nsqrt(2)/2\n\n# * Example 4 ####\n# \n# Calculate $\\omega$ such that a random variable X with probability\n# density:$f(x)=\\begin{cases} 0 & x < 0 \\\\ 3e^{-3x} & x \\geq 0 \\end{cases}$is\n# greater than $\\omega$ with probability 0.3.\n# \n\n\nF.dist = function(x){\n res = 1 - exp(-3*x)\n res[x < 0] = 0 # 0 for x<=0\n return(res)\n}\n\nx = seq(from = -1, to = 3, by = 0.001) # points on the x-axis\nFX = F.dist(x)\nplot(x, FX, type='l')\nlines(c(-1, 3),c(0.7, 0.7))\n\nx[FX >= 0.7][1]\n\n-1/3*log(0.3)\n\n\n\n", "meta": {"hexsha": "20b495f8ed46b6ef3edc6beda0d61a0fe406c5e8", "size": 5794, "ext": "r", "lang": "R", "max_stars_repo_path": "Exercise 4/T5_continuous_RV.r", "max_stars_repo_name": "Beremi/PS_eng_2022", "max_stars_repo_head_hexsha": "178bc329f3d67aa3bf6d8d16356692525502a87d", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Exercise 4/T5_continuous_RV.r", "max_issues_repo_name": "Beremi/PS_eng_2022", "max_issues_repo_head_hexsha": "178bc329f3d67aa3bf6d8d16356692525502a87d", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Exercise 4/T5_continuous_RV.r", "max_forks_repo_name": "Beremi/PS_eng_2022", "max_forks_repo_head_hexsha": "178bc329f3d67aa3bf6d8d16356692525502a87d", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2022-03-07T13:35:24.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-07T13:35:24.000Z", "avg_line_length": 19.7074829932, "max_line_length": 88, "alphanum_fraction": 0.5295132896, "num_tokens": 2205, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9273632876167045, "lm_q2_score": 0.8418256492357358, "lm_q1q2_score": 0.7806782016753187}} {"text": "#Random design\n\n'''\nA fast food franchise is test marketing 3 new menu items. \nTo find out if they the same popularity, 18 franchisee \nrestaurants are randomly chosen for participation in t\nhe study. In accordance with the completely randomized design, \n6 of the restaurants are randomly chosen to test market the\nfirst new menu item, another 6 for the second menu item, and\nthe remaining 6 for the last menu item.\n'''\n\n'''\nSuppose the following table represents the sales figures of \nthe 3 new menu items in the 18 restaurants after a week of \ntest marketing. At .05 level of significance, test whether \nthe mean sales volume for the 3 new menu items are all equal.\n\n'''\n\n#Cargar el archivo fastfood-1.txt\n\nlibrary(readr)\ndf1 <- read_csv('fastfood-1.csv')\nView(dataset)\n\n#Concatenar las filas\nr = c(t(as.matrix(df1)))\n\nf = c(\"Item1\",\"Item2\",\"Item3\") #niveles de tratamiento\nk = 3 #nro de niveles de tratamiento\nn = 6# #obesrvaciones por tratamiento\n\n#crear un vector de factores que corresponde a cada elemento de r en3 pasos\n\ntm = gl(k, 1, n*k, factor(f)) \n\n#aplicamos aov\nav = aov(formula formula = r ~ tm)\n\nsummary(av)\n\n'''\n Df Sum Sq Mean Sq F value Pr(>F)\ntm 2 745.4 372.7 2.541 0.112\nResiduals 15 2200.2 146.7 \n\nComo pvalue = 0.112>.05 niveles de significancia, aceptamos la hipotesis\n'''", "meta": {"hexsha": "5a504b9d940424956132985d66967046f5057374", "size": 1326, "ext": "r", "lang": "R", "max_stars_repo_path": "Parcial/4. ANOVA/CompletlyRandomizedDesign.r", "max_stars_repo_name": "jchudb93/Exp-Numerica", "max_stars_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Parcial/4. ANOVA/CompletlyRandomizedDesign.r", "max_issues_repo_name": "jchudb93/Exp-Numerica", "max_issues_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Parcial/4. ANOVA/CompletlyRandomizedDesign.r", "max_forks_repo_name": "jchudb93/Exp-Numerica", "max_forks_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 27.0612244898, "max_line_length": 75, "alphanum_fraction": 0.7209653092, "num_tokens": 381, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9343951698485603, "lm_q2_score": 0.8354835411997897, "lm_q1q2_score": 0.7806717853850541}} {"text": "\n#' @include Bayesian_Bricks.r\n\n\n\ncountFreq <- function(x,uniqx=NULL){\n if(!is.factor(x)){\n if(!is.null(uniqx)) x <- factor(x,levels=uniqx)\n else x <- factor(x)\n }\n as.numeric(tabulate(x,nbins = length(levels(x))))\n}\ncountFreq_Weighted <- function(x,uniqx=NULL,w){\n if(length(x)!=length(w)) stop(\"length of x and w don't match\")\n if(!is.factor(x)){\n if(!is.null(uniqx)) x <- factor(x,levels=uniqx)\n else x <- factor(x)\n }\n vapply(split(x=w,f=x),sum,FUN.VALUE = numeric(1),USE.NAMES = FALSE)\n}\n\n#' @title Random generation for Categorical distribution\n#' @description\n#' Generate random integer samples from a Categorical distribution. For a random variable x, the density function of categorical distribution is defined as\n#' \\deqn{prod_{k in 1:K} p_k^{I(x=k)}}\n#' Where K is the number of unique values.\n#' @seealso \\code{\\link{dCategorical}}\n#' @param n integer, number of samples.\n#' @param p numeric, probabilities. length(p)=K.\n#' @return An integer vector of length n.\n#' @export\n#' @examples\n#' rCategorical(n=20,p=c(1,2))\nrCategorical <- function(n,p){\n sample.int(n=length(p), size = n, replace = TRUE, prob = p)\n}\n\n#' @title Probability mass function for Categorical distribution\n#' @description\n#' Calculate probability masses for integer valued Categorical random samples.\n#' For a random variable x, the density function of categorical distribution is defined as\n#' \\deqn{prod_{k in 1:K} p_k^{I(x=k)}}\n#' Where K is the number of unique values.\n#' @seealso \\code{\\link{rCategorical}}\n#' @param x integer, categorical samples.\n#' @param p numeric, probabilities.\n#' @return A numeric vector of the same length of 'x'.\n#' @export\n#' @examples\n#' \\donttest{\n#' dCategorical(x=c(1L,2L,1L),p=c(1,2))\n#' }\ndCategorical <- function(x,p){\n p[x]\n}\n\n#' @title Random generation for Dirichelt distribution\n#' @description\n#' Generate random samples from Dirichlet distribution. For a random vector x, the density function is Dirichlet distribution is defined as:\n#' 1/Beta(alpha) prod_{i=1:p} x_i^{alpha_i -1}\n#' Where Beta() is the beta function. p is the dimension of x.\n#' @seealso \\code{\\link{dDir}}\n#' @param n integer, number of samples.\n#' @param alpha numeric, Dirichlet parameter.\n#' @return A numeric matrix of n rows and length(alpha) columns.\n#' @export\n#' @examples\n#' rDir(5,c(1,2,3)) #generate 5 samples with parameters c(1,2,3)\n#' @import stats\nrDir <- function(n, alpha){\n l <- length(alpha)\n x <- matrix(rgamma(l * n, alpha), ncol = l, byrow = TRUE)\n sm <- x %*% rep(1, l)\n x/as.vector(sm)\n}\n\n#' @title Density function for Dirichelt distribution\n#' @description\n#' Calculate the densities of a given set of Dirichlet samples. For a random vector x, the density function is defined as:\n#' 1/Beta(alpha) prod_{i=1:p} x_i^{alpha_i -1}\n#' Where Beta() is the beta function. p is the dimension of x.\n#' @seealso \\code{\\link{rDir}}\n#' @param x matrix or numeric vector, if matrix every row of x is an observation, if numeric vector, it's the same as a matrix with only one row.\n#' @param alpha numeric, Dirichlet parameter.\n#' @param LOG logical, return the log density if set to \"TRUE\".\n#' @return A numeric vector of density values.\n#' @export\n#' @examples\n#' x <- rDir(5,c(1,2,3)) #generate 5 samples with parameters c(1,2,3)\n#' dDir(x,c(1,2,3))\n#' dDir(x,c(1,2,3),LOG=TRUE)\ndDir <- function(x, alpha,LOG=FALSE){\n if(!is.matrix(x))\n if(is.numeric(x))\n x <- t(x)\n else\n stop(\"Error in ddir():x must be a matrix or an integer/numeric vector\")\n if(length(alpha)==1) alpha <- rep(alpha,ncol(x))\n if(ncol(x)!=length(alpha))\n stop(\"Error in ddir(): columns of x and length of alpha don't match\")\n out <- apply(x,1,function(l){\n s <- (alpha - 1) * log(l)\n s <- ifelse(alpha == 1 & l == 0, -Inf, s)\n sum(s)\n })\n logD <- sum(lgamma(alpha)) - lgamma(sum(alpha))\n out <- out- logD\n if(!LOG) out <- exp(out)\n return(out)\n}\n\n#' @title Create objects of type \"CatDirichlet\".\n#' @description\n#' Create an object of type \"CatDirichlet\", which represents the Categorical (Multinomial) and Dirichlet conjugate structure:\n#' \\deqn{pi|alpha \\sim Dir(alpha)}\n#' \\deqn{x|pi \\sim Categorical(pi)}\n#' Where Dir() is the Dirichlet distribution, Categorical() is the Categorical distribution. See \\code{?dDir} and \\code{dCategorical} for the definitions of these distribution. \\cr\n#' The created object will be used as a place for recording and accumulating information in the related inference/sampling functions such as posterior(), posteriorDiscard(), MAP(), marginalLikelihood(), dPosteriorPredictive(), rPosteriorPredictive() and so on. A categorical distribution is defined on a set of unique labels, usually these labels are integers, they can also be characters and factors.\n#' @seealso \\code{\\link{posterior.CatDirichlet}},\\code{\\link{posteriorDiscard.CatDirichlet}},\\code{\\link{MAP.CatDirichlet}},\\code{\\link{MPE.CatDirichlet}},\\code{\\link{marginalLikelihood.CatDirichlet}},\\code{\\link{rPosteriorPredictive.CatDirichlet}},\\code{\\link{dPosteriorPredictive.CatDirichlet}} ...\n#' @param objCopy an object of type \"CatDirichlet\". If \"objCopy\" is not NULL, the function create a new \"CatDirichlet\" object by copying the content from objCopy, otherwise this new object will be created by using \"ENV\" and \"gamma\". Default NULL.\n#' @param ENV environment, specify where the object will be created.\n#' @param gamma list, a named list of parameters, gamma=list(alpha,uniqueLabels). Where gamma$alpha is a numeric vector specifying the parameters of the Dirichlet distribution, gamma$uniqueLabels is a integer/character vector specifying the unique category labels of the Categorical distribution.\n#' @return An object of class \"CatDirichlet\".\n#' @export\n#' @examples\n#' obj <- CatDirichlet(gamma=list(alpha=c(1,2,1),uniqueLabels = letters[1:3]))\n#' obj #print the content\n#' @references Murphy, Kevin P. Machine learning: a probabilistic perspective. MIT press, 2012.\nCatDirichlet <- function(objCopy=NULL,ENV=parent.frame(),gamma=list(alpha=1,uniqueLabels=1L)){\n object <- BasicBayesian(ENV = ENV)\n\n if(!is.null(objCopy)){\n if(!.is(objCopy,\"CatDirichlet\")) stop(\"'objCopy' must be of class 'CatDirichlet'\")\n object$gamma <- objCopy$gamma\n object$H <- objCopy$H\n object$F <- objCopy$F\n }else{\n if(!missing(gamma))\n if((!is.list(gamma)) |\n (!all(names(gamma) %in% c(\"alpha\",\"uniqueLabels\"))))\n stop(\"gamma must be list(alpha,uniqueLabels)\")\n if(length(gamma$alpha)==1L) gamma$alpha <- rep(gamma$alpha,length(gamma$uniqueLabels))\n if(length(gamma$alpha)!=length(gamma$uniqueLabels)) stop(\"length of 'alpha' and 'uniqueLabels' in 'gamma' don't match!\")\n object$gamma <- gamma\n object$H <- \"Dirichlet\"\n object$F <- \"Categorical\"\n }\n \n class(object) <- c(\"CatDirichlet\",class(object))\n return(object)\n}\n\n#' @title Sufficient statistics of a \"CatDirichlet\" object\n#' @description\n#' For following Categorical-Dirichlet model structure:\n#' \\deqn{pi|alpha \\sim Dir(alpha)}\n#' \\deqn{x|pi \\sim Categorical(pi)}\n#' Where Dir() is the Dirichlet distribution, Categorical() is the Categorical distribution. See \\code{?dDir} and \\code{dCategorical} for the definitions of these distribution. \\cr\n#' The sufficient statistics of a set of samples x is: \\cr\n#' \\itemize{\n#' \\item the effective counts of each unique label in x. i.e. T(x)[i] = sum(uniqueLabels[i]%in%x). Unique values of x must be in obj$gamma$uniqueLabels, where \"obj\" is a \"CatDirichlet\" object, see examples below.\n#' }\n#' @seealso \\code{\\link{CatDirichlet}}, \\code{\\link{sufficientStatistics_Weighted.CatDirichlet}} \n#' @param obj A \"CatDirichlet\" object.\n#' @param x numeric,integer or character, samples of the Categorical distribution.\n#' @param foreach logical, specifying whether to return the sufficient statistics for each observation. Default FALSE.\n#' @param ... Additional arguments to be passed to other inherited types.\n#' @return An object of class \"ssCat\", the sufficient statistics of a set of categorical samples. Or an object of the same class as x if foreach=TRUE.\n#' @export\n#' @examples\n#' obj <- CatDirichlet(gamma=list(alpha=runif(26,1,2),uniqueLabels = letters))\n#' x <- sample(letters,size = 20,replace = TRUE)\n#' w <- runif(20)\n#' sufficientStatistics(obj=obj,x=x) #return the counts of each unique label\n#' sufficientStatistics_Weighted(obj=obj,x=x,w=w) #return the weighted counts of each unique lable\n#' sufficientStatistics(obj=obj,x=x,foreach = TRUE) #return the sample itself\n#' @references Murphy, Kevin P. Machine learning: a probabilistic perspective. MIT press, 2012.\nsufficientStatistics.CatDirichlet <- function(obj,x,foreach=FALSE,...){\n if(missing(x)) stop(\"'x' must be specified\")\n if(!is.vector(x)) x <- as.vector(x)\n if(foreach){\n x\n }else{\n ss <- countFreq(x=x,uniqx = obj$gamma$uniqueLabels)\n class(ss) <- \"ssCat\"\n ss\n }\n}\n\n#' @title Weighted sufficient statistics of a \"CatDirichlet\" object\n#' @description\n#' For following Categorical-Dirichlet model structure:\n#' \\deqn{pi|alpha \\sim Dir(alpha)}\n#' \\deqn{x|pi \\sim Categorical(pi)}\n#' Where Dir() is the Dirichlet distribution, Categorical() is the Categorical distribution. See \\code{?dDir} and \\code{dCategorical} for the definitions of these distribution. \\cr\n#' the sufficient statistics of a set of samples x and weights w are: \\cr\n#' the effective counts (in this case the sum of the weight w) of each unique label in x \\cr\n#' Unique values of x must be in obj$gamma$uniqueLabels, where \"obj\" is a \"CatDirichlet\" object, see examples below.\n#' \n#' @seealso \\code{\\link{sufficientStatistics.CatDirichlet}} \\code{\\link{CatDirichlet}}\n#' @param obj A \"CatDirichlet\" object.\n#' @param x numeric,integer or character, samples of the Categorical distribution.\n#' @param w numeric, sample weights.\n#' @param foreach logical, specifying whether to return the sufficient statistics for each observation. Default FALSE.\n#' @param ... Additional arguments to be passed to other inherited types.\n#' @return An object of class \"ssCat\", the sufficient statistics of a set of categorical samples. Or an object of the same class as x if foreach=TRUE.\n#' @export\n#' @examples\n#' obj <- CatDirichlet(gamma=list(alpha=runif(26,1,2),uniqueLabels = letters))\n#' x <- sample(letters,size = 20,replace = TRUE)\n#' w <- runif(20)\n#' sufficientStatistics(obj=obj,x=x) #return the counts of each unique label\n#' sufficientStatistics_Weighted(obj=obj,x=x,w=w) #return the weighted counts of each unique lable\n#' @references Murphy, Kevin P. Machine learning: a probabilistic perspective. MIT press, 2012.\nsufficientStatistics_Weighted.CatDirichlet <- function(obj,x,w,foreach=FALSE,...){\n if(missing(x)|missing(w)) stop(\"'x' and 'w' must be both specified\")\n if(!is.vector(x)) x <- as.vector(x)\n if(!is.vector(w)) w <- as.vector(w)\n if(length(x)!=length(w)) stop(\"length of 'x' and 'w' don't match!\")\n if(foreach){\n x\n }else{\n ss <- countFreq_Weighted(x=x,uniqx = obj$gamma$uniqueLabels,w=w)\n class(ss) <- \"ssCat\"\n ss\n }\n}\n\n#' @title Update a \"CatDirichlet\" object with sample sufficient statistics\n#' @description\n#' For the model structure:\n#' \\deqn{pi|alpha \\sim Dir(alpha)}\n#' \\deqn{x|pi \\sim Categorical(pi)}\n#' Where Dir() is the Dirichlet distribution, Categorical() is the Categorical distribution. See \\code{?dDir} and \\code{dCategorical} for the definitions of these distribution. \\cr\n#' update alpha by adding the information of newly observed samples x. \\cr\n#' The model structure and prior parameters are stored in a \"CatDirichlet\" object, the prior parameters in this object will be updated after running this function.\n#'\n#' @seealso \\code{\\link{CatDirichlet}},\\code{\\link{posteriorDiscard.CatDirichlet}}\n#' @param obj A \"CatDirichlet\" object.\n#' @param ss Sufficient statistics of x. In Categorical-Dirichlet case the sufficient statistic of sample x can be either x itself, of an \"ssCat\" object generated by the function sufficientStatistics.CatDirichlet().\n#' @param w Sample weights, default NULL.\n#' @param ... Additional arguments to be passed to other inherited types.\n#' @return None. the gamma stored in \"obj\" will be updated based on \"ss\".\n#' @export\n#' @examples\n#' obj <- CatDirichlet(gamma=list(alpha=rep(1,26),uniqueLabels = letters))\n#' x <- sample(letters,size = 20,replace = TRUE)\n#' w <- runif(20)\n#' posterior(obj=obj,ss=x)\n#' obj\n#' posteriorDiscard(obj=obj,ss=x)\n#' obj\n#' ## weighted sample\n#' posterior(obj=obj,ss=x,w=w)\n#' obj\n#' posteriorDiscard(obj=obj,ss=x,w=w)\n#' obj\n#' @references Murphy, Kevin P. Machine learning: a probabilistic perspective. MIT press, 2012.\nposterior.CatDirichlet <- function(obj,ss,w=NULL,...){\n if(missing(ss)) stop(\"'ss' must be specified\")\n if(.is(ss,\"ssCat\")){\n posterior_bySufficientStatistics.CatDirichlet(obj=obj,ss=ss)\n invisible(return())\n }\n if(!is.vector(ss)) ss <- as.vector(ss)\n idx <- match(ss,obj$gamma$uniqueLabels,nomatch = NA)\n if(anyNA(idx)) stop(\"Detect un-recorded label!\")\n if(!is.null(w)){\n if(!is.vector(w)) w <- as.vector(w)\n if(length(ss)!=length(w)) stop(\"length of 'ss' and 'w' don't match!\")\n if(length(ss)==1L){\n obj$gamma$alpha[idx] <- obj$gamma$alpha[idx]+w\n }else{\n for(i in 1L:length(ss)) obj$gamma$alpha[idx[i]] <- obj$gamma$alpha[idx[i]]+w[i]\n }\n }else{\n if(length(ss)==1L){\n obj$gamma$alpha[idx] <- obj$gamma$alpha[idx]+1\n }else{\n for(id in idx) obj$gamma$alpha[id] <- obj$gamma$alpha[id]+1\n }\n }\n}\n\n#' @title Update a \"CatDirichlet\" object with sample sufficient statistics\n#' @description Update a \"CatDirichlet\" object with sample sufficient statistics\n#' @param obj A \"CatDirichlet\" object.\n#' @param ss Sufficient statistics of x. In Categorical-Dirichlet case the sufficient statistic of sample x can be either x itself, of an \"ssCat\" object generated by the function sufficientStatistics.CatDirichlet().\n#' @param ... Additional arguments to be passed to other inherited types.\n#' @return None. the gamma stored in \"obj\" will be updated based on \"ss\".\n#' @references Murphy, Kevin P. Machine learning: a probabilistic perspective. MIT press, 2012.\nposterior_bySufficientStatistics.CatDirichlet <- function(obj,ss,...){\n if(missing(ss)) stop(\"'ss' must be specified\")\n if(!.is(ss,\"ssCat\")) stop(\"'ss' must be of class 'ssCat', you need to use sufficientStatistics() to generate 'ssCat' objects\")\n \n if(length(ss)!=length(obj$gamma$alpha)) stop(\"length 'ss' and dirichlet parameters don't match\")\n obj$gamma$alpha <- obj$gamma$alpha + as.numeric(ss)\n}\n\n#' @title Update a \"CatDirichlet\" object with sample sufficient statistics\n#' @description\n#' Contrary to posterior(), this function will update alpha by removing the information of observed samples x for the model structure:\n#' \\deqn{pi|alpha \\sim Dir(alpha)}\n#' \\deqn{x|pi \\sim Categorical(pi)}\n#' Where Dir() is the Dirichlet distribution, Categorical() is the Categorical distribution. See \\code{?dDir} and \\code{dCategorical} for the definitions of these distribution. \\cr\n#' The model structure and prior parameters are stored in a \"CatDirichlet\" object, the prior parameters in this object will be updated after running this function.\n#'\n#' @seealso \\code{\\link{CatDirichlet}},\\code{\\link{posterior.CatDirichlet}}\n#' @param obj A \"CatDirichlet\" object.\n#' @param ss Sufficient statistics of x. In Categorical-Dirichlet case the sufficient statistic of sample x can be either x itself, of an \"ssCat\" object generated by the function sufficientStatistics.CatDirichlet().\n#' @param w Sample weights,default NULL.\n#' @param ... Additional arguments to be passed to other inherited types.\n#' @return None. the prior parameters stored in \"obj\" will be updated with the information in \"ss\".\n#' @export\n#' @examples\n#' obj <- CatDirichlet(gamma=list(alpha=rep(1,26),uniqueLabels = letters))\n#' x <- sample(letters,size = 20,replace = TRUE)\n#' w <- runif(20)\n#' posterior(obj=obj,ss=x)\n#' obj\n#' posteriorDiscard(obj=obj,ss=x)\n#' obj\n#' ## weighted sample\n#' posterior(obj=obj,ss=x,w=w)\n#' obj\n#' posteriorDiscard(obj=obj,ss=x,w=w)\n#' obj\n#' @references Murphy, Kevin P. Machine learning: a probabilistic perspective. MIT press, 2012.\nposteriorDiscard.CatDirichlet <- function(obj,ss,w=NULL,...){\n if(missing(ss)) stop(\"'ss' must be specified\")\n if(.is(ss,\"ssCat\")){\n posteriorDiscard_bySufficientStatistics.CatDirichlet(obj = obj,ss = ss)\n invisible(return())\n }\n if(!is.vector(ss)) ss <- as.vector(ss)\n idx <- match(ss,obj$gamma$uniqueLabels,nomatch = NA)\n if(anyNA(idx)) stop(\"Detect un-recorded label!\")\n if(!is.null(w)){\n if(!is.vector(w)) w <- as.vector(w)\n if(length(ss)!=length(w)) stop(\"length of 'ss' and 'w' don't match!\")\n if(length(ss)==1L){\n obj$gamma$alpha[idx] <- obj$gamma$alpha[idx]-w\n }else{\n for(i in 1L:length(ss)) obj$gamma$alpha[idx[i]] <- obj$gamma$alpha[idx[i]]-w[i]\n }\n }else{\n if(length(ss)==1L){\n obj$gamma$alpha[idx] <- obj$gamma$alpha[idx]-1\n }else{\n for(id in idx) obj$gamma$alpha[id] <- obj$gamma$alpha[id]-1\n }\n }\n\n}\n\n#' @title Update the prior Dirichlet distribution with sample sufficient statistics\n#' @seealso \\code{\\link{posteriorDiscard}}\n#' @param obj A \"CatDirichlet\" object.\n#' @param ss Sufficient statistics of x. In Categorical-Dirichlet case the sufficient statistic of sample x can be either x itself, of an \"ssCat\" object generated by the function sufficientStatistics.CatDirichlet().\n#' @param ... Additional arguments to be passed to other inherited types.\n#' @return None. the gamma stored in \"obj\" will be updated based on \"ss\".\n#' @references Murphy, Kevin P. Machine learning: a probabilistic perspective. MIT press, 2012.\nposteriorDiscard_bySufficientStatistics.CatDirichlet <- function(obj,ss,...){\n if(missing(ss)) stop(\"'ss' must be specified\")\n if(!.is(ss,\"ssCat\")) stop(\"'ss' must be of class 'ssCat', you need to use sufficientStatistics() to generate 'ssCat' objects\")\n if(length(ss)!=length(obj$gamma$alpha)) stop(\"length 'ss' and dirichlet parameters don't match\")\n obj$gamma$alpha <- obj$gamma$alpha - as.numeric(ss)\n}\n\n#' @title MAP estimate of a \"CatDirichlet\" object\n#' @description\n#' Generate the MAP estimate of \"pi\" in following Categorical-Dirichlet structure: \n#' \\deqn{pi|alpha \\sim Dir(alpha)}\n#' \\deqn{x|pi \\sim Categorical(pi)}\n#' Where Dir() is the Dirichlet distribution, Categorical() is the Categorical distribution. See \\code{?dDir} and \\code{dCategorical} for the definitions of these distribution. \\cr\n#' The model structure and prior parameters are stored in a \"CatDirichlet\" object. \\cr\n#' MAP is pi_MAP = argmax p(pi|alpha,x).\n#' @seealso \\code{\\link{CatDirichlet}}\n#' @param obj A \"CatDirichlet\" object.\n#' @param ... Additional arguments to be passed to other inherited types.\n#' @return A numeric vector, the MAP estimate of \"pi\".\n#' @export\n#' @examples\n#' obj <- CatDirichlet(gamma=list(alpha=rep(1,26),uniqueLabels = letters))\n#' x <- sample(letters,size = 20,replace = TRUE)\n#' w <- runif(20)\n#' posterior(obj=obj,ss=x,w=w)\n#' MAP(obj)\n#' @references Murphy, Kevin P. Machine learning: a probabilistic perspective. MIT press, 2012.\nMAP.CatDirichlet <- function(obj,...){\n tmp <- obj$gamma$alpha-1\n tmp/sum(tmp)\n}\n\n#' @title MPE of a \"CatDirichlet\" object\n#' @description\n#' Generate the MPE of \"pi\" in following Categorical-Dirichlet structure:\n#' \\deqn{pi|alpha \\sim Dir(alpha)}\n#' \\deqn{x|pi \\sim Categorical(pi)}\n#' Where Dir() is the Dirichlet distribution, Categorical() is the Categorical distribution. See \\code{?dDir} and \\code{dCategorical} for the definitions of these distribution. \\cr\n#' The model structure and prior parameters are stored in a \"CatDirichlet\" object. \\cr\n#' MPE is pi_MPE = E(pi|alpha,x), E() is the expectation function.\n#' @seealso \\code{\\link{CatDirichlet}}\n#' @param obj A \"CatDirichlet\" object.\n#' @param ... Additional arguments to be passed to other inherited types.\n#' @return A numeric vector, the MPE of \"pi\".\n#' @export\n#' @examples\n#' obj <- CatDirichlet(gamma=list(alpha=rep(1,26),uniqueLabels = letters))\n#' x <- sample(letters,size = 20,replace = TRUE)\n#' w <- runif(20)\n#' posterior(obj=obj,ss=x,w=w)\n#' MPE(obj)\n#' @references Murphy, Kevin P. Machine learning: a probabilistic perspective. MIT press, 2012.\nMPE.CatDirichlet <- function(obj,...){\n obj$gamma$alpha/sum(obj$gamma$alpha)\n}\n\n#' @title Density function of the posterior distribution of a \"CatDirichlet\" object\n#' @description\n#' Generate the the density value of the posterior distribution of the following structure:\n#' \\deqn{pi|alpha \\sim Dir(alpha)}\n#' \\deqn{x|pi \\sim Categorical(pi)}\n#' Where Dir() is the Dirichlet distribution, Categorical() is the Categorical distribution. See \\code{?dDir} and \\code{dCategorical} for the definitions of these distribution. \\cr\n#' The model structure and prior parameters are stored in a \"CatDirichlet\" object. \\cr\n#' Posterior density is the density function of Dir(pi|alpha).\n#' @seealso \\code{\\link{CatDirichlet}}, \\code{\\link{rPosterior.CatDirichlet}}\n#' @param obj A \"CatDirichlet\" object.\n#' @param pi matrix or a numeric vector. When pi is a matrix, each row is an observation. When pi is a vector, it will be treated as only one observation.\n#' @param LOG Return the log density if set to \"TRUE\".\n#' @param ... Additional arguments to be passed to other inherited types.\n#' @return numeric vector, the posterior densities for each row of pi.\n#' @export\n#' @examples\n#' obj <- CatDirichlet(gamma=list(alpha=runif(26),uniqueLabels = letters))\n#' dPosterior(obj = obj,pi = runif(26))\n#' dPosterior(obj = obj,pi = matrix(runif(26*10),nrow = 10))\ndPosterior.CatDirichlet <- function(obj,pi,LOG=TRUE,...){\n if(is.vector(pi)) pi <- matrix(pi,nrow=1)\n if(ncol(pi)!=length(obj$gamma$alpha)) stop(\"Dimensions of pi and obj$gamma$alpha don't match!\")\n dDir(x=pi,alpha = obj$gamma$alpha,LOG = LOG)\n}\n\n#' @title Generate ramdom samples from the posterior distribution of a \"CatDirichlet\" object\n#' @description\n#' Generate random samples from the posterior distribution of the following structure:\n#' \\deqn{pi|alpha \\sim Dir(alpha)}\n#' \\deqn{x|pi \\sim Categorical(pi)}\n#' Where Dir() is the Dirichlet distribution, Categorical() is the Categorical distribution. See \\code{?dDir} and \\code{dCategorical} for the definitions of these distribution. \\cr\n#' The model structure and prior parameters are stored in a \"CatDirichlet\" object. \\cr\n#' Posterior distribution is Dir(pi|alpha).\n#' @seealso \\code{\\link{CatDirichlet}}, \\code{\\link{dPosterior.CatDirichlet}}\n#' @param obj A \"CatDirichlet\" object.\n#' @param n integer, the number of samples to be generated.\n#' @param ... Additional arguments to be passed to other inherited types.\n#' @return A matrix, each row is a sample of pi.\n#' @export\n#' @examples\n#' obj <- CatDirichlet(gamma=list(alpha=rep(1,26),uniqueLabels = letters))\n#' rPosterior(obj = obj,n=3)\nrPosterior.CatDirichlet <- function(obj,n=1,...){\n rDir(n=n,alpha = obj$gamma$alpha)\n}\n\n#' @title Marginal likelihood of a \"CatDirichlet\" object\n#' @description\n#' Generate the marginal likelihood of the following model structure:\n#' \\deqn{pi|alpha \\sim Dir(alpha)}\n#' \\deqn{x|pi \\sim Categorical(pi)}\n#' Where Dir() is the Dirichlet distribution, Categorical() is the Categorical distribution. See \\code{?dDir} and \\code{dCategorical} for the definitions of these distribution. \\cr\n#' The model structure and prior parameters are stored in a \"CatDirichlet\" object. \\cr\n#' Marginal likelihood is the likelihood of x|alpha.\n#' @seealso \\code{\\link{CatDirichlet}}, \\code{\\link{marginalLikelihood_bySufficientStatistics.CatDirichlet}}\n#' @param obj A \"CatDirichlet\" object.\n#' @param x numeric/integer/character vector, observed Categorical samples.\n#' @param LOG Return the log density if set to \"TRUE\".\n#' @param ... Additional arguments to be passed to other inherited types.\n#' @return numeric, the marginal likelihood.\n#' @export\n#' @examples\n#' obj <- CatDirichlet(gamma=list(alpha=runif(26,1,2),uniqueLabels = letters))\n#' x <- sample(letters,size = 20,replace = TRUE)\n#' marginalLikelihood(obj=obj,x=x,LOG = TRUE) #marginal likelihood\n#' ss <- sufficientStatistics(obj = obj,x=x)\n#' marginalLikelihood_bySufficientStatistics(obj=obj,ss = ss,LOG = TRUE)\n#' @references Murphy, Kevin P. Machine learning: a probabilistic perspective. MIT press, 2012.\nmarginalLikelihood.CatDirichlet <- function(obj,x,LOG=TRUE,...){\n if(missing(x)) stop(\"'x' must be specified\")\n if(!is.vector(x)) x <- as.vector(x)\n ss <- countFreq(x=x,uniqx = obj$gamma$uniqueLabels)\n class(ss) <- \"ssCat\"\n marginalLikelihood_bySufficientStatistics.CatDirichlet(obj=obj,ss=ss,LOG = LOG)\n}\n\n#' @title Marginal likelihood of a \"CatDirichlet\" object, using sufficient statistics\n#' @description\n#' Generate the marginal likelihood of a set of observations of the following model structure:\n#' \\deqn{pi|alpha \\sim Dir(alpha)}\n#' \\deqn{x|pi \\sim Categorical(pi)}\n#' Where Dir() is the Dirichlet distribution, Categorical() is the Categorical distribution. See \\code{?dDir} and \\code{dCategorical} for the definitions of these distribution. \\cr\n#' The model structure and prior parameters are stored in a \"CatDirichlet\" object. \\cr\n#' Marginal likelihood is the likelihood of x|alpha\n#' @seealso \\code{\\link{CatDirichlet}}, \\code{\\link{marginalLikelihood.CatDirichlet}}\n#' @param obj A \"CatDirichlet\" object.\n#' @param ss Sufficient statistics of x. In Categorical-Dirichlet case the sufficient statistic of sample x can be either x itself, of an \"ssCat\" object generated by the function sufficientStatistics.CatDirichlet().\n#' @param LOG Return the log density if set to \"TRUE\".\n#' @param ... Additional arguments to be passed to other inherited types.\n#' @return numeric, the marginal likelihood.\n#' @export\n#' @examples\n#' obj <- CatDirichlet(gamma=list(alpha=runif(26,1,2),uniqueLabels = letters))\n#' x <- sample(letters,size = 20,replace = TRUE)\n#' marginalLikelihood(obj=obj,x=x,LOG = TRUE) #marginal likelihood\n#' ss <- sufficientStatistics(obj = obj,x=x)\n#' marginalLikelihood_bySufficientStatistics(obj=obj,ss = ss,LOG = TRUE)\n#' @references Murphy, Kevin P. Machine learning: a probabilistic perspective. MIT press, 2012.\nmarginalLikelihood_bySufficientStatistics.CatDirichlet <- function(obj,ss,LOG=TRUE,...){\n if(missing(ss)) stop(\"'ss' must be specified\")\n if(!.is(ss,\"ssCat\")){\n ss <- sufficientStatistics.CatDirichlet(obj = obj,x=ss,foreach = FALSE)\n }\n if(length(ss)!=length(obj$gamma$alpha)) stop(\"length 'ss' and dirichlet parameters don't match\")\n a <- obj$gamma$alpha+as.numeric(ss)\n aa <- sum(a)\n aa0 <- sum(obj$gamma$alpha)\n logp <- lgamma(aa0) - lgamma(aa) + sum(lgamma(a)-lgamma(obj$gamma$alpha))\n if(!LOG) logp <- exp(logp)\n logp\n}\n\n#' @title Posterior predictive density function of a \"CatDirichlet\" object\n#' @description\n#' Generate the the density value of the posterior predictive distribution of the following structure:\n#' \\deqn{pi|alpha \\sim Dir(alpha)}\n#' \\deqn{x|pi \\sim Categorical(pi)}\n#' Where Dir() is the Dirichlet distribution, Categorical() is the Categorical distribution. See \\code{?dDir} and \\code{dCategorical} for the definitions of these distribution. \\cr\n#' The model structure and prior parameters are stored in a \"CatDirichlet\" object. \\cr\n#' Posterior predictive is a distribution of x|alpha.\n#' @seealso \\code{\\link{CatDirichlet}}, \\code{\\link{dPosteriorPredictive.CatDirichlet}}, \\code{\\link{marginalLikelihood.CatDirichlet}}\n#' @param obj A \"CatDirichlet\" object.\n#' @param x numeric/integer/character vector, observed Categorical samples.\n#' @param LOG Return the log density if set to \"TRUE\".\n#' @param ... Additional arguments to be passed to other inherited types.\n#' @return A numeric vector, the posterior predictive density.\n#' @export\n#' @examples\n#' obj <- CatDirichlet(gamma=list(alpha=runif(26,1,2),uniqueLabels = letters))\n#' x <- sample(letters,size = 20,replace = TRUE)\n#' ## res1 and res2 should provide the same result\n#' res1 <- dPosteriorPredictive(obj = obj,x=x,LOG = TRUE)\n#' res2 <- numeric(length(x))\n#' for(i in seq_along(x)) res2[i] <- marginalLikelihood(obj=obj,x=x[i],LOG = TRUE)\n#' @references Murphy, Kevin P. Machine learning: a probabilistic perspective. MIT press, 2012.\ndPosteriorPredictive.CatDirichlet <- function(obj,x,LOG=TRUE,...){\n if(missing(x)) stop(\"'x' must be specified\")\n if(!is.vector(x)) x <- as.vector(x)\n probs <- obj$gamma$alpha/sum(obj$gamma$alpha)\n out <- probs[match(x,obj$gamma$uniqueLabels)]\n if(LOG) out <- log(out)\n out\n}\n\n#' @title Generate random samples from the posterior predictive distribution of a \"CatDirichlet\" object\n#' @description\n#' Generate random samples from the posterior predictive distribution of the following structure:\n#' \\deqn{pi|alpha \\sim Dir(alpha)}\n#' \\deqn{x|pi \\sim Categorical(pi)}\n#' Where Dir() is the Dirichlet distribution, Categorical() is the Categorical distribution. See \\code{?dDir} and \\code{dCategorical} for the definitions of these distribution. \\cr\n#' The model structure and prior parameters are stored in a \"CatDirichlet\" object \\cr\n#' posterior predictive is a distribution of x|alpha\n#' @seealso \\code{\\link{CatDirichlet}}, \\code{\\link{dPosteriorPredictive.CatDirichlet}}\n#' @param obj A \"CatDirichlet\" object.\n#' @param n integer, number of samples.\n#' @param ... Additional arguments to be passed to other inherited types.\n#' @return A vector of the same type as obj$gamma$uniqueLabels.\n#' @export\n#' @examples\n#' obj <- CatDirichlet(gamma=list(alpha=runif(26,1,2),uniqueLabels = letters))\n#' rPosteriorPredictive(obj=obj,n=200)\n#' @references Murphy, Kevin P. Machine learning: a probabilistic perspective. MIT press, 2012.\nrPosteriorPredictive.CatDirichlet <- function(obj,n,...){\n if(missing(n)) stop(\"'n' must be specified\")\n n <- as.integer(n)\n obj$gamma$uniqueLabels[sample.int(n=length(obj$gamma$uniqueLabels), size = n, replace = TRUE,prob = obj$gamma$alpha/sum(obj$gamma$alpha))]\n}\n", "meta": {"hexsha": "bd1d0b6e472ddd57b0e5c3dcf741287ce73553f8", "size": 30491, "ext": "r", "lang": "R", "max_stars_repo_path": "R/Categorical_Inference.r", "max_stars_repo_name": "chenhaotian/Bayesian-Bricks", "max_stars_repo_head_hexsha": "4876e9bacf9561354220a18835829f5274598622", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 6, "max_stars_repo_stars_event_min_datetime": "2020-03-04T09:43:11.000Z", "max_stars_repo_stars_event_max_datetime": "2020-07-29T13:54:37.000Z", "max_issues_repo_path": "R/Categorical_Inference.r", "max_issues_repo_name": "chenhaotian/Bayesian-Bricks", "max_issues_repo_head_hexsha": "4876e9bacf9561354220a18835829f5274598622", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/Categorical_Inference.r", "max_forks_repo_name": "chenhaotian/Bayesian-Bricks", "max_forks_repo_head_hexsha": "4876e9bacf9561354220a18835829f5274598622", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-12-20T18:13:09.000Z", "max_forks_repo_forks_event_max_datetime": "2021-12-20T18:13:09.000Z", "avg_line_length": 52.0324232082, "max_line_length": 401, "alphanum_fraction": 0.7031911056, "num_tokens": 8257, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9343951680216529, "lm_q2_score": 0.8354835411997897, "lm_q1q2_score": 0.7806717838587031}} {"text": "A <- matrix(c(-8,1,-2,-20,2,-6,-1,-38,-3,-1,7,-34), 3, 4, byrow = T)\r\nGaussForward <- function(A) {\r\n n <- nrow(A)\r\n m <- ncol(A)\r\n for(i in 1:n) {\r\n A[i,] <- A[i, ]/A[i,i]\r\n if (i==n) {\r\n break\r\n }\r\n for(j in i+1:(n-i)){\r\n A[j,i:m] <- A[j,i:m] - (A[j,i] * A[i, i:m])\r\n }\r\n }\r\n return(A)\r\n}\r\n\r\nGaussBackward <- function(A) {\r\n n <- nrow(A)\r\n m <- ncol(A)\r\n x <- vector()\r\n for(i in 1:n){\r\n c <- 0\r\n t <- 1\r\n for(j in (m-i):(m-1)){\r\n if((j) == (m-1)){\r\n break\r\n }\r\n c <- c + (x[i-t] * A[(n+1)-i,j+1])\r\n t <- t + 1\r\n }\r\n x[i] <- A[(n+1)-i,m] - c\r\n }\r\n print(A)\r\n for (i in n:1) {\r\n print(x[i])\r\n }\r\n}\r\n", "meta": {"hexsha": "7cb0d6fad2870b789eae491a67cfec2c02f7e7a7", "size": 683, "ext": "r", "lang": "R", "max_stars_repo_path": "Lab-06/Extra/GaussElimination.r", "max_stars_repo_name": "hassaninamdar/legendesk", "max_stars_repo_head_hexsha": "f0487ac60167de97570bbe4d816cf434d1df6e39", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Lab-06/Extra/GaussElimination.r", "max_issues_repo_name": "hassaninamdar/legendesk", "max_issues_repo_head_hexsha": "f0487ac60167de97570bbe4d816cf434d1df6e39", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Lab-06/Extra/GaussElimination.r", "max_forks_repo_name": "hassaninamdar/legendesk", "max_forks_repo_head_hexsha": "f0487ac60167de97570bbe4d816cf434d1df6e39", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 17.9736842105, "max_line_length": 69, "alphanum_fraction": 0.345534407, "num_tokens": 293, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9416541561135441, "lm_q2_score": 0.828938806208442, "lm_q1q2_score": 0.7805736720299791}} {"text": "fatorial <- function(n) {\n res = 1\n for(i in 1:n) {\n res = res*i\n }\n return(res)\n}\n#fatorial(5)\n#res = 1\n#i = 1\n#res = res*1 = 1 (1)\n#i = 2\n#res = res*2 = 2 (1x2)\n#i = 3\n#res = res*3 = 6 (1x2x3)\n#i = 4\n#res = res*4 = 24 (1x2x3x4)\n#i = 5\n#res = res*5 = 120 (1x2x3x4x5)\n", "meta": {"hexsha": "0a5b0d86dd8662bfc6bc64f1275caf5de74055e6", "size": 275, "ext": "r", "lang": "R", "max_stars_repo_path": "resolucao/r/fatorial.r", "max_stars_repo_name": "rafaelbes/numericalAnalysis", "max_stars_repo_head_hexsha": "31f2b9cd5fb62cee9a649ac0257024de757eede4", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "resolucao/r/fatorial.r", "max_issues_repo_name": "rafaelbes/numericalAnalysis", "max_issues_repo_head_hexsha": "31f2b9cd5fb62cee9a649ac0257024de757eede4", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "resolucao/r/fatorial.r", "max_forks_repo_name": "rafaelbes/numericalAnalysis", "max_forks_repo_head_hexsha": "31f2b9cd5fb62cee9a649ac0257024de757eede4", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2020-12-15T00:31:38.000Z", "max_forks_repo_forks_event_max_datetime": "2021-09-09T14:52:19.000Z", "avg_line_length": 13.75, "max_line_length": 30, "alphanum_fraction": 0.4945454545, "num_tokens": 157, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9059898203834278, "lm_q2_score": 0.8615382147637196, "lm_q1q2_score": 0.7805448524472414}} {"text": "mu <- pi\nsigmaSq <- (1.3)^3\n\nn <- 10\nM <- 10000\n\nsvar <- function(x){\n n <- length(x)\n xb <- mean(x)\n sv <- sum((x-xb)^2)/n\n return(sv)\n}\n\ndata.sets <- matrix(rnorm(n = n*M, mean = mu, sd = sqrt(sigmaSq)), ncol = n, nrow = M)\n\nxbars <- apply(data.sets, 1, mean)\nsbars <- apply(data.sets, 1, svar)\n\npar(mfrow=c(1, 2))\n\nhist(xbars, probability = TRUE, main = \"Média amostral\", xlab = expression(bar(X[n])))\ncurve(dnorm(x, mean = mu, sd = sqrt(sigmaSq/n)), min(xbars), max(xbars), lwd = 2, add = TRUE)\n\nhist(sbars, probability = TRUE, main = \"Variância amostral\", xlab = expression(bar(S[n]^2)))\ncurve(dgamma(x, shape = (n-1)/2, rate = n/(2*sigmaSq) ), min(sbars), max(sbars), lwd = 2, add = TRUE)\n\n\n", "meta": {"hexsha": "7ee458c6b63d7375830ca2255b8b8a3e29c037ec", "size": 701, "ext": "r", "lang": "R", "max_stars_repo_path": "code/distribuicao_media_variancia_amostrais_normal.r", "max_stars_repo_name": "jlduim/Statistical_Inference_BSc", "max_stars_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 33, "max_stars_repo_stars_event_min_datetime": "2020-08-03T15:42:28.000Z", "max_stars_repo_stars_event_max_datetime": "2021-11-30T15:43:10.000Z", "max_issues_repo_path": "code/distribuicao_media_variancia_amostrais_normal.r", "max_issues_repo_name": "jlduim/Statistical_Inference_BSc", "max_issues_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 23, "max_issues_repo_issues_event_min_datetime": "2020-08-16T23:02:47.000Z", "max_issues_repo_issues_event_max_datetime": "2021-11-07T14:34:43.000Z", "max_forks_repo_path": "code/distribuicao_media_variancia_amostrais_normal.r", "max_forks_repo_name": "jlduim/Statistical_Inference_BSc", "max_forks_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 10, "max_forks_repo_forks_event_min_datetime": "2020-08-13T00:53:42.000Z", "max_forks_repo_forks_event_max_datetime": "2021-12-10T07:35:56.000Z", "avg_line_length": 25.0357142857, "max_line_length": 101, "alphanum_fraction": 0.5991440799, "num_tokens": 258, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9688561676667173, "lm_q2_score": 0.8056321959813275, "lm_q1q2_score": 0.7805417219473907}} {"text": "\r\n#Suppose the mean weight of King Penguins found in an Antarctic colony \r\n#last year was 15.4 kg. In a sample of 35 penguins same time this year in \r\n#the same colony, the mean penguin weight is 14.6 kg. Assume the sample \r\n#standard deviation is 2.5 kg. At .05 significance level, can we reject \r\n#the null hypothesis that the mean penguin weight does not differ from last \r\n#year?\r\n\r\n\r\nxbar = 14.6\r\n\r\nmu0 =15.4\r\n\r\ns = 2.5\r\n\r\nn = 35\r\n\r\nt = (xbar-mu0)/(s/(sqrt(n)))\r\n\r\nt #-1.89\r\n\r\n#valores criticos\r\nalpha = .05\r\nt.half.aplha = qt(1-alpha,df = n-1)\r\n\r\n#se rechaza la hipotesis\r\nc(-t.half.aplha,t.half.aplha)\r\n\r\n#pvalue\r\n\r\npval = 2*pt(t,df=n-1)\r\n\r\npval #0.0668\r\n", "meta": {"hexsha": "7c695eb994bc4f45a34c4371ae0783072acee872", "size": 662, "ext": "r", "lang": "R", "max_stars_repo_path": "Parcial/1. Prueba de hipotesis/TwoTailedMeanUknownVariance.r", "max_stars_repo_name": "jchudb93/Exp-Numerica", "max_stars_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Parcial/1. Prueba de hipotesis/TwoTailedMeanUknownVariance.r", "max_issues_repo_name": "jchudb93/Exp-Numerica", "max_issues_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Parcial/1. Prueba de hipotesis/TwoTailedMeanUknownVariance.r", "max_forks_repo_name": "jchudb93/Exp-Numerica", "max_forks_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 19.4705882353, "max_line_length": 77, "alphanum_fraction": 0.6616314199, "num_tokens": 229, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9715639669551474, "lm_q2_score": 0.803173791645582, "lm_q1q2_score": 0.7803347151655886}} {"text": "## Author: Sergio García Prado\n## Title: Statistical Inference - Goodness of Fit - Exercise 15\n\n\nrm(list = ls())\n\nobserved <- c(1.0, 2.3, 4.2, 7.1, 10.4)\n\n\n(k <- length(observed))\n# 5\n\n(lambda.hat <- 1 / mean(observed))\n# 0.2\n\ntest <- ks.test(observed, pexp, rate = 1 / mean(observed))\n\n(D <- test$statistic[[1]])\n# 0.181269246922018\n\n(criticvalue <- quantile(replicate(1000, ks.test(rexp(k, lambda.hat), pexp, rate = lambda.hat)$statistic), 0.95))\n# 95%: 0.56811734613071\n\nD > criticvalue\n# FALSE (H0 no refused)\n", "meta": {"hexsha": "e9e34682d7b784b21b8beb33be494e423c61497f", "size": 514, "ext": "r", "lang": "R", "max_stars_repo_path": "statistical-inference/goodness-of-fit/exercise-15.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "statistical-inference/goodness-of-fit/exercise-15.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "statistical-inference/goodness-of-fit/exercise-15.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 19.7692307692, "max_line_length": 113, "alphanum_fraction": 0.6517509728, "num_tokens": 189, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9539661002182845, "lm_q2_score": 0.8175744739711883, "lm_q1q2_score": 0.7799383325723099}} {"text": "## 2. The Mean ##\n\ndistribution <- c(0,2,3,3,3,4,13)\nmean <- sum(distribution) / length(distribution)\ncenter <- FALSE\n\nvalues_above <- distribution[distribution > mean]\nvalues_below <- distribution[distribution < mean]\n\ndistances_above <- values_above - mean\ndistances_below <- mean - values_below\n\nequal_distances <- sum(distances_above) == sum(distances_below)\n\n## 3. Generating a distribution ##\n\nset.seed(1)\ndistribution <- sample.int(100, size=10)\nndistribution <- replicate(n=50, expr=sample.int(25, size=5))\n\n## 4. The Mean as a Balance Point ##\n\nset.seed(1)\n\ncheckDist <- function(){\n distribution <- sample.int(1000, size=10)\n mean <- sum(distribution) / length(distribution)\n round(sum(distribution - mean)) == 0\n}\n\nequal_distances <- sum(replicate(n=5000, expr=checkDist()))\n\n## 5. Defining the Mean Algebraically ##\n\none <- FALSE # we don't use the symbol mu for the sample mean\ntwo <- FALSE # Should be N = 8, not n = 8\nthree <- FALSE # x-bar denotes the sample mean, not the population mean\n\n## 6. An Alternative Definition ##\n\ndistribution_1 <- c(42, 24, 32, 11)\ndistribution_2 <- c(102, 32, 74, 15, 38, 45, 22)\ndistribution_3 <- c(3, 12, 7, 2, 15, 1, 21)\ncompute_mean <- function(distribution) {\n N <- length(distribution)\n sum_of_the_distribution = 0\n for ( i in 1:N) {\n sum_of_the_distribution <- sum_of_the_distribution + distribution[i]\n }\n\n sum_of_the_distribution / N\n}\n\nmean_1 <- compute_mean(distribution_1)\nmean_2 <- compute_mean(distribution_2)\nmean_3 <- compute_mean(distribution_3)\n\n## 7. Introducing the Data ##\n\nlibrary(readr)\nhouses <- read_tsv('AmesHousing_1.txt')\n\none <- TRUE # every column that describes years is measured on an interval scale\ntwo <- FALSE # `SalePrice` is measured on a ratio scale\nthree <- TRUE # The data set has less values than the initial one with 3970 rows which we don't know either whether it represents a population\n\n## 8. Mean House Prices ##\n\ncompute_mean <- function(distribution) {\n N <- length(distribution)\n sum_of_the_distribution = 0\n for ( i in 1:N) {\n sum_of_the_distribution <- sum_of_the_distribution + distribution[i]\n }\n\n sum_of_the_distribution / N\n}\ncomputed_mean <- compute_mean(houses$SalePrice)\nr_mean <- mean(houses$SalePrice)\nmeans_are_equal <- (computed_mean == r_mean)\n\n## 9. Challenge: Estimating the Population Mean ##\n\nlibrary(tibble)\nlibrary(ggplot2)\nlibrary(purrr)\n\nset.seed(4)\n\nparameter <- mean(houses$SalePrice)\n\nsample_sizes <- seq(5, by=29, length.out=100)\n\nsampling_errors <- map_dbl(sample_sizes, \n function(x) parameter - mean(sample(houses$SalePrice, \n size=x)) )\n\ndf <- tibble(x = sample_sizes, y = sampling_errors)\n\nggplot(data = df, aes(x = sample_sizes, y = sampling_errors)) +\n geom_point(size=2) +\n geom_hline(yintercept = 0) +\n geom_vline(xintercept = 2930) + \n labs(x = \"Sample size\", \n y = \"Sampling error\")\n\n## 10. Estimates from Low-Sized Samples ##\n\nlibrary(tibble)\nlibrary(ggplot2)\nset.seed(1)\nmean_points <- replicate(n = 10000, \n expr = mean(sample(houses$SalePrice, \n size = 100)))\n\nggplot(data = tibble(mean_points), aes(x = mean_points)) +\n geom_histogram(bins = 100,\n position = \"identity\", \n alpha = 0.5) +\n geom_vline(aes(xintercept = mean(houses$SalePrice))) +\n xlab(\"Sample mean\") + \n ylab(\"Frequency\") +\n xlim(0, 500000)\n\n## 12. The Sample Mean as an Unbiased Estimator ##\n\npopulation <- c(3, 7, 2)\nlibrary(purrr)\n\nsamples <- list(c(3, 7), \n c(3, 2),\n c(7, 2), \n c(7, 3),\n c(2, 3),\n c(2, 7))\n\nsample_means <- map_dbl(samples, function(x) mean(x))\n\npopulation_mean <- mean(population)\n\nmean_of_sample_means <- mean(sample_means)\n\nunbiased <- (population_mean == mean_of_sample_means)", "meta": {"hexsha": "caaae7c7d8ec28c7656b773ecf4ef711ca93818f", "size": 4029, "ext": "r", "lang": "R", "max_stars_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/2. Statistics Intermediate in R Averages and Variability/1. The Mean.r", "max_stars_repo_name": "MyArist/Dataquest", "max_stars_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 8, "max_stars_repo_stars_event_min_datetime": "2020-07-27T12:04:54.000Z", "max_stars_repo_stars_event_max_datetime": "2021-03-01T04:39:33.000Z", "max_issues_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/2. Statistics Intermediate in R Averages and Variability/1. The Mean.r", "max_issues_repo_name": "myarist/Dataquest", "max_issues_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/2. Statistics Intermediate in R Averages and Variability/1. The Mean.r", "max_forks_repo_name": "myarist/Dataquest", "max_forks_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 15, "max_forks_repo_forks_event_min_datetime": "2021-03-30T06:45:19.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-17T03:55:02.000Z", "avg_line_length": 28.1748251748, "max_line_length": 144, "alphanum_fraction": 0.635889799, "num_tokens": 1128, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9111797100118214, "lm_q2_score": 0.8558511543206819, "lm_q1q2_score": 0.7798342066072016}} {"text": "library(ggplot2)\n\n# change these parameters if you want\nmax = 100\nnum_samples = 100\n\n# generate 100 samples from 0 to 100\nsamples <- max * runif(num_samples)\n\n# my power mean function\npowermean <- function(samples, d) {\n if (d == 0) {\n exp(sum(log(samples)) / length(samples))\n } else {\n (sum(samples ^ d) / length(samples)) ^ (1 / d)\n }\n}\n\n# x axis goes from -10 to 5 skipping 0\nd <- c(seq(-10,-0.01,by = 0.01), seq(0.01,10,by = 0.01))\n\n# calculate all the power means\ny <- sapply(d, function(d) powermean(samples, d))\n\nmyPlot <- ggplot() +\n geom_line(aes(x = d, y = y), color = \"#56B4E9\") +\n geom_point(size = 5,\n aes(x = -1, y = powermean(samples, -1),color = \"#E69F00\")) +\n geom_point(size = 5,\n aes(x = -0, y = powermean(samples, 0), color = \"#009E73\")) +\n geom_point(size = 5,\n aes(x = 1, y = powermean(samples, 1), color = \"#F0E442\")) +\n geom_point(size = 5,\n aes(x = 2, y = powermean(samples, 2), color = \"#0072B2\")) +\n scale_color_manual(values = c(\"#E69F00\",\"#009E73\",\"#F0E442\",\"#0072B2\"),\n breaks = c(\"#E69F00\", \"#009E73\", \"#F0E442\", \"#0072B2\"),\n labels = c(\"harmonic\",\n \"geometric\",\n \"arithmetic\",\n \"quadratic\")) +\n theme(axis.title.x = element_blank()) +\n theme(axis.title.y = element_blank()) +\n theme(legend.title = element_blank())\n\n# ...profit!\nplot(myPlot)", "meta": {"hexsha": "b2d94dafe392f6647faf783c57e7f82243e82302", "size": 1523, "ext": "r", "lang": "R", "max_stars_repo_path": "assets/data/meanmean.r", "max_stars_repo_name": "whatdoesthequantsay/whatdoesthequantsay.github.io", "max_stars_repo_head_hexsha": "07624d0759f9db577aa1f3ad2d3f8ae7d91cd924", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "assets/data/meanmean.r", "max_issues_repo_name": "whatdoesthequantsay/whatdoesthequantsay.github.io", "max_issues_repo_head_hexsha": "07624d0759f9db577aa1f3ad2d3f8ae7d91cd924", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "assets/data/meanmean.r", "max_forks_repo_name": "whatdoesthequantsay/whatdoesthequantsay.github.io", "max_forks_repo_head_hexsha": "07624d0759f9db577aa1f3ad2d3f8ae7d91cd924", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 33.1086956522, "max_line_length": 78, "alphanum_fraction": 0.5239658569, "num_tokens": 449, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9458012717045181, "lm_q2_score": 0.8244619285331332, "lm_q1q2_score": 0.7797771404785969}} {"text": "# spočítání pravděpodobnosti P(A) - věta o úplné pravděpodobnosti\r\nuplna_pravdepodobnost = function(P_B, P_AB)\r\n{ # uvažujeme P_B jako vektor hodnot P(B_i) a P_BA jako vektor hodnot P(A|B_i)\r\n P_A = 0\r\n for (i in 1:length(P_B))\r\n {\r\n P_A = P_A + P_B[i]*P_AB[i]\r\n }\r\n return(P_A)\r\n}\r\n\r\n# * Bayesova věta ####\r\n# $P(B_k|A)=\\frac{P(B_k)P(A|B_k)}{\\sum_{i=1}^{n}P(B_i)P(A|B_i)}$\r\n\r\n\r\n# spočítání podmíněné pravděpodobnosti P(B_k|A) - Bayesova věta\r\nbayes = function(P_B, P_AB, k)\r\n{ # uvažujeme P_B jako vektor hodnot P(B_i), P_BA jako vektor hodnot P(A|B_i)\r\n P_A = uplna_pravdepodobnost(P_B, P_AB)\r\n P_BkA = P_B[k]*P_AB[k]/P_A\r\n return(P_BkA)\r\n} \r\n\r\nsouhrn=function(x,p){\r\n EX = sum(x*p)\r\n EX2 = sum(x*x*p) \r\n DX = EX2-EX^2\r\n sigma.X = sqrt(DX)\r\n # zápis výsledků do tabulky\r\n tab = rbind(EX, DX, sigma.X)\r\n tab.popis = c(\"str. hodnota\",\"rozptyl\",\"smer. odchylka\")\r\n rownames(tab) = tab.popis\r\n return(tab)\r\n}\r\n\r\n\r\n\r\n# 1A\r\n# A B C\r\n# spok 70 85 55\r\n# nesp 30 15 45\r\n# clk 30 38 32\r\n\r\n0.3*0.3+0.15*0.38+0.45*0.32\r\n\r\n# 1B\r\np = c(0.7,0.85,0.55)\r\nc = c(0.3,0.38,0.32)\r\nbayes(c, p, 2)\r\n\r\n# 2A\r\nxvalue = c(-2,1,3)\r\nyvalue = c(0,1)\r\nzero = c(1/3,1/6,0)\r\none = c(1/6,1/6,1/6)\r\nsum(zero,one)\r\n\r\n# 2B marginální pravděpodobnostní a distribuční funkce\r\n# x -2 1 3\r\n# p 3/6 2/6 1/6\r\nx = c(zero[1]+one[1],zero[2]+one[2],zero[3]+one[3])\r\nx\r\ny = c(zero[1]+zero[2]+zero[3],one[1]+one[2]+one[3])\r\ny\r\n\r\n# 2C\r\n# stř. hodnota = \r\nsum(xvalue*x)\r\nsum(yvalue*y)\r\n\r\n# směr. odchylka\r\nsqrt(sum(xvalue*xvalue*x)-sum(xvalue*x)^2)\r\nsqrt(sum(yvalue*yvalue*y)-sum(yvalue*y)^2)\r\n\r\n\r\nsouhrn(xvalue,x)\r\nsouhrn(yvalue,y)\r\n\r\n# 2D sdružená dist. funkce\r\n# F(0,5;1) = 1/3\r\n\r\n# 3A pravděpodobnostní funkce\r\n\r\nx = seq(from = -1, to = 150, by = 1) # body na ose x\r\nFX = dexp(x,1/45) \r\nplot(x, FX, type='l', main=\"Distribucni funkce\") \r\n\r\n# 3B P(x > 68) = 1-P(x<68)\r\n1-pexp(68,1/45)\r\n\r\n# 3C z 30 baterií bude alespoň polovina s výdrží nad 68 měsíců\r\nn = 30\r\np = 1-pexp(68,1/45)\r\n1-pbinom(15,n,p)\r\n\r\n# 3D 40 náhodně vybraných baterií bude průměrna výdrž větší než 43 měsíců\r\n\r\nn = 40\r\nsigma = 45\r\nx = n*43\r\nmi = n*sigma\r\nrozptyl = n*sigma**2\r\n1 - pnorm(x,mi,sqrt(rozptyl))\r\n", "meta": {"hexsha": "4416a57094e4a3a15ebf77820e7b925383da84f1", "size": 2197, "ext": "r", "lang": "R", "max_stars_repo_path": "ZKPriprava/ponozky_2.r", "max_stars_repo_name": "Atheloses/VSB-S8-PS", "max_stars_repo_head_hexsha": "fdef214f8169094b6366ce0489f92ef20b460702", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "ZKPriprava/ponozky_2.r", "max_issues_repo_name": "Atheloses/VSB-S8-PS", "max_issues_repo_head_hexsha": "fdef214f8169094b6366ce0489f92ef20b460702", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "ZKPriprava/ponozky_2.r", "max_forks_repo_name": "Atheloses/VSB-S8-PS", "max_forks_repo_head_hexsha": "fdef214f8169094b6366ce0489f92ef20b460702", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 21.125, "max_line_length": 81, "alphanum_fraction": 0.5898953118, "num_tokens": 1064, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9621075733703927, "lm_q2_score": 0.8104789109591832, "lm_q1q2_score": 0.7797678982908183}} {"text": "## Author: Sergio García Prado\n## Title: Exercises with Solutions 6\n\nrm(list = ls())\n\nla <- 10\nlb <- 5\nmu1 <- 3 / 60\nmu2 <- 4 / 60\n\n(Q <- matrix(c(-(la + lb), la, lb, 0,\n 1/mu1, -(1/mu1 + lb + la), 0, lb + la,\n 1/mu2, 0, -(1/mu2 + la), la,\n 0, 1/mu2, 1/mu1, -(1/mu1 + 1/mu2)),\n 4, 4, byrow = TRUE))\n# -15\t 10 \t5\t 0\n# 20\t-35\t 0\t 15\n# 15\t 0\t-25\t 10\n# 0\t 15\t 20\t-35\n\n(A <- cbind(Q[, 1:(nrow(Q) - 1)], rep(1, nrow(Q))))\n# -15\t 10 5\t1\n# 20\t-35\t 0\t1\n# 15\t 0\t-25\t1\n# 0\t 15\t 20\t1\n\n(stationary <- solve(A)[nrow(A), ])\n# 0.461538461538462 0.192307692307692 0.205128205128205 0.141025641025641\n\n(la * (1 - (stationary[4])))\n# 8.58974358974359\n\nlb * (1 - (stationary[3] + stationary[4]))\n# 3.26923076923077\n", "meta": {"hexsha": "591e14991d1965bb7176863b3c414cbedbadd2c3", "size": 899, "ext": "r", "lang": "R", "max_stars_repo_path": "stochastic-processes/proposed-exercises/continuous-7.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "stochastic-processes/proposed-exercises/continuous-7.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "stochastic-processes/proposed-exercises/continuous-7.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 25.6857142857, "max_line_length": 80, "alphanum_fraction": 0.4238042269, "num_tokens": 383, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9381240125464114, "lm_q2_score": 0.8311430562234877, "lm_q1q2_score": 0.7797152589044659}} {"text": "'''\r\nSuppose the food label on a cookie bag states that there is at most 2 grams of saturated fat in a single cookie. \r\nIn a sample of 35 cookies, it is found that the mean amount of saturated fat per cookie is 2.1 grams.Assume that \r\nthe population standard deviation is 0.25 grams. At .05 significance level, can we reject the\r\nclaim on food label?\r\n'''\r\n\r\nxbar=2.1\r\nmu0=2\r\nsigma = 0.25\r\n\r\nn = 35\r\n\r\nz = (xbar-mu0)/(sigma/sqrt(n))\r\nz #2.2366\r\n\r\nalpha = 0.05\r\n\r\nz.alpha = qnorm(1-alpha)\r\nz.alpha #1.644\r\n\r\n#se rechaza la hipotesis\r\n\r\n#pvalue\r\npvalue = pnorm(z,lower.tail = FALSE)\r\n", "meta": {"hexsha": "0e70980e488750e109211d8e4193c3f5217591d8", "size": 582, "ext": "r", "lang": "R", "max_stars_repo_path": "Parcial/1. Prueba de hipotesis/UpperTailMeanKnownVariance.r", "max_stars_repo_name": "jchudb93/Exp-Numerica", "max_stars_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Parcial/1. Prueba de hipotesis/UpperTailMeanKnownVariance.r", "max_issues_repo_name": "jchudb93/Exp-Numerica", "max_issues_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Parcial/1. Prueba de hipotesis/UpperTailMeanKnownVariance.r", "max_forks_repo_name": "jchudb93/Exp-Numerica", "max_forks_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.3846153846, "max_line_length": 114, "alphanum_fraction": 0.6872852234, "num_tokens": 181, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9284088045171238, "lm_q2_score": 0.8397339696776499, "lm_q1q2_score": 0.7796164109008457}} {"text": "# Example : 2 Chapter : 4.2 Page No: 209\r\n# Find the projection matrix onto the line\r\n\r\nprojection_matrix<-function(a){\r\n a<-matrix(c(a),ncol=1)\r\n P<-a%*%t(a)\r\n temp<-t(a)%*%a\r\n temp<-1/temp\r\n t<-temp[1,1]\r\n P<-t*P\r\n return(P)\r\n}\r\na<-c(1,2,2)\r\nP<-projection_matrix(a)\r\nprint(\"The projection matrix is \")\r\nprint(P)\r\n#The answer may slightly vary due to rounding off values", "meta": {"hexsha": "134d20fac65cac9ac43bc0185d4fedd3b9cb10a4", "size": 386, "ext": "r", "lang": "R", "max_stars_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH4/EX4.2.2/Ex4.2_2.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH4/EX4.2.2/Ex4.2_2.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH4/EX4.2.2/Ex4.2_2.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 22.7058823529, "max_line_length": 58, "alphanum_fraction": 0.6191709845, "num_tokens": 132, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9284087926320944, "lm_q2_score": 0.8397339756938818, "lm_q1q2_score": 0.7796164065061053}} {"text": "euclidean <- function(a, b) {\n return (sqrt(sum((a - b) ^ 2)))\n}\n\nkNN <- function(dataset, points, k, dist = euclidean) {\n answer <- array(dim=c(length(points[,1])))\n \n for (i in 1:length(points[,1])) {\n cat(\"\\rPoint\", i, \"of\", length(points[,1]))\n distance <- array(dim=dim(dataset)[1])\n for (j in 1:dim(dataset)[1]) {\n distance[j] <- dist(dataset[j, 3:4], points[i,])\n }\n sortedDataset <- dataset[order(distance),]\n \n classesCount <- c(0, 0, 0)\n names(classesCount) = unique(iris$Species)\n for (j in 1:k) {\n classesCount[sortedDataset$Species[j]] <- classesCount[sortedDataset$Species[j]] + 1\n }\n answer[i] = names(which.max(classesCount))[1]\n }\n \n return (answer)\n}\n\npar(mfrow=c(1,1), pty=\"s\")\n\nxs <- seq(from = 0.5, to = 7.5, by = 0.2)\nys <- seq(from = -2, to = 5, by = 0.2)\n\nz <- array(dim = c(length(xs) * length(ys), 2))\n\nindex <- 1\nfor (i in xs) {\n for (j in ys) {\n z[index,] <- c(i, j)\n index <- index + 1\n }\n}\n\nresult <- kNN(iris, z, 6)\n\ncolors <- c(\"setosa\" = \"blue\", \"virginica\" = \"red\", \"versicolor\" = \"green\")\nplot(iris[, 3:4], bg = colors[paste(iris$Species)], pch=23, asp=1)\npoints(z[,1], z[,2], col = colors[result], pch = 21)", "meta": {"hexsha": "78dfb75b0dac91215502521355abd28c2fd74d41", "size": 1201, "ext": "r", "lang": "R", "max_stars_repo_path": "1 - Nearest neighbors algorithm/knn-map.r", "max_stars_repo_name": "shadowusr/ml-course", "max_stars_repo_head_hexsha": "5e336dc47ed9dff71877e830a4d67afd8a23a8a1", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "1 - Nearest neighbors algorithm/knn-map.r", "max_issues_repo_name": "shadowusr/ml-course", "max_issues_repo_head_hexsha": "5e336dc47ed9dff71877e830a4d67afd8a23a8a1", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "1 - Nearest neighbors algorithm/knn-map.r", "max_forks_repo_name": "shadowusr/ml-course", "max_forks_repo_head_hexsha": "5e336dc47ed9dff71877e830a4d67afd8a23a8a1", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.1086956522, "max_line_length": 90, "alphanum_fraction": 0.5628642798, "num_tokens": 428, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9481545304202039, "lm_q2_score": 0.8221891261650247, "lm_q1q2_score": 0.7795623448355968}} {"text": "K = 5;\nL = 6;\n\n# 1. I.\nn = K*20;\nu = runif(n = n, min = 0, max = 1);\nx = qexp(u, rate = L);\n\n# 1. II.\nhist(x = u, freq = FALSE);\nhist(x = x, freq = FALSE);\n\nxWidth = max(x) - min(x);\nxGrid = seq(min(x) - 0.2 * xWidth, max(x) + 0.2 * xWidth, length = 30);\nlines(xGrid, dexp(xGrid, rate = L), col='red', lw = 2, lty = 2);\n\n\n# !. III.\nplot(ecdf(x), verticals=TRUE, do.points = FALSE, main = \"Empiricka distribucni funkce\");\nlines(xGrid, pexp(xGrid, rate = L), col='red', lw = 2, lty = 2);\n\n# 1. IV.\ny = rexp(1000, rate = L)\nqqplot(x, y); abline(0,1, col='red', lwd=2);\n\n# 1. V.\n\n\n# 1. VI.\n# H_0 data maji distribuci ~ exp(rate = L)\n# H_a data nemaji tuto distribuci\n# significance level = 0.05\n\n\nprob.exp <- dexp(c(1:n), rate = L)\naaa=chisq.test(x, p=prob.exp, rescale.p = TRUE)\n\nret = ks.test(x, 'pexp', rate = L)$p.value\nif(ret <= 0.05) {\n print('H_0 Rejected -> x doesn\\'t have the exp distribution.');\n} else {\n print(\"H_0 Can't be rejected, data may be exponential.\");\n}\n\nreturn\n\n# 2. I.\nlambda = function(t) { 100 + 50/exp((t - 420)^2/(3600*L)) + 100/exp((L*(t - 480 - 30*L)^2)/360000)};\n\n# 2. II.\nt = 0;\ni = 0;\ntotalArrivals = K*10;\narrivals = numeric(totalArrivals);\nfor(i in 1:totalArrivals) {\n t = t + rexp(1, rate = lambda(t));\n arrivals[i] = t;\n}\nyGrid = numeric(totalArrivals);\nplot(arrivals, yGrid, type='p');\n\n\n# 2. III.\ntotalTime = 24*60;\narrivals = numeric(totalTime);\nwhile(t < totalTime) {\n t = t + rexp(1, rate = lambda(t));\n minute = t %/% 1;\n arrivals[minute] = arrivals[minute] + 1;\n}\narrivals[totalTime] = arrivals[totalTime - 1];\n\nxGrid = c(1:totalTime);\nplot(xGrid, arrivals, type='l', col=\"grey\");\ncurve(lambda, 1, totalTime, col='red', add=TRUE);\n\n# 2. IV. \n# Diskuze kvality dat\n\n# 3. I.\nratio_courier = K/(K+L);\nratio_state = 1-ratio_courier;\n\n# 3. II.\narrivals_courier = numeric(totalTime);\narrivals_state = numeric(totalTime);\nfor (i in (1:totalTime)) {\n arrivals_courier[i] = ratio_courier * arrivals[i];\n arrivals_state[i] = ratio_state * arrivals[i];\n}\n\n\n# 3. III.\nlambda_courier = function(t) { lambda(t) * ratio_courier };\nlambda_state = function(t) { lambda(t) * ratio_state };\n\nplot(xGrid, arrivals_courier, type='l', col=\"grey\");\ncurve(lambda_courier, 1, totalTime, col='red', add=TRUE);\n\nplot(xGrid, arrivals_state, type='l', col=\"grey\");\ncurve(lambda_state, 1, totalTime, col='red', add=TRUE);\n\n", "meta": {"hexsha": "8135c409d8999b4670f97afdeceb33ba42aee727", "size": 2343, "ext": "r", "lang": "R", "max_stars_repo_path": "task_1/task1.r", "max_stars_repo_name": "holoubekm/MI-SPI", "max_stars_repo_head_hexsha": "22cae9226de2a5c08fb769b725cefa06dd4064fd", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "task_1/task1.r", "max_issues_repo_name": "holoubekm/MI-SPI", "max_issues_repo_head_hexsha": "22cae9226de2a5c08fb769b725cefa06dd4064fd", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "task_1/task1.r", "max_forks_repo_name": "holoubekm/MI-SPI", "max_forks_repo_head_hexsha": "22cae9226de2a5c08fb769b725cefa06dd4064fd", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.7475728155, "max_line_length": 100, "alphanum_fraction": 0.6218523261, "num_tokens": 863, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.948154531885212, "lm_q2_score": 0.8221891239865619, "lm_q1q2_score": 0.7795623439745911}} {"text": "# Selecting seed to be reproducible\nset.seed(42)\n\n# \"best\" predictor/algorithm\n# One can try to modify the denominator inside the cosine to change the complexity of f*\nf = function(x){\n y=2+x^(.2)*cos(x/.15)/x^-.45\n return(y)\n}\nplot(f,0,5)\n\n# Simulating data points: change n and sigma\nN=400\n#sigma=1.2\nsigma=2.0\nx=runif(N,0,5); x=sort(x) # For convenience, the input x is sorted\ny=rep(0,times=N)\nfor (i in 1:N) {\n y[i] = f(x[i]) + rnorm(1,0,sigma) # rnorm(size, mean, std)\n}\nplot(x,y)\npoints(x,f(x), type=\"l\", col=2, lwd=2)\n\n# k-neighbors estimator\n# k is number of neighbors and test=TRUE/FALSE tells if you estimate\n# over any grid (FALSE) or over the x sampled in test data set (TRUE)\nkn = function(k, test){\n if (test==\"FALSE\") {\n z = seq(0, 5, by=0.01)\n ll = length(z)\n }\n if (test==\"TRUE\"){\n z = x_test\n ll = length(z)\n }\n nk = rep(0, times=ll)\n for (j in 1:ll) {\n veci = which(abs(z[j]-x_train) %in% sort(abs(z[j]-x_train))[1:k])\n nk[j] = sum(y_train[veci])/k\n }\n return(nk)\n}\n\n# Sampling data between train and test\nindices = sample(c(1:N), size=300) # getting indices randmonly\nx_train = x[indices]\ny_train = y[indices]\nx_test = x[-indices]\ny_test = y[-indices]\n\n# Plotting train and test data in same figure\nplot(x_train, y_train)\npoints(x_test, y_test, col=2, pch=4)\n\n# MSE computation (test data)\nklist = 1:200 # List of k to test\nMSE = rep(0, times=length(klist)) # I make a zeroes array with length of ksize to store MSEs\nfor (ki in klist) {\n y_pred = kn(ki, \"TRUE\")\n MSEi = mean(sum((y_test - y_pred)^2))\n MSE[ki] = MSEi\n}\n\n# Getting best k from MSE\nplot(klist, MSE, xlab=\"k\", ylab=\"MSE\", main=\"MSE as a function of k\")\nkbest = which.min(MSE)\npoints(kbest, MSE[kbest], col=2, pch=8, cex=3.0)\n\n# plot for N=600\nplot(klist, MSE, xlab=\"k\", ylab=\"MSE\", main=\"MSE as a function of k (n=600)\")\n\n# Plotting best estimator\nplot(x,y)\npoints(x, f(x), type=\"l\", col=2, lwd=2)\npoints(x_test, kn(kbest,\"TRUE\"), type=\"l\", col=3, lwd=2)\n\n\n####### CROSS VALIDATION (4.3) #######\n\n# k-fold cross validation\nfolds = 10 # ex. folds=10 means 10-fold CV\nfold_size = N/10\n\nklist = 1:200 # List of k to test\nMSE_complete = list() # List to store the MSE list of each k-fold iteration\nindices = sample(c(1:N), size=400) # getting indices randmonly\nfor (iteration in 1:folds){\n metaindices_test = ((iteration-1)*fold_size+1):(iteration*fold_size) # Parenthesis are really important to separate :\n ss1 = indices[-metaindices_test] # Choosing indices for train (ss1) and test (ss2)\n ss2 = indices[metaindices_test]\n # choosing partition train/test data\n y_train=y[ss1]\n x_train=x[ss1]\n y_test=y[ss2]\n x_test=x[ss2]\n # Plotting train and test data in same figure\n #plot(x_train, y_train)\n #points(x_test, y_test, col=2, pch=4)\n #browser() # breakpoint\n # MSE computation (test data)\n MSE = rep(0, times=length(klist)) # I make a zeroes array with length of ksize to store MSEs\n for (ki in klist) {\n y_pred = kn(ki, \"TRUE\")\n MSEi = mean(sum((y_test - y_pred)^2))\n MSE[ki] = MSEi\n }\n MSE_complete[[iteration]] <- MSE # Store the MSE for this k in the complete MSE list.\n}\n\n# Plotting all MSE curves\nfor (i in 1:folds) {\n if (i==1){\n plot(klist, MSE_complete[[i]])\n }\n else{\n points(klist, MSE_complete[[i]]) \n }\n}\n\n# Computing mean MSE curve\nMSE_mean_10fold = list()\nfor (i in klist) {\n sum = 0\n for (j in 1:folds) {\n sum = sum + MSE_complete[[j]][i]\n }\n MSE_mean_10fold[i] <- sum/folds\n}\n# Plotting mean MSE curve\n#points(klist, MSE_mean, col=2)\nplot(klist, MSE_mean_10fold, xlab=\"k\", ylab=\"MSE\", main=\"MSE as a function of k for 10-fold CV\")\n# Taking the best k from mean MSE curve\nkbest_10fold = which.min(MSE_mean_10fold)\npoints(kbest_10fold, MSE_mean_10fold[kbest_10fold], col=2, pch=8, cex=3.0)\n\n# Plotting best estimator\nplot(x,y)\npoints(x, f(x), type=\"l\", col=2, lwd=2)\n# Sorting x_test for plotting\nx_test = sort(x_test)\npoints(x_test, kn(k_best,\"TRUE\"), col=3, pch=17)\n\n#### Leave-one-out cross-validation ###\nfor (i in 1:N){\n x_train = x[-i]\n y_train = y[-i]\n x_test = x[i]\n y_test = y[i]\n MSE = rep(0, times=length(klist)) # I make a zeroes array with length of ksize to store MSEs\n for (ki in klist) {\n y_pred = kn(ki, \"TRUE\")\n MSEi = mean(sum((y_test - y_pred)^2))\n MSE[ki] = MSEi\n }\n MSE_complete[[i]] <- MSE # Store the MSE for this k in the complete MSE list.\n}\n\n# Computing mean MSE curve\nMSE_mean_loocv = list()\nfor (i in klist) {\n sum = 0\n for (j in 1:N) {\n sum = sum + MSE_complete[[j]][i]\n }\n MSE_mean_loocv[i] <- sum/folds\n}\n# Plot MSE curve\nplot(klist, MSE_mean_loocv, xlab=\"k\", ylab=\"MSE\", main=\"MSE as a function of k for LOOCV\")\n# Taking the best k from mean MSE curve\nkbest_LOOCV = which.min(MSE_mean_loocv)\npoints(kbest_LOOCV, MSE_mean_loocv[kbest_LOOCV], col=2, pch=8, cex=3.0)\n\n# Plotting both mean_MSE curves\nplot(klist, MSE_mean_10fold)\npoints(klist, MSE_mean_loocv, col=2, pch=4)\n# adding legend\nlegend(150,80, legend=c(\"10-fold CV\", \"LOOCV\"),\n col=c(\"black\", \"red\"), lty=1:2, cex=1.0,\n box.lty=0)\n### ###\n\n####### END OF CROSS-VALIDATION (4.3) #######\n\n\n####### EFFECT OF IRREDUCIBLE ERROR 4.4 #######\n\n# Effect of irreducible error sigma^2\n# The error is related to the sigma somehow...\n\n# Effect of Irreducible error\n# Irreducible error is sigma^2 in y = f(x) + sigma\nsigma_list = seq(0.1, 4, by=0.1) # sigma from 1 to 10 in steps of 0.1\nkbest_list_10fold = rep(0, times=length(sigma_list))\nkbest_list_loocv = rep(0, times=length(sigma_list))\nfolds=10\nfold_size = N/folds\nklist = 1:200\n\nfor (si in 1:length(sigma_list)) {\n MSE_complete_kfold = list() # List to store the MSE list of each k-fold iteration\n MSE_complete_loocv = list() # List to store the MSE list of each k-fold iteration\n y=rep(0,times=N)\n for (i in 1:N) {\n y[i] = f(x[i]) + rnorm(1,0,sigma_list[si]) # rnorm(size, mean, std)\n }\n indices = sample(c(1:N), size=400) # getting indices randmonly\n ### KNN ###\n for (iteration in 1:folds){\n metaindices_test = ((iteration-1)*fold_size+1):(iteration*fold_size) # Parenthesis are really important to separate :\n ss1 = indices[-metaindices_test] # Choosing indices for train (ss1) and test (ss2)\n ss2 = indices[metaindices_test]\n # choosing partition train/test data\n y_train=y[ss1]\n x_train=x[ss1]\n y_test=y[ss2]\n x_test=x[ss2]\n # Plotting train and test data in same figure\n #plot(x_train, y_train)\n #points(x_test, y_test, col=2, pch=4)\n #browser() # breakpoint\n # MSE computation (test data)\n MSE = rep(0, times=length(klist)) # I make a zeroes array with length of ksize to store MSEs\n for (ki in klist) {\n y_pred = kn(ki, \"TRUE\")\n MSEi = mean(sum((y_test - y_pred)^2))\n MSE[ki] = MSEi\n }\n MSE_complete_kfold[[iteration]] <- MSE # Store the MSE for this k in the complete MSE list.\n }\n # Computing mean MSE curve\n MSE_mean_10fold = list()\n for (i in klist) {\n sum = 0\n for (j in 1:folds) {\n sum = sum + MSE_complete_kfold[[j]][i]\n }\n MSE_mean_10fold[i] <- sum/folds\n }\n # Taking the best k from mean MSE curve\n kbest_10fold = which.min(MSE_mean_10fold)\n kbest_list_10fold[si] <- kbest_10fold\n ### ###\n #### Leave-one-out cross-validation ###\n for (i in 1:N){\n x_train = x[-i]\n y_train = y[-i]\n x_test = x[i]\n y_test = y[i]\n MSE = rep(0, times=length(klist)) # I make a zeroes array with length of ksize to store MSEs\n for (ki in klist) {\n y_pred = kn(ki, \"TRUE\")\n MSEi = mean(sum((y_test - y_pred)^2))\n MSE[ki] = MSEi\n }\n MSE_complete_loocv[[i]] <- MSE # Store the MSE for this k in the complete MSE list.\n }\n \n # Computing mean MSE curve\n MSE_mean_loocv = list()\n for (i in klist) {\n sum = 0\n for (j in 1:N) {\n sum = sum + MSE_complete_loocv[[j]][i]\n }\n MSE_mean_loocv[i] <- sum/folds\n }\n kbest_LOOCV = which.min(MSE_mean_loocv)\n kbest_list_loocv[si] <- kbest_LOOCV\n ### ###\n}\n\n## Plotting results\nplot(sigma_list, kbest_list_10fold, xlab=\"eps\", ylab=\"k_best\", main=\"Best k as a function of irreducible error.\")\npoints(sigma_list, kbest_list_loocv, col=\"blue\", pch=4)\n# adding legend\nlegend(0.25,30, legend=c(\"10-fold CV\", \"LOOCV\"),\n col=c(\"black\", \"blue\"), lty=1:2, cex=1.0,\n box.lty=0)\n\n# Doing a linear fit\nlmfit = lm(c(kbest_list_10fold, kbest_list_loocv)~c(sigma_list,sigma_list))\nabline(lmfit)\nsummary(lmfit)\n\n####### END OF EFFECT OF IRREDUCIBLE ERROR 4.4 #######\n\n\n", "meta": {"hexsha": "534229271417ee6b98baaff58904eb3632076e4a", "size": 8430, "ext": "r", "lang": "R", "max_stars_repo_path": "Rcode/homework1/problema4.r", "max_stars_repo_name": "ijpulidos/statlearn", "max_stars_repo_head_hexsha": "fbe0964247d6466396d1e26fd63dae04be56a3ec", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Rcode/homework1/problema4.r", "max_issues_repo_name": "ijpulidos/statlearn", "max_issues_repo_head_hexsha": "fbe0964247d6466396d1e26fd63dae04be56a3ec", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Rcode/homework1/problema4.r", "max_forks_repo_name": "ijpulidos/statlearn", "max_forks_repo_head_hexsha": "fbe0964247d6466396d1e26fd63dae04be56a3ec", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 29.2708333333, "max_line_length": 122, "alphanum_fraction": 0.650059312, "num_tokens": 2911, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9005297941266013, "lm_q2_score": 0.8652240738888188, "lm_q1q2_score": 0.7791600571324773}} {"text": "#Copyright (c) 2016 Riccardo Francescato\na <- c(108,124,124,106,115,138,163,159,134,139)\n#confidency level\nalpha = .01 \n#type of test: 0 left tail 1 double tail 2 right tail\ntype = 2\n#calculations....\nn0 = length(a)\t\t# number of reps for sample 0\nxbar0 = mean(a)\t\t# sample 0 mean \nmu = 120\t\t\t# given mean \ns0 = sd(a)\t\t\t# sample 0 standard deviation \nt = (xbar0−mu)/(s0/sqrt(n0))\nif(type == 0){\n\tt.alpha = qt(1−alpha, df=n0−1) \n\tpval = pt(t, df=n0−1) \n\tcat(\"Results of lower tail\\n\")\n\tcat(\"Sample\\n\")\n\tcat(paste(\"# of elements: \", n0, \" Mean: \", xbar0, \" St Dev: \",s0))\n\tcat(paste(\"\\nt0: \",t))\n\tcat(paste(\"\\ntalpha: \",−t.alpha))\n\tcat(paste(\"\\np-value: \",pval))\n\tif(t<−t.alpha) cat(\"\\nREJECT H0\\n\") else cat(\"\\nACCEPT H0\\n\")\n}else if(type == 1){\n\tt.half.alpha = qt(1−alpha/2, df=n0−1) \n\tpval = 2 * pt(t, df=n0−1)\n\tcat(\"Results of 2-tail tail\\n\")\n\tcat(\"Sample\\n\")\n\tcat(paste(\"# of elements: \", n0, \" Mean: \", xbar0, \" St Dev: \",s0))\n\tcat(paste(\"\\nt0: \",t))\n\tcat(paste(\"\\ntalpha +: \",t.half.alpha))\n\tcat(paste(\"\\ntalpha -: \",-t.half.alpha))\n\tcat(paste(\"\\np-value: \",pval))\n\tif(t<-t.half.alpha || t>t.half.alpha) cat(\"\\nREJECT H0\\n\") else cat(\"\\nACCEPT H0\\n\")\n\n}else if(type == 2){\n\tt.alpha = qt(1−alpha, df=n0−1) \n\tpval = pt(t, df=n0−1, lower.tail=FALSE) \n\tcat(\"Results of upper tail\\n\")\n\tcat(\"Sample\\n\")\n\tcat(paste(\"# of elements: \", n0, \" Mean: \", xbar0, \" St Dev: \",s0))\n\tcat(paste(\"\\nt0: \",t))\n\tcat(paste(\"\\ntalpha: \",t.alpha))\n\tcat(paste(\"\\np-value: \",pval))\n\tif(t>t.alpha) cat(\"\\nREJECT H0\\n\") else cat(\"\\nACCEPT H0\\n\")\n}\n", "meta": {"hexsha": "016f5e392f978befa6480ba35044f891e17ad611", "size": 1525, "ext": "r", "lang": "R", "max_stars_repo_path": "Test_of_hp_1_serie_and_one_mu.r", "max_stars_repo_name": "RiccardoFrancescato/DataDesignScrips", "max_stars_repo_head_hexsha": "92d19d1cd5da9fb1486d53bc97c444714a3e5aa1", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Test_of_hp_1_serie_and_one_mu.r", "max_issues_repo_name": "RiccardoFrancescato/DataDesignScrips", "max_issues_repo_head_hexsha": "92d19d1cd5da9fb1486d53bc97c444714a3e5aa1", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Test_of_hp_1_serie_and_one_mu.r", "max_forks_repo_name": "RiccardoFrancescato/DataDesignScrips", "max_forks_repo_head_hexsha": "92d19d1cd5da9fb1486d53bc97c444714a3e5aa1", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 33.152173913, "max_line_length": 85, "alphanum_fraction": 0.6019672131, "num_tokens": 586, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9399133515091157, "lm_q2_score": 0.828938806208442, "lm_q1q2_score": 0.779130651539342}} {"text": "set.seed(32)\n\nm = 10000\na = 2.0\nb = 1.0 / 3.0\n\ntheta = rgamma(n=m, shape=a, rate=b)\n\nse = sd(theta) / sqrt(m)\n\nhist(theta, freq=FALSE)\ncurve(dgamma(x,shape=a, rate=b),col=\"blue\",add=TRUE)\n\n# 2 standard errors\nmean(theta) + (2 * se)\nmean(theta) - (2 * se)\n\n\n#indicator\nind = theta < 5\nmean(ind)\npgamma(5.0, shape=a, rate=b)\n\nse = sd(ind) / sqrt(m)\n\n2*se", "meta": {"hexsha": "753012b6f7bd5bfbcfd51fe3863c5a4ff461c803", "size": 352, "ext": "r", "lang": "R", "max_stars_repo_path": "montyCarlo/mMEstimateError.r", "max_stars_repo_name": "CharlieShelbourne/algos_practice", "max_stars_repo_head_hexsha": "bf32a739a9ab88f177461057fededb42e2d7fe10", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "montyCarlo/mMEstimateError.r", "max_issues_repo_name": "CharlieShelbourne/algos_practice", "max_issues_repo_head_hexsha": "bf32a739a9ab88f177461057fededb42e2d7fe10", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "montyCarlo/mMEstimateError.r", "max_forks_repo_name": "CharlieShelbourne/algos_practice", "max_forks_repo_head_hexsha": "bf32a739a9ab88f177461057fededb42e2d7fe10", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 13.5384615385, "max_line_length": 52, "alphanum_fraction": 0.6079545455, "num_tokens": 140, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.939913343093499, "lm_q2_score": 0.8289388083214156, "lm_q1q2_score": 0.779130646549323}} {"text": "weight <-c (150,180,140,128,133,152,131)\nheight <-c (62,84,55,52,54,63,53)\nmodel <- lm (height ~ weight)\nprint (model)\n\n\ntest <- data.frame (weight = 165)\nresult <- predict (model , test)\nprint (result)\n\nplot ( weight, height, col = \"red\", main = \"Example of Linear Regression\" , abline (lm(height~weight)), cex = 1.3, pch = 16, xlab = \"Weight\" , ylab = \"Height\")\n", "meta": {"hexsha": "77a438bbe11e63eb2355400e74671b9655d6fc23", "size": 364, "ext": "r", "lang": "R", "max_stars_repo_path": "IoT_Domain_Analyst_ECE_3502/Lab_3/Heights_Linear_Regression.r", "max_stars_repo_name": "aadhityasw/VIT-Labs", "max_stars_repo_head_hexsha": "2c449f64f4fdd8c0ed5f2b51d05a7c586e6ab2ab", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2021-11-18T05:30:24.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-07T06:28:06.000Z", "max_issues_repo_path": "IoT_Domain_Analyst_ECE_3502/Lab_3/Heights_Linear_Regression.r", "max_issues_repo_name": "aadhityasw/VIT-Labs", "max_issues_repo_head_hexsha": "2c449f64f4fdd8c0ed5f2b51d05a7c586e6ab2ab", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "IoT_Domain_Analyst_ECE_3502/Lab_3/Heights_Linear_Regression.r", "max_forks_repo_name": "aadhityasw/VIT-Labs", "max_forks_repo_head_hexsha": "2c449f64f4fdd8c0ed5f2b51d05a7c586e6ab2ab", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2021-10-14T01:10:34.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-18T14:33:52.000Z", "avg_line_length": 30.3333333333, "max_line_length": 159, "alphanum_fraction": 0.6428571429, "num_tokens": 125, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9449947101574298, "lm_q2_score": 0.824461928533133, "lm_q1q2_score": 0.7791121611900036}} {"text": "#### Suponha que x_1, ..., x_n ~ exponencial(theta)\n#### A MLE de theta é theta_hat = n/sum(x)\n#### Vamos derivar a distribuição amostral de theta_hat\n#### Note que a soma de x_i, S, tem distribuição Gamma com parametros n e theta.\n#### Depois note que 1/S tem distribuição gama inversa com parametros n e theta.\n#### Por ultimo note que se X tem distribuição gama inversa com parametros a e b.\n##### cX tem distribuição gama inversa com parametros a e cb.\n\n\nlibrary(invgamma)\n\ncomputa_emv <- function(x){\n 1/mean(x)\n}\n\ntheta.vdd <- 2\nM <- 10000\nn <- 100\n\namostras <- matrix(NA, ncol = n, nrow = M)\nfor (j in 1:M){\n amostras[j, ] <- rexp(n = n, rate = theta.vdd)\n}\n\nEMVs <- apply(amostras, 1, computa_emv)\n\nhist(EMVs, probability = TRUE) \ncurve(invgamma::dinvgamma(x, shape = n, rate = n*theta.vdd),\n min(EMVs), max(EMVs), add = TRUE, lwd = 2)", "meta": {"hexsha": "fc102ca5ff69e729fd285ecc154a305b2cd61847", "size": 851, "ext": "r", "lang": "R", "max_stars_repo_path": "code/sampling_distribution_mle_exponential.r", "max_stars_repo_name": "jlduim/Statistical_Inference_BSc", "max_stars_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 33, "max_stars_repo_stars_event_min_datetime": "2020-08-03T15:42:28.000Z", "max_stars_repo_stars_event_max_datetime": "2021-11-30T15:43:10.000Z", "max_issues_repo_path": "code/sampling_distribution_mle_exponential.r", "max_issues_repo_name": "jlduim/Statistical_Inference_BSc", "max_issues_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 23, "max_issues_repo_issues_event_min_datetime": "2020-08-16T23:02:47.000Z", "max_issues_repo_issues_event_max_datetime": "2021-11-07T14:34:43.000Z", "max_forks_repo_path": "code/sampling_distribution_mle_exponential.r", "max_forks_repo_name": "jlduim/Statistical_Inference_BSc", "max_forks_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 10, "max_forks_repo_forks_event_min_datetime": "2020-08-13T00:53:42.000Z", "max_forks_repo_forks_event_max_datetime": "2021-12-10T07:35:56.000Z", "avg_line_length": 29.3448275862, "max_line_length": 81, "alphanum_fraction": 0.6662749706, "num_tokens": 278, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9553191335436405, "lm_q2_score": 0.8152324983301568, "lm_q1q2_score": 0.7788072039413827}} {"text": "\r\n## simulate two clusters of data\r\nx <- c(rnorm(20,0,1), rnorm(20,4,1))\r\ny <- c(rnorm(20,0,1), rnorm(20,4,1))\r\nX <- cbind(x,y)\r\nones <- matrix(1, dim(X)[1],1)\r\n\r\n\r\n## set up some parameters for plotting\r\nxlims <- c(min(x), max(x)) * 1.3\r\nylims <- c(min(y), max(y)) * 1.3\r\n\r\n## plot the data\r\nplot(X, xlim = xlims, ylim = ylims)\r\n\r\n## And add some very silly seed points\r\nmu1 <- c(0,6)\r\nmu2 <- c(5,-2)\r\nseed <- list(mu1 = mu1, mu2 = mu2)\r\npoints(rbind(seed$mu1, seed$mu2), pch = c(2,3),col = c(\"red\", \"black\"))\r\nlegend(\"topright\", pch = c(1,2,3), col = c(\"black\", \"red\", \"black\"), legend = c(\"Data\", \"Seed 1\", \"Seed 2\" ), cex = 0.5)\r\n##mtext(paste(\"Seed points: \\n Group 1 \", formatC(seed[[1]],2), \"Group 2 \", formatC(seed[[2]],2)))\r\n\r\nseed <- step(X, seed$mu1, seed$mu2)\r\nseed <- step(X, seed$mu1, seed$mu2)\r\nseed <- step(X, seed$mu1, seed$mu2)\r\n\r\n\r\nstep <- function(X, mu1, mu2){\r\n## classify according to current seed point (expectation step)\r\none <- sqrt(rowSums((X - t(t(t(mu1)) %*% t(ones)))^2))\r\ntwo <- sqrt(rowSums((X - t(t(t(mu2)) %*% t(ones)))^2))\r\nplot(x,y, col = 1 + as.numeric(one < two), pch = 16, xlim = xlims, ylim = ylims )\r\nlegend(\"topright\", pch = c(16,16,2,3), col = c(\"red\", \"black\"), legend = c(\"Group1\", \"Group2\", \"Seed 1\", \"Seed 2\" ), cex = 0.5)\r\npoints(rbind(seed$mu1, seed$mu2), pch = c(2,3), col = c(\"red\", \"black\"))\r\nfixed <- (mu1 + mu2)/2\r\nslope <- -(mu1[1] - mu2[1])/(mu1[2] - mu2[2])\r\nabline(c(fixed[2] - slope * fixed[1], slope))\r\n\r\n## calculate new seed points (maximisation step)\r\nmu1 <- colMeans(X[one < two,])\r\nmu2 <- colMeans(X[one >= two,])\r\nreturn(seed = list(mu1 = mu1, mu2 = mu2))\r\n}\r\n\r\n\r\nperp <- function(x, y) {\r\n m <- (x+y)/2\r\n s <- - (x[1] - y[1])/(x[2] - y[2])\r\n abline(c(m[2] - s*m[1], s))\r\n invisible()\r\n}\r\n\r\n", "meta": {"hexsha": "6ae215efbc4a47e403ce6162ad3c5aece75abcbc", "size": 1765, "ext": "r", "lang": "R", "max_stars_repo_path": "code/kmeansdemo.r", "max_stars_repo_name": "phewson/mvstats", "max_stars_repo_head_hexsha": "f39ab1c1b97c89e26c708bd6d532fe13c063a95c", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "code/kmeansdemo.r", "max_issues_repo_name": "phewson/mvstats", "max_issues_repo_head_hexsha": "f39ab1c1b97c89e26c708bd6d532fe13c063a95c", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": 11, "max_issues_repo_issues_event_min_datetime": "2020-08-28T16:37:22.000Z", "max_issues_repo_issues_event_max_datetime": "2020-08-28T16:49:11.000Z", "max_forks_repo_path": "code/kmeansdemo.r", "max_forks_repo_name": "phewson/mvstats", "max_forks_repo_head_hexsha": "f39ab1c1b97c89e26c708bd6d532fe13c063a95c", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 32.6851851852, "max_line_length": 128, "alphanum_fraction": 0.5535410765, "num_tokens": 697, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9161096135894201, "lm_q2_score": 0.8499711718571775, "lm_q1q2_score": 0.7786667618122255}} {"text": "# Make a sequence of 100 x-values going from -4*sigma to 4*sigma\nxvals <- seq(from = -4*sigma, to = 4*sigma, length.out = 100)\n\n# Compute the density of a N(mu, sigma^2) distribution at xvals\nndens <- dnorm(xvals, mean = mu, sd = sigma)\n\n# Plot ndens against xvals\nplot(xvals, ndens, type=\"l\")\n\n# Compute the 99% VaR and 99% ES of a N(mu, sigma^2) distribution\nVaR99 <- qnorm(0.99, mean = mu, sd = sigma)\nES99 <- ESnorm(0.99, mu = mu, sd = sigma)\n\n# Draw vertical lines at VaR99 and ES99 in red and green\nabline(v = VaR99, col = \"red\")\nabline(v = ES99, col = \"green\")\n\n# Plot the risk-factor data\nplot.zoo(riskfactors)\n\n# Calculate the log-returns, assign to returns, and plot\nreturns <- diff(log(riskfactors))[-1, ]\nplot.zoo(returns)\n\n# Use apply() to carry out the Jarque-Bera test for all 5 series\napply(returns, 2, jarque.test)\n\n# Make a Q-Q plot against normal for the 5th return series and add a reference line\nqqnorm(returns[, 5])\nqqline(returns[, 5])\n\n# Make a picture of the sample acfs for returns and their absolute values\nacf(returns)\nacf(abs(returns))\n\n# Calculate the loss from a log-return of -0.1 for all risk factors\nlossop(rep(-0.1, 5))\n\n# Apply lossop() to returns and plot hslosses\nhslosses <- lossop(returns)\nplot(hslosses)\n\n# Form a Q-Q plot of hslosses against normal\nqqnorm(hslosses)\n\n\n# Plot the sample acf of hslosses and their absolute values\nacf(hslosses)\nacf(abs(hslosses))\n\n# Estimate the 99th sample percentile of the distribution of hslosses\nquantile(hslosses, 0.99)\n\n# Estimate the 99% ES\nmean(hslosses[hslosses >= quantile(hslosses, 0.99)])\n\n# Estimate the mean and standard deviation of hslosses\nmu <- mean(hslosses)\nsigma <- sd(hslosses)\n\n# Compute the 99% quantile of a normal distribution\nqnorm(0.99, mean = mu, sd = sigma)\n\n# Compute the 99% ES of a normal distribution\nESnorm(0.99, mu = mu, sd = sigma)\n", "meta": {"hexsha": "5e98b945d9791563bb83d528f912b04b573b2ee7", "size": 1843, "ext": "r", "lang": "R", "max_stars_repo_path": "DataCamp/QRM_Value at Risk and ES.r", "max_stars_repo_name": "eddyzhang2018/quantwithR", "max_stars_repo_head_hexsha": "1c4ce1619ea53c2a392c5d21b660780ef7318038", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "DataCamp/QRM_Value at Risk and ES.r", "max_issues_repo_name": "eddyzhang2018/quantwithR", "max_issues_repo_head_hexsha": "1c4ce1619ea53c2a392c5d21b660780ef7318038", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "DataCamp/QRM_Value at Risk and ES.r", "max_forks_repo_name": "eddyzhang2018/quantwithR", "max_forks_repo_head_hexsha": "1c4ce1619ea53c2a392c5d21b660780ef7318038", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 27.9242424242, "max_line_length": 83, "alphanum_fraction": 0.7173087358, "num_tokens": 586, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.966410494349896, "lm_q2_score": 0.8056321936479701, "lm_q1q2_score": 0.778571406527526}} {"text": "phi = (1+sqrt(5))/2\nN = 501\na = (3-sqrt(5))*pi\nn = 0:(N-1)\nth = n*a\nr = sqrt(n)\n\nx = r*cos(th)\ny = r*sin(th)\nplot(x,y,asp = 1)\n\nthc = seq(0,10*2*pi,length.out = 1000)\nrc = sqrt(1/a)*sqrt(thc)\nplot(rc*cos(thc),rc*sin(thc),col = \"red\",asp = 1,type = 'l')\npoints(x,y)\nw = 3\npoints(x[seq(1,N,w)],y[seq(1,N,w)],col = \"green\")\n\nfibo = function(n){\n a = c(1,1,rep(0,n-2))\n for(i in 3:n){\n a[i] = a[i-1]+a[i-2]\n }\n return(a)\n}\n\ns = fibo(50)\n\nfb = 10#s[6]\n#colors = brewer.pal(fb,\"Paired\")\ncolors = hsv(seq(0,1,length.out = fb+1),1,1)\nplot(x,y,asp = 1)\nz = sapply(1:fb,function(s){\n points(x[seq(s,N,fb)],y[seq(s,N,fb)],col = colors[s])\n lines(x[seq(s,N,fb)],y[seq(s,N,fb)],col = colors[s])})\n\nq = sapply(5:25,function(fb){\n#fb = 10#s[6]\n#colors = brewer.pal(fb,\"Paired\")\ncolors = hsv(seq(0,1,length.out = fb+1),1,1)\nplot(x,y,asp = 1)\nz = sapply(1:fb,function(s){\n points(x[seq(s,N,fb)],y[seq(s,N,fb)],col = colors[s])\n lines(x[seq(s,N,fb)],y[seq(s,N,fb)],col = colors[s])})\n})\n\nss = s[7:10]\nplot(x,y,asp = 1)\ncolors = hsv(seq(0,1,length.out = length(ss)+1),1,1)\nq = sapply(ss,function(fb){\n z = sapply(1:fb,function(s){\n lines(x[seq(s,N,fb)],y[seq(s,N,fb)],col = colors[ss == fb])})\n})\n\nlibrary(tidyverse)\nds = data.frame(x = x, y= y)\nds$n = seq(1,length(x))\n\nk = s[9]\nds$fb = factor(ds$n %% k)\ncolors = hsv(seq(0,1,length.out = k + 1),1,1)\nds$colors = factor(colors[ds$fb])\n\np = ggplot(ds) + geom_path(aes(x = x, y = y,color = colors))+ theme(legend.position = \"none\")+\n # geom_text(data = ds %>% filter(n <= k ),aes(x = x, y = y, label = n))+\n coord_fixed()+scale_color_manual(values = levels(ds$colors))#+theme_void()\nprint(p)\n\n\nk = s[5]\nds$fb = factor(ds$n %% k)\ncolors = hsv(seq(0,1,length.out = k + 1),1,1)\nds$colors = factor(colors[ds$fb])\n\np = ggplot(ds) + geom_path(aes(x = x, y = y,color = fb),size = 0.2)+ theme(legend.position = \"none\")+\n # geom_text(data = ds %>% filter(n <= k ),aes(x = x, y = y, label = n))+\n coord_fixed()+scale_color_manual(values = levels(ds$colors))#+theme_void()\nprint(p)\n\n\nfseq= 1:30\nz = sapply(ds$n,function(x) x %% fseq) %>% t() #%>% add_column(x = x, y = y)\ncolnames(z) = paste0(\"fn_\",fseq)\nz = as.data.frame(z)\ndm = data.frame(x = x, y = y, n = 1:length(x),z)\ntdm = gather(dm,key = \"fn\",value = \"track\",starts_with(\"fn\"))\ntdm$ff = as.numeric(sub(\"fn_\",\"\",tdm$fn))\ntdm$colors = hsv(h = tdm$track/(tdm$ff+1))\n\ntdm$fn = factor(tdm$fn,levels = paste0(\"fn_\",fseq))\n#tdm$track = factor(tdm$track )\np = ggplot(data = tdm) + geom_path(aes(x = x,y = y, color = colors),size = 0.2)+facet_wrap(~fn) +\n coord_fixed()+theme_void()+theme(legend.position = \"none\")\nprint(p)\n\np = ggplot(data = tdm) + geom_point(aes(x = x,y = y, color = colors),size = 0.2)+facet_wrap(~fn) +\n coord_fixed()+theme_void()+theme(legend.position = \"none\")\nprint(p)\n\n\nk = s[9]\nds$fb = factor(ds$n %% k)\ncolors = hsv(seq(0,1,length.out = k + 1),1,1)\nds$colors = factor(colors[ds$fb])\n\nd0 = data.frame(x = rep(0,k),y = rep(0,k),n = rep(0,k),fb = seq(0,k-1),colors = colors[1:k])\n\np = ggplot() +geom_path(data = rbind(d0,ds),aes(x = x, y = y,color = colors))+ theme(legend.position = \"none\")+\n coord_fixed()+scale_color_manual(values =levels(ds$colors))#+theme_void()\nprint(p)\n\n\nN = 1501\na = (3-sqrt(5))*pi #137.5/180*pi\nn = 0:(N-1)\nth = n*a\nr = sqrt(n)\n\nx = r*cos(th)\ny = r*sin(th)\n\nthc = seq(0,500*2*pi,length.out = 6000)\nrc = sqrt(1/a)*sqrt(thc)\n\nw = 55 #34 #21 #13 #8 #5 # 3 #2\nl = -1/2584 #1/987#-1/377 #-1/144#1/55#1/21 #1/8#1/3\nplot(x,y,asp = 1,col = \"gray\")\n#lines(rc*cos(thc),rc*sin(thc),col = \"lightblue\")\npoints(x[seq(1,N,w)],y[seq(1,N,w)],col = \"red\")\nlines(rc*cos(thc*l),-rc*sin(thc*l),col = \"black\")\nprint(s)\n#text(x[w+1],y[w+1],toString(w))\n\n\nw = 55 #34 #21 #13 #8 #5 # 3 #2\nl = -1/2584 #1/987#-1/377 #-1/144#1/55#1/21 #1/8#1/3\nplot(x,y,asp = 1,col = \"gray\")\n#lines(rc*cos(thc),rc*sin(thc),col = \"lightblue\")\npoints(x[seq(2,N,w)],y[seq(2,N,w)],col = \"red\")\nlines(rc*cos(thc*l-a),-rc*sin(thc*l-a),col = \"black\")\nprint(s)\n#text(x[w+1],y[w+1],toString(w))\n\nw = 13 #34 #21 #13 #8 #5 # 3 #2\nl = 1/144 #1/987#-1/377 #-1/144#1/55#1/21 #1/8#1/3\nplot(x,y,asp = 1,col = \"gray\")\n#lines(rc*cos(thc),rc*sin(thc),col = \"lightblue\")\npoints(x[seq(3,N,w)],y[seq(3,N,w)],col = \"red\")\nlines(rc*cos(thc*l-2*a),-rc*sin(thc*l-2*a),col = \"black\")\nprint(s)\n#text(x[w+1],y[w+1],toString(w))\n\ns = fibo(50)\nk = seq(0,1000)\nss = 5\ntheta = pi*(3-sqrt(5))*(ss + s[9]*k)\nrho = sqrt(ss+s[3]*k)\nxt = rho*cos(theta)\nyt = rho*sin(theta)\nplot(x,y,asp = 1, col = \"gray\")\npoints(xt,yt,col = \"red\")\n\n\nN = 1501\na = (3-sqrt(5))*pi #137.5/180*pi\nn = 0:(N-1)\nth = n*a\n\nii = seq(2,20)\nk = length(ii)\ncolors = hsv(h = seq(0,1,length.out = k +1))\nfor(j in seq(1,k)){\n ind = seq(1,N,ii[j])\n plot(th %% (2*pi),col = \"gray\",main = toString(ii[j]))\n points(ind, th[ind] %%(2*pi),col = colors[j],pch = 3)\n lines(ind,th[ind] %% (2*pi),col= colors[j])\n #points(ind, th[ind+1] %%(2*pi),col = colors[j],pch = 3)\n}\n\nj = 19\nind = seq(1,N,ii[j])\nplot(th %% (2*pi),col = \"gray\",main = toString(ii[j]))\npoints(ind, th[ind] %%(2*pi),col = colors[j],pch = 3)\nlines(ind, th[ind] %%(2*pi),col = colors[j])\n\nw = 21\nind = seq(1,N,w)\nplot(x,y,asp = 1, col = \"gray\",main = toString(w))\nlines(x[ind],y[ind],pch = 3)\nplot(th %% (2*pi),col = \"gray\",main = toString(w))\npoints(ind, th[ind] %%(2*pi),pch = 3)\nlines(ind, th[ind] %%(2*pi),col = \"gray\")\n\n\nw = s[7:10]\nk = length(w)\ncolors = hsv(h = seq(0,1,length.out = k +1))\nplot(th %% (2*pi),col = \"gray\")\nfor(j in 1:k ){\n ind = seq(1,N,w[j])\n lines(ind, th[ind] %%(2*pi),col = colors[j])\n cat(w[j])\n cat(\" => \")\n print(diff(th[ind[1:3]] %% (2*pi)) %% (2*pi))\n}\n\nw = 55\nind = seq(1,N,w)\nh = diff(th[ind[1:2]] %% (2*pi)) %% (2*pi)\nif(h > 1) h = h - 2*pi\nh = h/w\n\nt = seq(0,N,length.out = 1e4)\nthc = h*t\nrc = sqrt(t)\n\nplot(th %% (2*pi),col = \"gray\",main = toString(w))\npoints(ind, th[ind] %%(2*pi),pch = 3)\nlines(ind, th[ind] %%(2*pi),col = \"gray\")\nlines(t,thc,col = \"red\")\n\nplot(x,y,asp = 1,col = \"gray\")\npoints(x[ind],y[ind],col = \"red\")\nlines(rc*cos(thc),rc*sin(thc),col = \"black\")\n\n\n\nw = 55\nst = 44\nind = seq(st,N,w)\nh = diff(th[ind[1:2]] %% (2*pi)) %% (2*pi)\nif(h > 1) h = h - 2*pi\nh = h/w\nb = th[st] %% (2*pi)\nt = seq(0,N,length.out = 1e4)\nthc = h*(t-ind[1]) + b #t = ind[1] => thc = b with slop h\nrc = sqrt(t)\n\nplot(th %% (2*pi),col = \"gray\",main = toString(w))\npoints(ind, th[ind] %%(2*pi),pch = 3)\nlines(ind, th[ind] %%(2*pi),col = \"gray\")\nlines(t,thc,col = \"red\")\n\nplot(x,y,asp = 1,col = \"gray\")\npoints(0,0,pch=3)\npoints(x[ind],y[ind],col = \"red\")\nlines(rc*cos(thc),rc*sin(thc),col = \"black\")\n\n\nw = 55\nplot(x,y,asp = 1,col = \"gray\")\npoints(0,0,pch=3)\nt = seq(0,N,length.out = 1e4)\ncolors = hsv(h = seq(0,1,length.out = w+1))\nfor(st in seq(1,w)){\n ind = seq(st,N,w)\n h = diff(th[ind[1:2]] %% (2*pi)) %% (2*pi)\n if(h > 1) h = h - 2*pi\n h = h/w\n print(paste0(st,\" => \", h))\n thc = h*(t-ind[1]) + th[st] %% (2*pi) #t = ind[1] => thc = b with slop h\n rc = sqrt(t)\n \n points(x[ind],y[ind],col = colors[st])\n lines(rc*cos(thc),rc*sin(thc),col = colors[st])\n #print(paste0(c(\"done with \",toString(st))))\n}\n\nu = 3-sqrt(5)\nuu = u*seq(1,1000)\nplot(uu %% 2,col = \"gray\")#,pch =20)\nind = seq(1,1000,11)\npoints(ind,uu[ind] %% 2,pch = 3)\nlines(ind,uu[ind] %% 2,col = \"blue\")\n\n\nphi = (1-sqrt(5))/2\nphiz = phi %% 1\nu = phi*seq(0,1000)\nw = 17\nind = seq(1,1000,w)\nplot(u %% 1,col = \"gray\",main = toString(w))\npoints(ind,u[ind] %% 1,pch = 3)\nlines(ind,u[ind] %% 1,col = \"blue\")\nh = diff(u[ind[1:5]]) %% 1\nprint(1 %/% h + 1)\nif(h[1] > phiz) h = h - 1\n\nphi = (1-sqrt(5))/2\nphiz = phi %% 1\nu = phi*seq(0,1000)\nfor(w in seq(2:60)){\n ind = seq(1,1000,w)\n plot(u %% 1,col = \"gray\",main = toString(w))\n points(ind,u[ind] %% 1,pch = 3)\n lines(ind,u[ind] %% 1,col = \"blue\")\n h = diff(u[ind[1:5]]) %% 1\n if(h[1] > phiz) h = h - 1\n hw = 1+ 1 %/% h\n if(h[1] <0 ) hw = (1 - 1 %/% h )\n if(hw[1] > 0){\n cat(paste0(w,\" => \"))\n print(hw)\n }\n \n}\n\nN = 1000\nu = seq(1,N)\nplot(u,(phi*u) %% 1,col = \"gray\")\nuu = seq(3,N,s[9])\npoints(uu,(phi*uu) %% 1,pch = 3)\nv = (phi*u) %% 1\nvs = sort(v,index.return=TRUE)\n\n\n\nw = 3*55\nst = 44\nind = seq(st,N,w)\nh = diff(th[ind[1:2]] %% (2*pi)) %% (2*pi)\nif(h > 1) h = h - 2*pi\nh = h/w\nb = th[st] %% (2*pi)\nt = seq(0,N,length.out = 1e4)\nthc = h*(t-ind[1]) + b #t = ind[1] => thc = b with slop h\nrc = sqrt(t)\n\nplot(th %% (2*pi),col = \"gray\",main = toString(w))\npoints(ind, th[ind] %%(2*pi),pch = 3)\nlines(ind, th[ind] %%(2*pi),col = \"gray\")\nlines(t,thc,col = \"red\")\n\nplot(x,y,asp = 1,col = \"gray\")\npoints(0,0,pch=3)\npoints(x[ind],y[ind],col = \"red\")\nlines(rc*cos(thc),rc*sin(thc),col = \"black\")\n\nw = 11\nst = 1\nl = 10\nind = seq(st,N,w)\nh = diff(th[ind],l) %% (2*pi)\nh = h[1]\nif(h > pi) h = h - 2*pi\nh = h/w/l\nb = th[st] %% (2*pi)\nt = seq(0,N,length.out = 1e4)\nthc = h*(t-ind[1]) + b #t = ind[1] => thc = b with slop h\nrc = sqrt(t)\n\nplot(th %% (2*pi),col = \"gray\",main = toString(w))\npoints(ind, th[ind] %%(2*pi),pch = 3)\nlines(ind, th[ind] %%(2*pi),col = \"gray\")\nlines(t+ind[2],thc+th[ind[2]] %% (2*pi),col = \"red\")\n\nplot(x,y,asp = 1,col = \"gray\")\npoints(0,0,pch=3)\npoints(x[ind],y[ind],col = \"red\")\nlines(rc*cos(thc),rc*sin(thc),col = \"black\")\n\n\n\nw = 33\nst = 3\nind = seq(st,N,w)\nzl = min((w-1),length(ind)-1)\nzm = sapply(1:zl, function(l){\n h = diff(th[ind],l) %% (2*pi)\n h = h[1]\n if(h > pi) h = h - 2*pi\n return(h)\n})\n\nhi = which.min(abs(zm)/(1:zl))\ncat(\"# of branches:\")\nprint(hi)\nh = zm[hi]\nh = h/w/hi\nb = th[st] %% (2*pi)\nt = seq(0,N,length.out = 1e4)\nthc = h*(t-ind[1]) + b #t = ind[1] => thc = b with slop h\nrc = sqrt(t)\n\nplot(th %% (2*pi),col = \"gray\",main = toString(w))\npoints(ind, th[ind] %%(2*pi),pch = 3)\nlines(ind, th[ind] %%(2*pi),col = \"gray\")\nlines(t+ind[2],(-b+thc+th[ind[2]] )%% (2*pi),col = \"red\")\n\nplot(x,y,asp = 1,col = \"gray\")\npoints(0,0,pch=3)\npoints(x[ind],y[ind],col = \"red\")\nlines(rc*cos(thc),rc*sin(thc),col = \"black\")\n\nplot(zm/(1:zl))\n\nlibrary(numbers)\nprimeFactors(610)\n\n\nw = 61\nN = 100*w + 10\na = (3-sqrt(5))*pi\nn = 0:(N-1)\nth = n*a\nr = sqrt(n)\n\nx = r*cos(th)\ny = r*sin(th)\n#plot(x,y,asp = 1)\n\nw = 33\nst = 1\nl = 5\nind = seq(st,N,w)\nh = diff(th[ind],l) %% (2*pi)\nh = h[1]\nif(h > pi) h = h - 2*pi\nh = h/w/l\nb = th[st] %% (2*pi)\nt = seq(0,N,length.out = 1e4)\nthc = h*(t-ind[1]) + b #t = ind[1] => thc = b with slop h\nrc = sqrt(t)\n\n\nplot(th %% (2*pi),col = \"gray\",main = toString(w))\npoints(ind, th[ind] %%(2*pi),pch = 3)\nlines(ind, th[ind] %%(2*pi),col = \"gray\")\nlines(t+ind[2],(-b+thc+th[ind[2]] )%% (2*pi),col = \"red\")\n\nplot(x,y,asp = 1,col = \"gray\")\npoints(0,0,pch=3)\npoints(x[ind],y[ind],col = \"red\")\n\nlines(rc*cos(thc),rc*sin(thc),col = \"black\")\n\n\n\nw = 8*18\nst = 3\nind = seq(st,N,w)\nzl = min((w-1),length(ind)-1)\nzm = sapply(1:zl, function(l){\n h = diff(th[ind],l) %% (2*pi)\n h = h[1]\n if(h > pi) h = h - 2*pi\n return(h)\n})\nplot(x[ind],y[ind],col = \"red\",asp = 1)\n\n\nw =18\nst = 3\nind = seq(st,N,w)\nplot(x[ind],y[ind],col = \"red\",asp = 1,main = toString(w))\nw =8\nind = seq(st,N,w)\npoints(x[ind],y[ind],pch = 3,col = \"gray\")\nw =8*18\nind = seq(st,N,w)\npoints(x[ind],y[ind],pch = 2,col = \"blue\")\n\nsprintf(\"%.50f\",phi*8*18) #144\nsprintf(\"%.50f\",phi*233)\n\nps = c(2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97)\n\nw = 377\nsth = function(w){\n N = 30*w + 10\n #print(N)\n a = (3-sqrt(5))*pi\n n = 0:(N-1)\n th = n*a\n r = sqrt(n)\n \nst = 1\nind = seq(st,N,w)\nh = diff(th[ind[1:2]] %% (2*pi)) %% (2*pi)\nif(h > pi) h = h - 2*pi\nh = h/w\nb = th[st] %% (2*pi)\nt = seq(0,N,length.out = 1e4)\nthc = h*(t-ind[1]) + b #t = ind[1] => thc = b with slop h\nrc = sqrt(t)\nx = r*cos(th)\ny = r*sin(th)\n\n\n#plot(th %% (2*pi),col = \"gray\",main = toString(w))\n#points(ind, th[ind] %%(2*pi),pch = 3)\nplot(ind, th[ind] %%(2*pi),pch = 3,main = toString(w))\n#lines(ind, th[ind] %%(2*pi),col = \"gray\")\nlines(t,thc %% (2*pi),col = \"red\")\n\n#plot(x,y,asp = 1,col = \"gray\")\n#points(0,0,pch=3)\n#points(x[ind],y[ind],col = \"red\")\nplot(x[ind],y[ind],col = \"red\",main = toString(w),asp = 1)\nlines(rc*cos(thc),rc*sin(thc),col = \"black\")\n}\n\n", "meta": {"hexsha": "29fa5ce846016ca8f8732c8dd98dc4e3a0d53011", "size": 11986, "ext": "r", "lang": "R", "max_stars_repo_path": "phyllotaxis_thing.r", "max_stars_repo_name": "surecalois/random_R_stuff", "max_stars_repo_head_hexsha": "1e3dc4cf0960effb581800ceb6020488aab26ae0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "phyllotaxis_thing.r", "max_issues_repo_name": "surecalois/random_R_stuff", "max_issues_repo_head_hexsha": "1e3dc4cf0960effb581800ceb6020488aab26ae0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "phyllotaxis_thing.r", "max_forks_repo_name": "surecalois/random_R_stuff", "max_forks_repo_head_hexsha": "1e3dc4cf0960effb581800ceb6020488aab26ae0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 23.8290258449, "max_line_length": 111, "alphanum_fraction": 0.5435508093, "num_tokens": 5150, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.944176863577751, "lm_q2_score": 0.8244619306896955, "lm_q1q2_score": 0.7784378798578538}} {"text": "# y denote the number of successes in the n sample trials,\r\n# sample proportion\r\ny=330\r\nn=870\r\npie=y/n\r\nsigma=sqrt((pie*(1-pie))/n)\r\n\r\nalpha=0.05\r\nz.alpha=qnorm(1-alpha)\r\nerror=z.alpha*sigma\r\n# the 90% confidence interval on the proportion of cancer\r\n#patients who will survive at least 5 years\r\nleft_i=pie-error\r\nright_i=pie+error\r\nprint(left_i)\r\nprint(right_i)\r\n\r\n\r\n", "meta": {"hexsha": "63f8e6b50db723b3fdcf21fdd1adce5bd25cfb53", "size": 369, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH10/EX10.1/Ex10_1.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH10/EX10.1/Ex10_1.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH10/EX10.1/Ex10_1.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 19.4210526316, "max_line_length": 59, "alphanum_fraction": 0.7181571816, "num_tokens": 107, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9441768557238084, "lm_q2_score": 0.8244619306896955, "lm_q1q2_score": 0.7784378733825772}} {"text": "\r\n\r\n# Goal: Experiment with fitting nonlinear functional forms in\r\n# OLS, using orthogonal polynomials to avoid difficulties with\r\n# near-singular design matrices that occur with ordinary polynomials.\r\n# Shriya Anand, Gabor Grothendieck, Ajay Shah, March 2006.\r\n\r\n# We will deal with noisy data from the d.g.p. y = sin(x) + e\r\nx <- seq(0, 2*pi, length.out=50)\r\nset.seed(101)\r\ny <- sin(x) + 0.3*rnorm(50)\r\nbasicplot <- function(x, y, minx=0, maxx=3*pi, title=\"\") {\r\n plot(x, y, xlim=c(minx,maxx), ylim=c(-2,2), main=title)\r\n lines(x, sin(x), col=\"blue\", lty=2, lwd=2)\r\n abline(h=0, v=0)\r\n}\r\nx.outsample <- seq(0, 3*pi, length.out=100)\r\n\r\n# Severe multicollinearity with ordinary polynomials\r\nx2 <- x*x\r\nx3 <- x2*x\r\nx4 <- x3*x\r\ncor(cbind(x, x2, x3, x4))\r\n# and a perfect design matrix using orthogonal polynomials\r\nm <- poly(x, 4)\r\nall.equal(cor(m), diag(4)) # Correlation matrix is I.\r\n\r\npar(mfrow=c(2,2))\r\n# Ordinary polynomial regression --\r\n p <- lm(y ~ x + I(x^2) + I(x^3) + I(x^4))\r\n summary(p)\r\n basicplot(x, y, title=\"Polynomial, insample\") # Data\r\n lines(x, fitted(p), col=\"red\", lwd=3) # In-sample\r\n basicplot(x, y, title=\"Polynomial, out-of-sample\")\r\n predictions.p <- predict(p, list(x = x.outsample)) # Out-of-sample\r\n lines(x.outsample, predictions.p, type=\"l\", col=\"red\", lwd=3)\r\n lines(x.outsample, sin(x.outsample), type=\"l\", col=\"blue\", lwd=2, lty=2)\r\n # As expected, polynomial fitting gives terrible results out of sample.\r\n\r\n# These IDENTICAL things using orthogonal polynomials\r\n d <- lm(y ~ poly(x, 4))\r\n summary(d)\r\n basicplot(x, y, title=\"Orth. poly., insample\") # Data\r\n lines(x, fitted(d), col=\"red\", lwd=3) # In-sample\r\n basicplot(x, y, title=\"Orth. poly., out-of-sample\")\r\n predictions.op <- predict(d, list(x = x.outsample)) # Out-of-sample\r\n lines(x.outsample, predictions.op, type=\"l\", col=\"red\", lwd=3)\r\n lines(x.outsample, sin(x.outsample), type=\"l\", col=\"blue\", lwd=2, lty=2)\r\n\r\n# predict(d) is magical! See ?SafePrediction\r\n# The story runs at two levels. First, when you do an OLS model,\r\n# predict()ion requires applying coefficients to an appropriate\r\n# X matrix. But one level deeper, the polynomial or orthogonal-polynomial\r\n# needs to be utilised for computing the X matrix based on the\r\n# supplied x.outsample data.\r\n# If you say p <- poly(x, n)\r\n# then you can say predict(p, new) where predict.poly() gets invoked.\r\n# And when you say predict(lm()), the full steps are worked out for\r\n# you automatically: predict.poly() is used to make an X matrix and\r\n# then prediction based on the regression results is done.\r\n\r\nall.equal(predictions.p, predictions.op) # Both paths are identical for this\r\n # (tame) problem.\r\n\r\n", "meta": {"hexsha": "238611773093eb5541127dedd82a1d0ae6036d8f", "size": 2758, "ext": "r", "lang": "R", "max_stars_repo_path": "RFrontEndSolution/Tests Repo/Rscripts All (163 files)/o9.r", "max_stars_repo_name": "AlexandrosPlessias/CompilerFrontEndForRLanguage", "max_stars_repo_head_hexsha": "71e3e60476f6f83b05cc97c625265edbde086341", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "RFrontEndSolution/Tests Repo/Rscripts All (163 files)/o9.r", "max_issues_repo_name": "AlexandrosPlessias/CompilerFrontEndForRLanguage", "max_issues_repo_head_hexsha": "71e3e60476f6f83b05cc97c625265edbde086341", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "RFrontEndSolution/Tests Repo/Rscripts All (163 files)/o9.r", "max_forks_repo_name": "AlexandrosPlessias/CompilerFrontEndForRLanguage", "max_forks_repo_head_hexsha": "71e3e60476f6f83b05cc97c625265edbde086341", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 42.4307692308, "max_line_length": 77, "alphanum_fraction": 0.6544597534, "num_tokens": 812, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9073122288794594, "lm_q2_score": 0.8577681049901037, "lm_q1q2_score": 0.7782634912002812}} {"text": "## Dale W.R. Rosenthal, 2018\n## You are free to distribute and use this code so long as you attribute\n## it to me or cite the text.\n## The legal disclaimer in _A Quantitative Primer on Investments with R_\n## applies to this code. Use or distribution without these comment lines\n## is forbidden.\n\nx <- seq(-5,5, 0.01) # sequence of values to plot a standardized distribution\n\n# Plot normal, logistic, and standardized t_5 densities; add a legend to look nice.\nplot(x, dnorm(x), type='l', ylim=c(0,0.5), lty=1, lwd=2, col=\"cyan\", xlab=\"\", ylab=\"\", main=\"\")\nlines(x, dlogis(x, scale=sqrt(3)/pi), lty=2, lwd=2)\nlines(x, dt(x/sqrt((5-2)/5), df=5)/sqrt((5-2)/5), lty=4, lwd=2, col=\"red\")\nlegend.text <- c(expression(paste('t'[5], \" \", kappa, \"=9\")),\n expression(paste(\"logistic \", kappa,\"=4.2\")),\n expression(paste(\"normal \", kappa, \"=3\")))\nlegend(\"topright\", legend.text, lty=c(4,2,1), lwd=2, col=c(\"red\", \"black\", \"cyan\"))\n\n# Then plot logs of densities to show the tail behavior\nplot(x, log(dnorm(x)), type='l', lty=1, lwd=2, col=\"cyan\", xlab=\"\", ylab=\"\", main=\"\")\nlines(x, log(dlogis(x, scale=sqrt(3)/pi)), type='l', lty=2, lwd=2)\nlines(x, log(dt(x/sqrt((5-2)/5), df=5)/sqrt((5-2)/5)), type='l', lty=4, lwd=2, col=\"red\")\nlegend.text <- c(expression(paste('t'[5], \" \", kappa, \"=9\")),\n expression(paste(\"logistic \", kappa,\"=4.2\")),\n expression(paste(\"normal \", kappa, \"=3\")))\nlegend(\"topright\", legend.text, lty=c(4,2,1), lwd=2, col=c(\"red\", \"black\", \"cyan\"))\n", "meta": {"hexsha": "0910a0f7005a981803089875963424d61fc0f170", "size": 1528, "ext": "r", "lang": "R", "max_stars_repo_path": "Quantitative Primer/samples/ch7-kurtosisplots.r", "max_stars_repo_name": "bmoretz/Quantitative-Investments", "max_stars_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 7, "max_stars_repo_stars_event_min_datetime": "2020-03-26T05:47:30.000Z", "max_stars_repo_stars_event_max_datetime": "2022-02-18T21:50:54.000Z", "max_issues_repo_path": "Quantitative Primer/samples/ch7-kurtosisplots.r", "max_issues_repo_name": "bmoretz/Quantitative-Investments", "max_issues_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Quantitative Primer/samples/ch7-kurtosisplots.r", "max_forks_repo_name": "bmoretz/Quantitative-Investments", "max_forks_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2020-11-03T09:23:54.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-18T21:50:55.000Z", "avg_line_length": 56.5925925926, "max_line_length": 95, "alphanum_fraction": 0.6086387435, "num_tokens": 511, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9073122238669025, "lm_q2_score": 0.8577681049901037, "lm_q1q2_score": 0.7782634869006697}} {"text": "# [Contoh | Langkah 1: Standarisasi Data](https://academy.dqlab.id/main/livecode/89/173/839)\r\nlibrary(openxlsx)\r\ndf <- read.xlsx(\"https://academy.dqlab.id/dataset/dqlab_pcadata.xlsx\", sheet=\"3varb\")\r\n# standarisasi variabel (centering dan scaling)\r\ndf <- scale(df, center = TRUE, scale = TRUE)\r\nhead(df, 3)\r\n\r\n\r\n# [Contoh | Langkah 2: Menghitung Matrik Korelasi Data](https://academy.dqlab.id/main/livecode/89/173/840)\r\nlibrary(openxlsx)\r\n\r\ndf <- read.xlsx(\"https://academy.dqlab.id/dataset/dqlab_pcadata.xlsx\", sheet=\"3varb\")\r\ndf <- scale(df, center = TRUE, scale = TRUE)\r\n\r\ncormat <- cor(df)\r\ncormat\r\n\r\n\r\n# [Contoh | Langkah 3: Menghitung Nilai Eigen dan Vektor Eigen](https://academy.dqlab.id/main/livecode/89/173/841)\r\nlibrary(openxlsx)\r\n\r\ndf <- read.xlsx(\"https://academy.dqlab.id/dataset/dqlab_pcadata.xlsx\", sheet=\"3varb\")\r\ndf <- scale(df, center = TRUE, scale = TRUE)\r\n\r\ncormat <- cor(df)\r\n\r\neig <- eigen(cormat)\r\neig\r\n\r\n\r\n# [Contoh | Langkah 4: Memilih Banyaknya Principal Component](https://academy.dqlab.id/main/livecode/89/173/842)\r\nlibrary(openxlsx)\r\n\r\ndf <- read.xlsx(\"https://academy.dqlab.id/dataset/dqlab_pcadata.xlsx\", sheet=\"3varb\")\r\ndf <- scale(df, center = TRUE, scale = TRUE)\r\n\r\ncormat <- cor(df)\r\neig <- eigen(cormat)\r\n\r\nround(eig$values/ncol(df),3)\r\nround(cumsum(eig$values/ncol(df)),3)\r\n\r\npr.out <- prcomp(df, scale. = TRUE, center = TRUE)\r\npr.out\r\nsummary(pr.out)\r\n\r\nlibrary(factoextra)\r\n\r\nfviz_eig(pr.out, addlabels = TRUE)\r\n\r\nscreeplot(pr.out, type = \"line\")\r\nabline(h = 1, lty = 3, col = \"red\")\r\n\r\n\r\n# [Contoh | Langkah 5: Visualisasi dengan Biplot](https://academy.dqlab.id/main/livecode/89/173/843)\r\nlibrary(openxlsx)\r\n\r\ndf <- read.xlsx(\"https://academy.dqlab.id/dataset/dqlab_pcadata.xlsx\", sheet=\"3varb\")\r\ndf <- scale(df, center = TRUE, scale = TRUE)\r\n\r\npr.out <- prcomp(df, scale. = TRUE, center = TRUE)\r\n\r\npr.out$rotation\r\nbiplot(pr.out, scale = 0)\r\n\r\n\r\n# [Contoh | Langkah 6: Menghitung Skor Baru](https://academy.dqlab.id/main/livecode/89/173/844)\r\nlibrary(openxlsx)\r\n\r\ndf <- read.xlsx(\"https://academy.dqlab.id/dataset/dqlab_pcadata.xlsx\", sheet=\"3varb\")\r\ndf <- scale(df, center = TRUE, scale = TRUE)\r\n\r\npr.out <- prcomp(df, scale. = TRUE, center = TRUE)\r\n\r\nhead(df)\r\n\r\ndf_new <- df %*% pr.out$rotation\r\ndf_new[1:6,1:2]\r\n\r\n\r\n# [Tugas Praktik](https://academy.dqlab.id/main/livecode/89/173/845)\r\n# Panggil library openxlsx untuk membaca file data Excel\r\nlibrary(openxlsx)\r\n# Baca data pada sheet \"3varb\" dalam file https://academy.dqlab.id/dataset/dqlab_pcadata.xlsx\r\n# dan simpan data dengan nama df_raw\r\ndf_raw <- read.xlsx(\"https://academy.dqlab.id/dataset/dqlab_pcadata.xlsx\", sheet = \"3varb\")\r\n# Tampilkan struktur data\r\nstr(df_raw)\r\n# Tampilkan beberapa baris observasi dengan fungsi head()\r\nhead(df_raw)\r\n# Lakukan analisa PCA dengan fungsi prcomp()\r\n# simpan output dengan nama pr.out\r\npr.out <- prcomp(df_raw, center = TRUE, scale = TRUE, retx = TRUE)\r\n# Tampilkan komponen output fungsi prcomp()\r\nnames(pr.out)\r\n# Tampilkan output PCA\r\npr.out\r\n# Tampilkan summary dari output PCA\r\nsummary(pr.out)\r\n# Gambarkan scree plot\r\nscreeplot(pr.out, type = \"line\")\r\n# Tambahkan garis horizontal sebagai panduan untuk menggunakan kriteria Kaiser\r\nabline(h = 1, col = \"red\", lty = 3)\r\n# Gambarkan biplot dengan menggunakan fungsi biplot()\r\nbiplot(pr.out, scale = 0)\r\n\r\n\r\n# [Tugas Praktik: 4 Variabel](https://academy.dqlab.id/main/livecode/89/174/852)\r\n# Panggil library openxlsx untuk membaca file data Excel\r\n# [1]\r\nlibrary(openxlsx)\r\n# Baca data pada sheet \"csdata\" dalam file \"https://academy.dqlab.id/dataset/dqlab_pcadata.xlsx\"\r\n# dan simpan data dengan nama \"csdat_raw\"\r\n# [2]\r\ncsdat_raw <- read.xlsx(\"https://academy.dqlab.id/dataset/dqlab_pcadata.xlsx\", sheet = \"csdata\")\r\n# Tampilkan struktur data\r\n# [3]\r\nstr(csdat_raw)\r\n# Tampilkan beberapa baris observasi dengan fungsi head()\r\n# [4]\r\nhead(csdat_raw)\r\n# Tampilkan statistika deskriptif untuk semua variabel dalam data.\r\n# [5]\r\nsummary(csdat_raw)\r\n# Gambarkan distribusi Income berdasarkan Dependents\r\nlibrary(ggplot2)\r\nggplot(csdat_raw, aes(as.factor(dependents), income)) +\r\n geom_boxplot() + xlab(\"Dependents\") + ggtitle(\"Boxplot Income Berdasarkan Dependents\")\r\n# Pisahkan data untuk traning set dan testing set\r\n# untuk tiap-tiap risk rating\r\n# Catat indeks/ nomor baris untuk tiap-tiap risk rating\r\nindex1 <- which(csdat_raw$riskrating == 1)\r\nindex2 <- which(csdat_raw$riskrating == 2)\r\n# Lakukan pencatatan indeks untuk risk rating berikutnya\r\n# [6]\r\nindex3 <- which(csdat_raw$riskrating == 3)\r\nindex4 <- which(csdat_raw$riskrating == 4)\r\nindex5 <- which(csdat_raw$riskrating == 5)\r\n# 80% data akan digunakan sebagai traning set.\r\n# [7]\r\nntrain1 <- round(0.8 * length(index1))\r\nntrain2 <- round(0.8 * length(index2))\r\nntrain3 <- round(0.8 * length(index3))\r\nntrain4 <- round(0.8 * length(index4))\r\nntrain5 <- round(0.8 * length(index5))\r\n# set seed agar sampling ini bisa direproduksi\r\nset.seed(100)\r\n# sampling data masing-masing rating untuk training set\r\n# [8]\r\ntrain1_index <- sample(index1, ntrain1)\r\ntrain2_index <- sample(index2, ntrain2)\r\ntrain3_index <- sample(index3, ntrain3)\r\ntrain4_index <- sample(index4, ntrain4)\r\ntrain5_index <- sample(index5, ntrain5)\r\n# menyimpan data ke dalam testing set\r\n# [9]\r\ntest1_index <- setdiff(index1, train1_index)\r\ntest2_index <- setdiff(index2, train2_index)\r\ntest3_index <- setdiff(index3, train3_index)\r\ntest4_index <- setdiff(index4, train4_index)\r\ntest5_index <- setdiff(index5, train5_index)\r\n# Menggabungkan hasil sampling masing-masing risk rating ke dalam training set\r\ncsdattrain <- do.call(\"rbind\", list(csdat_raw[train1_index,],\r\n csdat_raw[train2_index,], csdat_raw[train3_index,],\r\n csdat_raw[train4_index,], csdat_raw[train5_index,]))\r\ncstrain <- subset(csdattrain, select =\r\n -c(contractcode,riskrating))\r\n# Menggabungkan hasil sampling masing-masing risk rating ke dalam testing set\r\ncsdattest <- do.call(\"rbind\", list(csdat_raw[test1_index,],\r\n csdat_raw[test2_index,], csdat_raw[test3_index,],\r\n csdat_raw[test4_index,], csdat_raw[test5_index,])) # [10]\r\ncstest <- subset(csdattest,\r\n select = -c(contractcode,riskrating)) # [11]\r\n\r\n# Menghitung korelasi antar variabel\r\ncor(cstrain)\r\n# Lakukan analisa PCA dengan fungsi prcomp() dan\r\n# simpan output ke dalam obyek dengan nama pr.out\r\n# [12]\r\npr.out <- prcomp(cstrain, scale = TRUE, center = TRUE)\r\n# Tampilkan output PCA dengan memanggil obyek pr.out\r\n# [13]\r\npr.out\r\n# Tampilkan summary dari output PCA\r\n# [14]\r\nsummary(pr.out)\r\n# Gambarkan scree plot dengan menggunakan fungsi screeplot()\r\n# [15]\r\nscreeplot(pr.out, type = \"line\", ylim = c(0,2))\r\n# Tambahkan garis horizontal sebagai panduan untuk menggunakan kriteria Kaiser\r\nabline(h = 1, lty = 3, col = \"red\")\r\n# Gambarkan biplot dengan menggunakan fungsi biplot()\r\n# [16]\r\nbiplot(pr.out, scale = 0) # draw first 2 principal components\r\n\r\n\r\n# [Tugas Praktik: 8 Variabel](https://academy.dqlab.id/main/livecode/89/175/859)\r\n# Panggil library openxlsx untuk membaca file data Excel\r\nlibrary(openxlsx)\r\n# Baca data pada sheet \"cslarge\" dalam file \"https://academy.dqlab.id/dataset/dqlab_pcadata.xlsx\"\r\n# dan simpan data dengan nama \"cslarge_raw\"\r\ncslarge_raw <- read.xlsx(\"https://academy.dqlab.id/dataset/dqlab_pcadata.xlsx\", sheet = \"cslarge\")\r\n# Tampilkan struktur data\r\nstr(cslarge_raw)\r\n# Tampilkan beberapa baris observasi dengan fungsi head()\r\nhead(cslarge_raw)\r\n# Tampilkan statistika deskriptif untuk semua variabel dalam data frame.\r\nsummary(cslarge_raw)\r\n# Gambarkan distribusi income berdasarkan dependents.\r\nlibrary(ggplot2)\r\nggplot(cslarge_raw, aes(as.factor(dependents), income)) +\r\n geom_boxplot() + xlab(\"Dependents\") + ggtitle(\"Boxplot Income Berdasarkan Dependents\")\r\n# Gambarkan distribusi debt berdasarkan dependents.\r\nggplot(cslarge_raw, aes(as.factor(dependents), debt)) +\r\n geom_boxplot() + xlab(\"Dependents\") + ggtitle(\"Boxplot Debt Berdasarkan Dependents\")\r\n# Pisahkan data untuk traning set dan testing set\r\n# untuk tiap-tiap risk rating\r\n# Catat indeks/ nomor baris untuk tiap-tiap risk rating\r\nindex1 <- which(cslarge_raw$riskrating == 1)\r\nindex2 <- which(cslarge_raw$riskrating == 2)\r\n# Lakukan pencatatan indeks untuk risk rating berikutnya\r\nindex3 <- which(cslarge_raw$riskrating == 3)\r\nindex4 <- which(cslarge_raw$riskrating == 4)\r\nindex5 <- which(cslarge_raw$riskrating == 5)\r\n# 80% data akan digunakan sebagai traning set.\r\nntrain1 <- round(0.8 * length(index1))\r\nntrain2 <- round(0.8 * length(index2))\r\nntrain3 <- round(0.8 * length(index3))\r\nntrain4 <- round(0.8 * length(index4))\r\nntrain5 <- round(0.8 * length(index5))\r\n# set seed agar sampling ini bisa direproduksi\r\nset.seed(100)\r\n# sampling data masing-masing rating untuk training set\r\ntrain1_index <- sample(index1, ntrain1)\r\ntrain2_index <- sample(index2, ntrain2)\r\ntrain3_index <- sample(index3, ntrain3)\r\ntrain4_index <- sample(index4, ntrain4)\r\ntrain5_index <- sample(index5, ntrain5)\r\n# menyimpan data ke dalam testing set\r\ntest1_index <- setdiff(index1, train1_index)\r\ntest2_index <- setdiff(index2, train2_index)\r\ntest3_index <- setdiff(index3, train3_index)\r\ntest4_index <- setdiff(index4, train4_index)\r\ntest5_index <- setdiff(index5, train5_index)\r\n# Menggabungkan hasil sampling masing-masing risk rating ke dalam training set\r\ncslarge_train <- do.call(\"rbind\", list(cslarge_raw[train1_index,],\r\n cslarge_raw[train2_index,], cslarge_raw[train3_index,],\r\n cslarge_raw[train4_index,], cslarge_raw[train5_index,]))\r\ncstrain <- subset(cslarge_train, select = -c(contractcode,riskrating))\r\n# Menggabungkan hasil sampling masing-masing risk rating ke dalam testing set\r\ncslarge_test <- do.call(\"rbind\", list(cslarge_raw[test1_index,],\r\n cslarge_raw[test2_index,], cslarge_raw[test3_index,],\r\n cslarge_raw[test4_index,], cslarge_raw[test5_index,]))\r\ncstest <- subset(cslarge_test, select = -c(contractcode,riskrating))\r\n# Menghitung korelasi antar variabel\r\ncor(cstrain)\r\n# Menggambarkan matrik korelasi dengan ggcorrplot\r\nlibrary(ggcorrplot)\r\nggcorrplot(cor(cstrain))\r\n# Lakukan analisa PCA dengan fungsi prcomp() dan\r\n# simpan output ke dalam obyek dengan nama pr.out\r\npr.out <- prcomp(cstrain, scale = TRUE, center = TRUE)\r\n# Tampilkan output PCA dengan memanggil obyek pr.out\r\npr.out\r\n# Tampilkan summary dari output PCA\r\nsummary(pr.out)\r\n# Gambarkan scree plot dengan menggunakan fungsi screeplot()\r\nscreeplot(pr.out, type = \"line\", ylim = c(0,2))\r\n# Tambahkan garis horizontal sebagai panduan untuk menggunakan kriteria Kaiser\r\nabline(h = 1, lty = 3, col = \"red\")\r\n# Gambarkan biplot dengan menggunakan fungsi biplot()\r\nbiplot(pr.out, scale = 0) #draw first 2 principal components\r\n# Gambarkan Principal Component dan risk rating dengan menggunakan\r\n# fungsi autoplot() dari package ggfortify.\r\nlibrary(ggfortify)\r\nautoplot(pr.out, data = cslarge_train, colour = 'riskrating',\r\n loadings = TRUE, loadings.label = TRUE, loadings.label.size = 3, scale = 0)\r\n# Gambarkan Principal Component dan risk rating dengan menggunakan\r\n# fungsi fviz_pca_ind() package factoextra.\r\nlibrary(factoextra)\r\nfviz_pca_ind(pr.out, label=\"none\", habillage=cslarge_train$riskrating)\r\n\r\n\r\n# [Contoh](https://academy.dqlab.id/main/livecode/89/179/874)\r\n(A <- as.matrix(data.frame(c(1,0,1),c(0,1,1),c(1,1,0))))\r\ne <- eigen(A)\r\nstr(e)\r\ne\r\n\r\n\r\n# [Tugas Praktik](https://academy.dqlab.id/main/livecode/89/179/875)\r\n# Ketik perintah berikut ini untuk membaca help tentang matriks\r\n?matrix\r\n# Buatlah matriks 3 x 3 dan simpan dengan nama matriks A.\r\nA <- matrix(c(1, 1, 0, 0, -2, 1, 0, 0, 3), nrow = 3, ncol = 3, byrow = TRUE)\r\n# Tuliskan perintah untuk menampilkan matriks A\r\nA\r\n# Tuliskan perintah R untuk menghitung nilai eigen dan vektor eigen\r\n# dan simpanlah hasilnya dalam variable ev\r\nev <- eigen(A)\r\n# Tuliskan perintah untuk melihat struktur obyek eigen\r\nstr(ev)\r\n# Tuliskan perintah untuk melihat hasil output\r\nev\r\n# Tuliskan perintah untuk mengakses nilai eigen\r\nev$values\r\n# Tuliskan perintah untuk mengakses vektor eigen\r\nev$vectors", "meta": {"hexsha": "ebbb14d148122dc9f75ff1554bb5e00a4ba397ec", "size": 12228, "ext": "r", "lang": "R", "max_stars_repo_path": "R/Kelas Penerapan/Data Science in Finance Dimension Reduction/Data Science in Finance Dimension Reduction.r", "max_stars_repo_name": "Miadwicynthia/DQLab", "max_stars_repo_head_hexsha": "711e9650224683844a67963e76b10c1d4a38ebf4", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/Kelas Penerapan/Data Science in Finance Dimension Reduction/Data Science in Finance Dimension Reduction.r", "max_issues_repo_name": "Miadwicynthia/DQLab", "max_issues_repo_head_hexsha": "711e9650224683844a67963e76b10c1d4a38ebf4", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/Kelas Penerapan/Data Science in Finance Dimension Reduction/Data Science in Finance Dimension Reduction.r", "max_forks_repo_name": "Miadwicynthia/DQLab", "max_forks_repo_head_hexsha": "711e9650224683844a67963e76b10c1d4a38ebf4", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 39.7012987013, "max_line_length": 115, "alphanum_fraction": 0.7123814197, "num_tokens": 3562, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9263037302939516, "lm_q2_score": 0.8397339596505965, "lm_q1q2_score": 0.7778486992788582}} {"text": "options(width=60, keep.source=TRUE, prompt=\" \", continue=\" \")\nset.seed(76543); # recompile will have same random numbers\n\n\n###################################################\n### code chunk number 4: ex (eval = FALSE)\n###################################################\n#An example with 100 Confidence Intervals (CIs).\n#Consider drawing a sample of 25 observations from a normally distributed population with mean 10 and sd 2. Calculate the 95% t-CI. Now do that 100 times. The plot belows reflects the variability of that process. We expect 95 of the 100 CIs to contain the true population mean of 10, that is, on average 5 times out of 100 we draw the incorrect inference that the population mean is in an interval when it does not contain the true value of 10.\nlibrary(TeachingDemos)\n## # look at examples at bottom of the help page\n## ?clt.examp\nci.examp(mean.sim = 10, sd = 2, n = 25\n , reps = 100, conf.level = 0.95, method = \"t\")\n\n\n###################################################\n### code chunk number 5: 02_tdist_normal\n###################################################\n#With higher degrees of freedom, the t distribution gets closer to the normal distribution, as illustrated by this example:\nx <- seq(-8, 8, length = 1000)\npar(mfrow=c(1,1))\nplot(x, dnorm(x), type = \"l\", lwd = 2, col = \"red\"\n , main = \"Normal (red) vs t-dist with df=1, 2, 6, 12, 30, 100\")\npoints(x, dt(x, 1), type = \"l\")\npoints(x, dt(x, 2), type = \"l\")\npoints(x, dt(x, 6), type = \"l\")\npoints(x, dt(x, 12), type = \"l\")\npoints(x, dt(x, 30), type = \"l\")\npoints(x, dt(x,100), type = \"l\")\n\n\n###################################################\n### code chunk number 8: ex\n###################################################\n#Example data\n#Page 13 of ADA1_02_OneSample.pdf\n# enter data as a vector\n#Example: Age at First Transplant (Revisited) The ages (in years) at first transplant for a sample of 11 heart transplant patients are as follows: 54, 42, 51, 54, 49, 56, 33, 58, 54, 64, 49.\nage <- c(54, 42, 51, 54, 49, 56, 33, 58, 54, 64, 49)\n\n\n###################################################\n### code chunk number 9: 02_age\n###################################################\n#Let's look at the example data.\npar(mfrow=c(2,1))\n# Histogram overlaid with kernel density curve\nhist(age, freq = FALSE, breaks = 6)\npoints(density(age), type = \"l\")\nrug(age)\n\n# violin plot\nlibrary(vioplot)\nvioplot(age, horizontal=TRUE, col=\"gray\")\n\n\n###################################################\n### code chunk number 10: ex\n###################################################\n#Calculating the critical value from a t distribution:\n# t.crit\n#qt(desired confidence level, degrees of freedom)\n#http://stackoverflow.com/questions/11526041/critical-t-values-in-r\n#The graph on page 11 of ADA1_02_OneSample.pdf may help clarify the following.\n#95% confidence level for two sided test:\nqt(1 - 0.05/2, df = length(age) - 1)\n#95% confidence level for one sided test:\nqt(1 - 0.05, df = length(age) - 1)\n#Note that these are the same:\nabs(qt(0.05, df = length(age) - 1))\nqt(0.95, df = length(age) - 1)\n", "meta": {"hexsha": "8512ae0089341c4176d3c731fdbd636f1523f854", "size": 3086, "ext": "r", "lang": "R", "max_stars_repo_path": "assignments/x.r", "max_stars_repo_name": "LSaldyt/Modeling", "max_stars_repo_head_hexsha": "f47481856bf1ef1227bb92cb86f6f0f639e9cd7c", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "assignments/x.r", "max_issues_repo_name": "LSaldyt/Modeling", "max_issues_repo_head_hexsha": "f47481856bf1ef1227bb92cb86f6f0f639e9cd7c", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "assignments/x.r", "max_forks_repo_name": "LSaldyt/Modeling", "max_forks_repo_head_hexsha": "f47481856bf1ef1227bb92cb86f6f0f639e9cd7c", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 42.2739726027, "max_line_length": 444, "alphanum_fraction": 0.5722618276, "num_tokens": 846, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9433475746920261, "lm_q2_score": 0.8244619263765707, "lm_q1q2_score": 0.7777541586732537}} {"text": "## Simulate data from Zero Inflated Poisson, NB, Beta Binomial, Beta Negative Binomial, Half Normal##\r\nsample.zero.inflated <- function(n, phi, theta, dist=\"Poisson\") {\r\n fsample <- function(m) { rpois(m, lambda=theta[1]); };\r\n if(dist==\"Negative Binomial\") fsample <- function(m) {rnbinom(m, size=theta[1], prob=1-theta[2])};#size=r, p=p(failure), so our p is (1-p)\r\n if(dist==\"Beta Binomial\") fsample <- function(m) {rbbinom(m, theta[1], theta[2], theta[3])} #{extraDistr}\r\n if(dist==\"Beta Negative Binomial\") fsample <- function(m) {rbnbinom(m, theta[1], theta[2], theta[3])} #{extraDistr}\r\n if(dist==\"Half Normal\") fsample <- function(m) {rhnorm(m, theta[1])}\r\n if(dist==\"Log Normal\") fsample <- function(m) {rlnorm(m, theta[1], theta[2])} #theta[2]=sigma, not sig squar\r\n ans=rbinom(n, size=1, prob=1-phi);\r\n m=sum(ans==1);\r\n if(m>0) ans[ans==1]=fsample(m);\r\n ans;\r\n}\r\n# For examle:\r\nx= sample.zero.inflated(n=300, phi=0.03, theta=0.1, dist=\"Poission\")\r\nx= sample.zero.inflated(n=10000, phi=0.2, theta=c(15,0.3), dist=\"Negative Binomial\")\r\nx= sample.zero.inflated(10000, phi=0.50, theta=c(20, 2,5), dist=\"Beta Binomial\")\r\nx= sample.zero.inflated(50000, phi=0.50, theta=c(5, 1,10), dist=\"Beta Negative Binomial\")\r\nx= sample.zero.inflated(500, phi=0.50, theta=4, dist=\"Half Normal\")\r\nx= sample.zero.inflated(400, phi=0.50, theta=c(1,4), dist=\"Log Normal\")\r\n\r\n######### Next: Simulate from Hurdle ditributions####\r\n\r\n##### Simulate from Hurdle Poisson###########\r\nrhpois <- function(n, phi, theta) {\r\n ans=rbinom(n, size=1, prob=1-phi);\r\n m=sum(ans==1);\r\n p0=exp(-theta) \r\n M=ceiling(m+m*p0+3*sqrt(m*p0*(1-p0)))\r\n z=rpois(M, theta)\r\n u=z[z>0]\r\n t=length(u)\r\n if(t < m ) {\r\n u1=rep(0, m-t);\r\n itemp=0;\r\n while(itemp<(m-t)) {\r\n temp=rpois(1,theta);\r\n if(temp>0) {itemp=itemp+1; u1[itemp]=temp; };\r\n };\r\n u=c(u,u1);\r\n };\r\n ans[ans==1]=u[1:m];\r\n ans;\r\n}\r\n\r\n##### Simulate from Hurdle NB###########\r\nrhnb <- function(n, phi, theta=c(theta[1], theta[2])) { # function(m) {rnbinom(m, size=theta[1], prob=1-theta[2])}\r\n ans=rbinom(n, size=1, prob=1-phi);\r\n m=sum(ans==1);\r\n p0=(1-theta[2])^(theta[1]) #(1-p) ^r\r\n M=ceiling(m+m*p0+3*sqrt(m*p0*(1-p0)))\r\n z=rnbinom(M, size=theta[1], prob=1-theta[2])\r\n u=z[z>0]\r\n t=length(u)\r\n if(t < m ) {\r\n u1=rep(0, m-t);\r\n itemp=0;\r\n while(itemp<(m-t)) {\r\n temp=rnbinom(1,size=theta[1], prob=1-theta[2]);\r\n if(temp>0) {itemp=itemp+1; u1[itemp]=temp; };\r\n };\r\n u=c(u,u1);\r\n };\r\n ans[ans==1]=u[1:m];\r\n ans;\r\n} \r\n\r\n##### Simulate from Hurdle Beta Binomial###########\r\nrhbb <- function(n, phi, theta=c(theta[1], theta[2], theta[3])) { # function(m) {rnbinom(m, size=theta[1], prob=1-theta[2])}\r\n ans=rbinom(n, size=1, prob=1-phi);\r\n m=sum(ans==1);\r\n p0=gamma(theta[1]+theta[3])*gamma(theta[2]+theta[3])/(gamma(theta[1]+theta[2]+theta[3])*gamma(theta[3]))\r\n M=ceiling(m+m*p0+3*sqrt(m*p0*(1-p0)))\r\n z=rbbinom(M, theta[1], theta[2], theta[3]) \r\n u=z[z>0]\r\n t=length(u)\r\n if(t < m ) {\r\n u1=rep(0, m-t);\r\n itemp=0;\r\n while(itemp<(m-t)) {\r\n temp=rbbinom(1,theta[1], theta[2], theta[3]);\r\n if(temp>0) {itemp=itemp+1; u1[itemp]=temp; };\r\n };\r\n u=c(u,u1);\r\n };\r\n ans[ans==1]=u[1:m];\r\n ans;\r\n} \r\n\r\n", "meta": {"hexsha": "f0338b264b02a79e0db02bc78100b5b511caf2a0", "size": 3241, "ext": "r", "lang": "R", "max_stars_repo_path": "Simulation from Zero inflated and Hurdle.r", "max_stars_repo_name": "aametwally/Stat", "max_stars_repo_head_hexsha": "56f0fc04954ecbdca4853a8286338487a5ee486b", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Simulation from Zero inflated and Hurdle.r", "max_issues_repo_name": "aametwally/Stat", "max_issues_repo_head_hexsha": "56f0fc04954ecbdca4853a8286338487a5ee486b", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Simulation from Zero inflated and Hurdle.r", "max_forks_repo_name": "aametwally/Stat", "max_forks_repo_head_hexsha": "56f0fc04954ecbdca4853a8286338487a5ee486b", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 36.0111111111, "max_line_length": 141, "alphanum_fraction": 0.5735883986, "num_tokens": 1243, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9381240142763573, "lm_q2_score": 0.828938806208442, "lm_q1q2_score": 0.7776474004697149}} {"text": "## Code Skeleton for Series 8, task 1\n\nrequire(ROCR)\n\nd.baby <- read.table(\"http://stat.ethz.ch/Teaching/Datasets/baby.dat\", header=TRUE)\n\n## task a)\n\nfit <- glm(Survival ~ ., family = binomial(link=\"logit\"), data = d.baby)\n\npred <- prediction(predictions = fit$fitted.values, labels = d.baby$Survival)\nperf <- performance(pred, \"tpr\", \"fpr\" )\ntitle <- \"logist.regr: glm(Survival ~ . , d.baby) [in-sample]\"\nplot(perf, main = paste(\"ROC: \", title))\n\nperf.cost <- performance(pred, \"cost\")\nplot(perf.cost, main = title)\n\n## task b)\n\nn <- nrow(d.baby)\nK <- 10\nall.y.true <- all.y.pred <- vector(\"list\", length = K)\nset.seed(101)\n## define folds\nfolds <- sample(cut(seq(1, n), breaks = K, labels = FALSE), replace = FALSE)\nfor (i in 1:K){\n test.ind <- which(folds == i)\n df.train<- d.baby[-test.ind,]\n df.test <- d.baby[test.ind,]\n fit.glm <- glm(formula = Survival ~ ., data = df.train, family = binomial(link=\"logit\"))\n y.true <- df.test$Survival\n y.pred <- predict(fit.glm, newdata = df.test, type = \"response\")\n all.y.true[[i]] <- y.true\n all.y.pred[[i]] <- y.pred\n}\n\npred.cv <- prediction(predictions = all.y.pred, labels = all.y.true)\n\nperf.cv <- performance(pred.cv, \"tpr\", \"fpr\" )\ntitle <- \"logist.regr: glm(Survival ~ . , d.baby) [cross-validated]\"\nplot(perf.cv, avg = \"threshold\", main = paste(\"ROC: \", title))\n## add the in-sample curve\nplot(perf, col = 2, add = TRUE)\n\nperf.cv.cost <- performance(pred.cv, \"cost\")\nplot(perf.cv.cost, avg = \"vertical\", main = title)\n## add the in-sample curve\nplot(perf.cost, col = 2, add = TRUE)\n\n## task c)\n\nc1 <- seq(0, 2, 0.2)\nfor (j in 1:length(c1)) {\n ## cost for given cost function\n perf.cv.cost.pen <- performance(pred.cv, \"cost\", cost.fp = c1[j], cost.fn = 2. - c1[j])\n plot(perf.cv.cost.pen, avg = \"vertical\", col = j - 6 * (j > 6), lty = 1 + 1 * (j > 6), add = (j > 1),\n ylim = c(0, 1))\n}\nlegend(\"topleft\", legend = paste(\"c1 =\", c1), col = c(rep(1:6, 2)),\n lty = c(rep(1, 6), rep(2, 5)), ncol = 3)\n\n", "meta": {"hexsha": "41ac012bc89a4cc1a930704cd0eeec69f88e2463", "size": 1980, "ext": "r", "lang": "R", "max_stars_repo_path": "Computational_Statistics/Exercices/8_1.r", "max_stars_repo_name": "DanDoge/course_ethz", "max_stars_repo_head_hexsha": "73e5f77e3694d6134169127c0500898402683c32", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Computational_Statistics/Exercices/8_1.r", "max_issues_repo_name": "DanDoge/course_ethz", "max_issues_repo_head_hexsha": "73e5f77e3694d6134169127c0500898402683c32", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Computational_Statistics/Exercices/8_1.r", "max_forks_repo_name": "DanDoge/course_ethz", "max_forks_repo_head_hexsha": "73e5f77e3694d6134169127c0500898402683c32", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 31.4285714286, "max_line_length": 103, "alphanum_fraction": 0.6070707071, "num_tokens": 675, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9086178994073577, "lm_q2_score": 0.8558511506439708, "lm_q1q2_score": 0.7776416747034948}} {"text": "\n# 5.2 Generación de números pseudo-aleatorios y distribuciones de probabilidad en R\nrnorm(n = 10, mean = 10, sd = 2) # Normal con media 10 y desviación típica 2\nrunif(10) # Uniforme en (0,1)\nrpois(n = 10, lambda = 1) # Poisson con media 1\n\nsample(1:5, 5) # permutación\nsample(1:5, 10, replace = TRUE) # muestra con reemplazo\nsample(c(0, 1), 5, replace = TRUE, prob = c(0.4, 0.5)) # Bernoulli\nsample(cars$speed, 3) # tres valores aleatorios de cars$speed\n\nmx <- numeric()\nfor (i in 1:10) {\n set.seed(i)\n x <- rnorm(100, mean = 2)\n mx[i] <- mean(x)\n}\nmean(mx)\n\ndpois(x = 0:10, lambda = 3)\nplot(\n dpois(x = 0:10, lambda = 3),\n type = \"h\",\n xlab = \"x\",\n ylab = \"P(X=x)\",\n main = expression(Poisson(lambda == 3))\n)\n\nplot(ppois(q = 0:10, lambda = 3),\n type = \"s\", xlab = \"x\", ylab = expression(P(X <= x)),\n main = expression(Poisson(lambda == 3))\n)\nqnorm(0.025, lower.tail = FALSE) # valor crítico (Normal) alpha=0.05\n\n# 5.3 Ley de los grandes números\n# Probamos primero algunos lanzamientos (uno, diez):\nsample(c(cara = 1, cruz = 0), 1, replace = TRUE, prob = c(0.5, 0.5))\nx <- sample(c(cara = 1, cruz = 0), 10, replace = TRUE, prob = c(0.5, 0.5))\nx\nmean(x) # frecuencia relativa de cara en 10 lanzamientos\nx <- sample(c(cara = 1, cruz = 0), 50, replace = TRUE, prob = c(0.5, 0.5))\nmean(x) # frecuencia relativa de cara en 50 lanzamientos\n\n# Representamos gráficamente la solución\nset.seed(1) # para poder reproducir los resultados de abajo\nnsim <- 1000\nx <- sample(c(cara = 1, cruz = 0), nsim, replace = TRUE, prob = c(0.5, 0.5))\nn <- 1:nsim\nplot(n, cumsum(x) / n,\n type = \"l\", ylab = \"Proporción de caras\",\n xlab = \"Número de lanzaamientos\", ylim = c(0, 1)\n)\nabline(h = 0.5, lty = 2, col = 2)\n\n# alternativamente podríamos haber hecho:\nx <- rbinom(nsim, size = 1, prob = 0.5)\nhead(x)\n# ó\nx <- runif(nsim) < 0.5\nhead(x)\n\n\n# 5.3.2. Detección de problemas de convergencia\n# Esperanza no finita\nset.seed(1)\nnsim <- 10000\nx <- rcauchy(nsim)\nn <- 1:nsim\nplot(n, cumsum(x) / n,\n type = \"l\", ylab = \"Media muestral\",\n xlab = \"Número de simulaciones\",\n main = \"Secuencia de medias de una Cauchy\"\n)\nabline(h = 0, lty = 2, col = 2)\n\n# probando con varias semillas\nfor (i in 2:4) {\n set.seed(i)\n x <- rcauchy(nsim)\n plot(n, cumsum(x) / n,\n type = \"l\", ylab = \"Media muestral\",\n xlab = \"Número de simulaciones\"\n )\n abline(h = 0, lty = 2, col = 2)\n}\n# cajas para observar cómo se comporta: muchos datos anómalos\nfor (i in 2:4) {\n set.seed(i)\n x <- rcauchy(nsim)\n boxplot(x, ylab = \"Media muestral\")\n}\n\n# 5.3.3 Precisión de la aproximación\n\n# ~~> intervalos de confianza\n# Teorema central del límite: Teorema Central del Límite.\n# Dada una secuencia X1, ..., Xn variables aleatorias iid\n# con esperanza E[Xi] = µ y varianza V(Xi) = s^2 < 8\n# ==> Z_n = (mean(c(X1,...Xn)) - \\mu )/(\\sigma/sqrt(n))\n# para n --> \\infty\n# ~~> intervalo de confianza\n# X_n -+ z_{\\alpha/2}S_n/sqrt(n)\n\nset.seed(1)\nnsim <- 10000\nx <- rnorm(nsim)\n# Aproximación de la media:\nmean(x)\n# error estándar\nsd(x) / sqrt(nsim)\n# error máximo admisible al nivel de confianza 0.95\nqnorm(0.975) * sd(x) / sqrt(nsim)\n\n# representamos con intervalos de confianza\nn <- 1:nsim\n# medias muestrales para n=1,2,...,nsim\nestim <- cumsum(x) / n\n# correspondientes errores de estimación\n# por simplicidad con varianza muestral en lugar de cuasivarianza\nestim.err <- sqrt(cumsum((x - estim)^2)) / n\n# gráfico de convergencia\nplot(n, estim,\n type = \"l\", xlab = \"Número de simulaciones\",\n ylab = \"Aproximación de la media y error\", ylim = c(-1, 1)\n)\n# media teórica:\nabline(h = 0, col = 2)\n# intevalos de confianza (1-alpha=0.95)\nz <- qnorm(0.975)\nlines(estim - z * estim.err, lty = 3, lwd = 2, col = \"blue\")\nlines(estim + z * estim.err, lty = 3, lwd = 2, col = \"blue\")\n\n# Ejercicio. Comprueba y visualiza la convergencia en el caso variables con distribución\n# uniforme, U(-3, 3).\n\n# --------------------------------------------------------------------------------\n# descando\n# --------------------------------------------------------------------------------\n\n# 5.3.4. Determinación del número de simulaciones\n\n# En el caso en que la varianza de las X_i, \\sigma^2 sea conocida, resolver el problema es\n# determinar n tal que z_{\\alpha/2} * \\sigma / \\sqrt(n) < \\epsilon\n# n = (z_{\\alpha/2} \\sigma / \\epsilon )^2\n\n# Ejercicio. Calcular el número de simulaciones necesario para aproximar la media µ\n# de la siguientes distribuciones con un error máximo admisible de 0.1|µ|:\n# 1. Normal con media µ = 10 y desviación típica s = 5.\n# 2. Chi-cuadrado con 10 grados de libertad (µ = 10, s^2 = 2 * µ).\n# 3. Poisson con parámetro = 10 (µ = 10, s^2 = µ)\n\ndetermina.n <- function(epsilon, sigma, alpha) {\n z <- qnorm(alpha / 2, lower.tail = F)\n n <- z * sigma / epsilon\n return(n^2)\n}\n# 1.\ndetermina.n()\n# 2.\n# 3.\n\n# --------------------------------------------------------------------------------\n\n# En el caso \\sigma^2 desconocidam, ste algoritmo\n# 1. Fijar tamaño inicial n0.\n# 2. Generarlos.\n# 3. Si querías más precisión, genera\n\n\n# --------------------------------------------------------------------------------\n# Integración de MC\n# Clásica\n# Observación: la integral de h en [0,1] es la esperanza de h(X) con X ~> U(0,1)\n\n# EG int. en [0,1] de 4x^4\nh <- function(x) (4 * x^4) * (x > 0 & x < 1)\n# visualizamos la función en el dominio de integración\ncurve(h, 0, 1)\n# fijamos el número de simulaciones (n=nsim)\nnsim <- 100\n# calculamos la aproximación\nset.seed(1)\nx <- runif(nsim) # x1,...,xn\nhx <- sapply(x, h) # h(x1),...h(xn)\nmean(hx) # la aproximación final\n# valor exacto\n4 / 5\n# --------------------------------------------------------------------------------\n# gráfica de ello:\nnsim <- 1000\nset.seed(1)\nx <- runif(nsim)\nhx <- sapply(x, h)\n# aproximaciones para $n=1,...,nsim$\nestim <- cumsum(hx) / (1:nsim)\n# errores de estimación correspondientes\nestim.err <- sqrt(cumsum((hx - estim)^2)) / (1:nsim)\nplot(1:nsim, estim,\n type = \"l\", ylab = \"Aproximación y límites de error\",\n xlab = \"Número de simulaciones\"\n)\nz <- qnorm(0.025, lower.tail = FALSE)\nlines(estim - z * estim.err, col = \"blue\", lwd = 2, lty = 3)\nlines(estim + z * estim.err, col = \"blue\", lwd = 2, lty = 3)\nabline(h = 4 / 5, col = 2)\n# Aproximación final y su error\nestim[nsim]\nestim.err[nsim]\n# --------------------------------------------------------------------------------\n# Caso general: integrales con límites infinitos\n# idea: factorizar la función en producto de f densidad por otra\n# I = \\int h(x) = \\int c(x)f(x) = E[c(X)]\n# ~~> I \\aproxeq 1/n \\sum c(X_i)\n# EG \\int_2^\\infty \\frac{e^{-x^2/2}}{\\sqrt{2\\pi}}dx\n# ~~> c(x) = I(x>2)\n\nnsim <- 1000\nset.seed(1)\nx <- rnorm(nsim) # x1,...,xn\ncc <- function(x) (x > 2)\ncx <- cc(x) ## c(x1),...,c(xn)\n# aproximación:\nmean(cx)\n# error\nqnorm(0.025, lower.tail = FALSE) * sd(cx) / sqrt(nsim)\n# valor exacto\npnorm(2, lower.tail = FALSE)\n# --------------------------------------------------------------------------------\n# ej la misma integral pero con límite inferior en 4.5\nnsim <- 1000\nset.seed(1)\nx <- rnorm(nsim) # x1,...,xn\ncc <- function(x) (x > 4.5)\ncx <- cc(x) ## c(x1),...,c(xn)\n# aproximación:\nmean(cx)\n# error\nqnorm(0.025, lower.tail = FALSE) * sd(cx) / sqrt(nsim)\n# valor exacto\npnorm(4.5, lower.tail = FALSE)\n# Falla para valores muy pequeños\n\n#\n# --- 5.4.2 MUESTREO POR IMPORTANCIA ---------------------------------------------------\n#\n\n# Idea: cambiar la función de densidad por otra con una cola más pesada\n# generar Z_1..Z_n desde f densidad g(z) con soporte incluyendo el de f(x)\n# I = \\int c(x) f(x) dx = \\int c(z) w(z) g(z) dz = E[c(Z)w(Z)]\n# w(z) = f(z)/g(z)\n# ~~> I \\aproxeq 1/n \\sum c(Z_i)w(z_i)\n\nnsim <- 1000\nset.seed(1)\nz <- rexp(nsim) + 4.5\nw <- dnorm(z) / dexp(z - 4.5)\nboxplot(w)\n# aproximación:\nmean(w)\n\n# error\nqnorm(0.025, lower.tail = FALSE) * sd(w) / sqrt(nsim)", "meta": {"hexsha": "1bcca8bea28ec65e05290f78125093bb509bf630", "size": 7855, "ext": "r", "lang": "R", "max_stars_repo_path": "clases/Clase 2022-05-17.r", "max_stars_repo_name": "LucasFA/EC", "max_stars_repo_head_hexsha": "a3822b94fc1c97f3096c9fd40cd3140ee85a5ac8", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "clases/Clase 2022-05-17.r", "max_issues_repo_name": "LucasFA/EC", "max_issues_repo_head_hexsha": "a3822b94fc1c97f3096c9fd40cd3140ee85a5ac8", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "clases/Clase 2022-05-17.r", "max_forks_repo_name": "LucasFA/EC", "max_forks_repo_head_hexsha": "a3822b94fc1c97f3096c9fd40cd3140ee85a5ac8", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 29.9809160305, "max_line_length": 90, "alphanum_fraction": 0.5819223425, "num_tokens": 2810, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9086178969328286, "lm_q2_score": 0.855851143290548, "lm_q1q2_score": 0.7776416659042147}} {"text": "# assigning values to variables\na <- 1\nb <- 1\nc <- -1\n\n# test 1 solving the quadratic equation\n(-b + sqrt(b^2 - 4*a*c) / (2*a))\n(-b - sqrt(b^2 - 4*a*c) / (2*a))\n\n# test 2 using the correct formula\n(-b + sqrt(b^2 - 4*a*c)) / (2*a)\n(-b - sqrt(b^2 - 4*a*c)) / (2*a)\n\n# assisgning solutions\nsolution1 <- (-b + sqrt(b^2 - 4*a*c)) / (2*a)\nsolution2 <- (-b - sqrt(b^2 - 4*a*c)) / (2*a)\n", "meta": {"hexsha": "8f6dac715a4c730758bc77e6425ce1639f93f418", "size": 379, "ext": "r", "lang": "R", "max_stars_repo_path": "Quadratic Equation.r", "max_stars_repo_name": "Proff-Matth/R-Basics", "max_stars_repo_head_hexsha": "5055d8b2e4a52f8809f729f48f77f9481e606048", "max_stars_repo_licenses": ["Unlicense"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2020-05-24T00:52:37.000Z", "max_stars_repo_stars_event_max_datetime": "2020-05-24T00:52:37.000Z", "max_issues_repo_path": "Quadratic Equation.r", "max_issues_repo_name": "Proff-Matth/R-Basics", "max_issues_repo_head_hexsha": "5055d8b2e4a52f8809f729f48f77f9481e606048", "max_issues_repo_licenses": ["Unlicense"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Quadratic Equation.r", "max_forks_repo_name": "Proff-Matth/R-Basics", "max_forks_repo_head_hexsha": "5055d8b2e4a52f8809f729f48f77f9481e606048", "max_forks_repo_licenses": ["Unlicense"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2021-03-24T15:19:14.000Z", "max_forks_repo_forks_event_max_datetime": "2021-11-17T22:27:40.000Z", "avg_line_length": 22.2941176471, "max_line_length": 45, "alphanum_fraction": 0.5277044855, "num_tokens": 160, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9511422269175634, "lm_q2_score": 0.8175744828610095, "lm_q1q2_score": 0.7776296142993959}} {"text": "## Author: Sergio García Prado\n\nrm(list = ls())\n\n\n## a)\n####\n\n##\n## Asymptotic distibution of lambda.hat as parameter lambda of Pois(lambda)\n## lambda.hat ~ N(lambda, lambda / n)\n##\n\n\n## b)\n####\nn <- 50\ny <- 75 # sum(x_i)\nalpha <- 0.05\n\nLogLikelihood <- function(lambda, y, n) {\n y * log(lambda) - n * lambda\n}\n\nNegativeLogLikelihood <- function(...) {\n - LogLikelihood(...)\n}\n\nopt <- optim(runif(1), NegativeLogLikelihood, y = y, n = n, hessian = TRUE,\n lower = 10e-3, upper = 10e3, method=\"Brent\")\n\n(lambda.hat <- opt$par)\n# 1.49999997506721\n\n(lambda.hat.var <- 1 / opt$hessian[1])\n# 0.0299999723347587\n\n## Wald's Confidence Interval at (1 - alpha)% level.\nlambda.hat + c(-1, 1) * qnorm(1 - alpha / 2) * sqrt(lambda.hat.var)\n# 1.16052441137235 1.83947553876206\n\n\n## c)\n####\nlambda.zero <- 1\n\n(W <- (lambda.hat - lambda.zero) ^ 2 / lambda.hat.var)\n# 8.33334018703586\n\n(W.pvalue <- 1 - pchisq(W, df = 1))\n# 0.00389240243808919\n\n\n## d)\n####\n\n(LRT <- 2 * (LogLikelihood(lambda.hat, y, n) - LogLikelihood(lambda.zero, y, n)))\n# 10.8197662162247\n\n(LRT.pvalue <- 1 - pchisq(LRT, df = 1))\n# 0.0010042216868813\n", "meta": {"hexsha": "8b36a6ad56bb1fe323a94b9418f7072e3f73c7bf", "size": 1119, "ext": "r", "lang": "R", "max_stars_repo_path": "statistical-inference/likelihood/exercise-02.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "statistical-inference/likelihood/exercise-02.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "statistical-inference/likelihood/exercise-02.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 18.0483870968, "max_line_length": 81, "alphanum_fraction": 0.6121537087, "num_tokens": 411, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9511422186079557, "lm_q2_score": 0.8175744806385543, "lm_q1q2_score": 0.7776296053918016}} {"text": "stirling <- function(z) sqrt(2*pi/z) * (exp(-1)*z)^z\n\nnemes <- function(z) sqrt(2*pi/z) * (exp(-1)*(z + (12*z - (10*z)^-1)^-1))^z\n\nlanczos <- function(z)\n{\n if(length(z) > 1)\n {\n sapply(z, lanczos)\n } else\n {\n g <- 7\n p <- c(0.99999999999980993, 676.5203681218851, -1259.1392167224028,\n 771.32342877765313, -176.61502916214059, 12.507343278686905,\n -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7)\n z <- as.complex(z)\n if(Re(z) < 0.5)\n {\n pi / (sin(pi*z) * lanczos(1-z))\n } else\n {\n z <- z - 1\n x <- p[1] + sum(p[-1]/seq.int(z+1, z+g+1))\n tt <- z + g + 0.5\n sqrt(2*pi) * tt^(z+0.5) * exp(-tt) * x\n }\n }\n}\n\nspouge <- function(z, a=49)\n{\n if(length(z) > 1)\n {\n sapply(z, spouge)\n } else\n {\n z <- z-1\n k <- seq.int(1, a-1)\n ck <- rep(c(1, -1), len=a-1) / factorial(k-1) * (a-k)^(k-0.5) * exp(a-k)\n (z + a)^(z+0.5) * exp(-z - a) * (sqrt(2*pi) + sum(ck/(z+k)))\n }\n}\n\n# Checks\nz <- (1:10)/3\nall.equal(gamma(z), stirling(z)) # Mean relative difference: 0.07181942\nall.equal(gamma(z), nemes(z)) # Mean relative difference: 0.003460549\nall.equal(as.complex(gamma(z)), lanczos(z)) # TRUE\nall.equal(gamma(z), spouge(z)) # TRUE\ndata.frame(z=z, stirling=stirling(z), nemes=nemes(z), lanczos=lanczos(z), spouge=spouge(z), builtin=gamma(z))\n", "meta": {"hexsha": "b7002b6c904c5e353f6be0ffe7d84815f91093bf", "size": 1430, "ext": "r", "lang": "R", "max_stars_repo_path": "Task/Gamma-function/R/gamma-function.r", "max_stars_repo_name": "LaudateCorpus1/RosettaCodeData", "max_stars_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Gamma-function/R/gamma-function.r", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Gamma-function/R/gamma-function.r", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 28.0392156863, "max_line_length": 109, "alphanum_fraction": 0.5111888112, "num_tokens": 574, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9005297754396141, "lm_q2_score": 0.8633916117313211, "lm_q1q2_score": 0.777509854228853}} {"text": "source('D:\\\\_VSB\\\\S8\\\\PS\\\\Beres\\\\GitPS\\\\CV2\\\\kombinatorika.R')\r\n#Kolik hesel o délce 15 znaků lze vygenerovat z velkých a malých písmen anglické abecedy, \r\n#má-li heslo obsahovat alespoň jedno velké písmeno a alespoň jedno malé písmeno? \r\n\r\n#Počet hesel o délce 15 znaků z 52 znaků, alespoň 2*26 znaků\r\n#Vypočítáme kolika různými způsoby se dá sestavit heslo o 15 místech z 52 znaků\r\n#od této hodnoty odečteme způsoby sestavení, které by podmínku alespoň dvou porušily\r\n\r\nvariace_opak(52,15)-2*variace_opak(26,15)\r\n\r\n\r\n#Ve třídě je 12 nadějných studentů, z nichž je možno sestavit tříčlenné soutěžní družstvo. \r\n#Mezi těmito studenty jsou dvě dívky (Anička a Bára), které nejsou schopny spolupracovat, \r\n#a tudíž je nejde do družstva zařadit obě najednou. Kolika způsoby lze provést výběr členů soutěžního družstva?\r\n\r\n#Vypočítáme kolika způsoby lze sestavit družstvo a odečteme kolika způsoby lze sestavit tým, ve kterém by byly dívky spolu\r\nn = 12\r\nk = 3\r\nx = 2\r\nkombinace(n,k)-kombinace(n-x,k-x)\r\nkombinace(12,3)-kombinace(12-2,3-2)\r\n\r\n#Z dopravních statistik vyplývá, že u 10 % řidičů, kteří způsobili dopravní nehodu, bylo prokázáno požití alkoholu. \r\n#V literatuře se uvádí, že riziko nehody se požitím alkoholu zvyšuje 7x. Na základě uvedených údajů odhadněte, kolik procent řidičů požilo před jízdou alkohol. \r\n\r\n#A = Alkohol\r\n#N = Nehoda\r\n#6/7*x=0.1\r\n#x=1/10/6/7\r\n#x=7/60\r\n\r\n\r\n\r\n#Bayesova věta\r\nP_O = c(0.1, 0.9) # P(O.), P(O-)\r\nP_PO = c(1/7, 6/7) # P(P.|O.), P(P.|O-)\r\nbayes(P_B = P_O, P_AB = P_PO, k = 1) \r\n\r\n\r\n#Hladina vody v tankeru je kontrolována pomocí čtyř na sobě nezávislých spínačů stejného typu zapojených dle obrázku. Spínače mají být sepnuty při nízké hladině vody. \r\n#Je-li hladina vody dostatečná, spínače by měly být vypnuty. Každý ze spínačů je s pravděpodobností 10 % v opačném stavu, než by měl být. Ve chvíli, \r\n#kdy se propojí uzly A a B (tj. např. sepnou spínače 1 a 4), je vyhlášen poplach. \r\n\r\n#S jakou pravděpodobností kontrolní systém (viz obrázek) vyhlásí poplach v případě, že v tankeru je nízká hladina vody? \r\n#Rozdělíme obvod na paralelní bloky P1 a P2, kde P1 obsahuje spínače 1 a 2, P2 obsahuje 3 a 4. \r\n#V paralelních blocích se šance na chybu změnšuje, ale mezi paralelními bloky, které jsou zapojeny sériově, se šance na chybu zvětšuje\r\n\r\nP1 = 0.1*0.1\r\nP2 = 0.1*0.1\r\n(1 - P1)*(1 - P2)*100\r\n\r\n#S jakou pravděpodobností kontrolní systém (viz obrázek) vyhlásí falešný poplach, tj. poplach v případě, že v tankeru je dostatečná hladina vody?\r\n#V tomto případě použijeme stejný výpočet, ale otočíme pravděpodobnost spínačů na správný stav\r\nP1 = 0.9*0.9\r\nP2 = 0.9*0.9\r\n(1 - P1)*(1 - P2)*100\r\n\r\n\r\n\r\n\r\nvariace(n=3,k=2)\r\nkombinace(n=5,k=3)-kombinace(n=3,k=2)\r\nkombinace(n=3,k=3)\r\nkombinace(n=2,k=2)\r\nkombinace(n=3,k=2)*2\r\nkombinace(n=12,k=3)\r\nkombinace(n=11,k=3)\r\nkombinace(n=11,k=3)*2\r\n\r\n\r\nkombinace(n=3,k=3)\r\n1\r\nkombinace(n=1,k=1)\r\nkombinace(n=4,k=3)\r\n2\r\nkombinace(n=2,k=1)\r\nkombinace(n=5,k=3)\r\n3\r\nkombinace(n=3,k=1)\r\nkombinace(n=6,k=3)\r\n4\r\nkombinace(n=4,k=1)\r\nkombinace(n=7,k=3)\r\n5\r\nkombinace(n=5,k=1)\r\n\r\nkombinace(n=4,k=2)\r\nkombinace(n=4,k=2)\r\nkombinace(n=4,k=1)\r\nkombinace(n=4,k=3)\r\n\r\n\r\n123\r\n124\r\n134\r\n234\r\n\r\n123\r\n124\r\n125\r\n126\r\n134\r\n135\r\n136\r\n145\r\n146\r\n156\r\n234\r\n235\r\n236\r\n245\r\n246\r\n256\r\n345\r\n346\r\n356\r\n456\r\n\r\n\r\nk = 18\r\nv1 = variace_opak(n = 26, k = k)\r\nv2 = variace_opak(n = 52, k = k)\r\nv3 = variace_opak(n = 62, k = k)\r\nv1\r\nv2\r\nv3/60/60/24/365/1000\r\nv2/v1", "meta": {"hexsha": "1a40af08d9081d836a9bdbdb8ad69c38c7bdcddc", "size": 3409, "ext": "r", "lang": "R", "max_stars_repo_path": "1P/1P.r", "max_stars_repo_name": "Atheloses/VSB-S8-PS", "max_stars_repo_head_hexsha": "fdef214f8169094b6366ce0489f92ef20b460702", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "1P/1P.r", "max_issues_repo_name": "Atheloses/VSB-S8-PS", "max_issues_repo_head_hexsha": "fdef214f8169094b6366ce0489f92ef20b460702", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "1P/1P.r", "max_forks_repo_name": "Atheloses/VSB-S8-PS", "max_forks_repo_head_hexsha": "fdef214f8169094b6366ce0489f92ef20b460702", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.842519685, "max_line_length": 168, "alphanum_fraction": 0.7037254327, "num_tokens": 1712, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.95598134762883, "lm_q2_score": 0.8128673178375734, "lm_q1q2_score": 0.7770859939497959}} {"text": "## Author: Sergio García Prado\n## Title: Statistical Inference - Goodness of Fit - Exercise 02\n\nrm(list = ls())\n\n\n## Test over sample 1.\n\ny1 <- c(9, 3, 8, 14, 2, 13, 12, 19, 9, 4)\n\n(k <- length(y))\n# 10\n\n(n1 <- sum(y1))\n# 93\n\n(e1 <- rep(1 / k * n1, k))\n# 9.3 9.3 9.3 9.3 9.3 9.3 9.3 9.3 9.3 9.3\n\n(Q1 <- sum((y1 - e1) ^ 2 / e1))\n# 27.9677419354839\n\n(pvalue1 <- 1 - pchisq(Q1, k - 1))\n# 0.000965777402160084\n\n\n## Test over sample 2.\n\ny2 <- c(3, 4, 2, 14, 5, 6, 3, 17, 14, 12)\n\n(n2 <- sum(y2))\n# 80\n\n(e2 <- rep(1 / k * n2, k))\n# 8 8 8 8 8 8 8 8 8 8\n\n(Q2 <- sum((y2 - e2) ^ 2 / e2))\n# 35.5\n\n(pvalue2 <- 1 - pchisq(Q2, k - 1))\n# 4.8618021638136e-05\n\n\n## Test between samples 1 and 2.\n\n(y <- (y1 + y2))\n# 12 7 10 28 7 19 15 36 23 16\n\na <- y * n1 / (n1 + n2)\n(Qa <- sum((y1 - a) ^ 2 / a))\n# 9.40743669989997\n\n(pvaluea <- 1 - pchisq(Qa, k - 1))\n# 0.400545165490795\n\nb <- y * n2 / (n1 + n2)\n(Qb <- sum((y2 - b) ^ 2 / b))\n# 10.9361451636337\n\n(pvalueb <- 1 - pchisq(Qb, k - 1))\n# 0.280111283415469\n", "meta": {"hexsha": "15d2524fd5d2965fb28a933bcb183316f5b87e9d", "size": 987, "ext": "r", "lang": "R", "max_stars_repo_path": "statistical-inference/goodness-of-fit/exercise-02.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "statistical-inference/goodness-of-fit/exercise-02.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "statistical-inference/goodness-of-fit/exercise-02.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 15.9193548387, "max_line_length": 63, "alphanum_fraction": 0.5217831814, "num_tokens": 527, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9425067228145364, "lm_q2_score": 0.8244619220634457, "lm_q1q2_score": 0.7770609042493919}} {"text": "# Introducción a modelos lineales: Qué es OLS?\n\ncat(\"\\014\")\nrm(list=ls())\ngraphics.off()\noptions(scipen=9999999)\n\n#######################################################\n# Cual es la relacion entre educacion y prestigio? \n#######################################################\n\n# Creemos una base de datos imaginaria\nbase = data.frame(\n nombre = c(\"Pedro\", \"Juan\", \"Diego\"),\n educacion = c(57,50,61), # vector de educacion\n prestigio = c(64,53,67)\n )\n\nbase # veamos como se ve nuestra base de datos.\n\n# ahora veamos la relacion que existe entre ambas variables. \nplot(base$educacion,base$prestigio) # Que tipo de relacion es esta? Positiva? Negativa?\n\n# Ahora creemos un modelo, es decir, estimemos beta_1\nmodelo = lm(prestigio ~ educacion, data = base)\n\nsummary(modelo) # veamos que nos dice nuestro \"modelo\"\n# interpretacion: Siempre partimos con nuestra X. Por cada unidad que subimos nuestra x (educacion), subimos la cantidad establecida en beta_1 (educacion) en nuestra y (prestigio). Supongamos que educacion esta medido en meses y prestigio en puntos. Esta sera nuestra unidad de medida. Es decir, si subo un mes de educacion, subo en prestigio 1.306 puntos. (Y ahi esta nuestra relacion positiva).\n\n\n# a) Por que se llama \"modelo\"? Pista: esta es la parte mas \"artistica\" de la estadistica. \n# b) Analogia del mapa.\n\n# cuan bien funciona nuestro modelo? Ocupemos el comando \"predict\" (\"predecir\" en espanol).\npredict(modelo)\n# Aqui vemos lo siguiente\n\n# Lo que observamos:\n# Pedro tenia 64, pero nuestro modelo predice 62.63\n# Juan tenia 53, pero nuestro modelo predice 53.49\n# Diego tenia 67, pero nuestro modelo predice 67.85\n\n# Discutir: Es esto \"suficientemente bueno\"?\n\n# El concepto de \"error\". La diferencia entre lo que observamos y lo que modelamos. Derivar algeibraicamente abajo.\n\n#######################################################\n# Modelo OLS en matriz.\n#######################################################\n\n# vector para el error. Algebra simple...pero con comandos.\n# Volvamos a la ecuacion de OLS: \n# y = b0 + b1*x1 + e\n# Reordenando los terminos, tenemos que e=\n# e = y-beta0-beta1*x\n# Hagamoslo con R...y metamos esos numeros en una nueva variable \"error\" dentro de nuestro objeto \"base\"\n\nbase$error <- c(\n base$prestigio[1] - as.numeric(modelo$coefficients[1]) - (base$educacion[1] * as.numeric(modelo$coefficients[2])),\n base$prestigio[2] - as.numeric(modelo$coefficients[1]) - (base$educacion[2] * as.numeric(modelo$coefficients[2])),\n base$prestigio[3] - as.numeric(modelo$coefficients[1]) - (base$educacion[3] * as.numeric(modelo$coefficients[2]))\n )\n\nbase\n\n# Comprobemos que esta correcto\nbase$error\nmodelo$residuals\n\n# vector para el intercepto. Ojo: es un intercepto para todos. Por eso no esta indexado.\nbase$intercepto <- c(\n as.numeric(\n modelo$coefficients[1]\n )\n )\n\n# vector para el beta. Ojo: es un beta para todos. Por eso no esta indexado.\nbase$beta1 <- c(\n as.numeric(\n modelo$coefficients[2]\n )\n)\n\nbase # llamemos al a base.\n\n# Llevar esta base a matrices en OLS.\n\n#######################################################\n# Prediccion\n#######################################################\n\nx=base$educacion # crea objeto\n\ny=base$prestigio # crea objeto\n\nlm.out <- lm(y ~ x) # estima modelo de nuevo. el mismo modelo.\n\nnewx = seq(min(x),max(x),by = 1) # crea sequencia de numeros para el rango X del grafico\n\nconf_interval <- predict(lm.out, newdata=data.frame(x=newx), interval=\"confidence\", level = 0.95) \n\n# usando el modelo estimado, predice (a) distintos valores de educacion NO OBSERVADOS (fit), y el 95% de intervalo de confianza, con \"lower bound\" o \"lwr\" (parte de ABAJO del intervalo), y \"upper bound\" o \"upr\" (parte de ARRIBA del intervalo).\n\nplot(x, y, xlab=\"Educ\", ylab=\"Prest\", main=\"Regression\", ylim = c(30,90)) # ploteamos\nabline(lm.out, col=\"lightblue\") # agregamos linea \"fit\"\nlines(newx, conf_interval[,2], col=\"blue\", lty=2) # lower bound\nlines(newx, conf_interval[,3], col=\"blue\", lty=2) # upper bound\n\n\n\n#######################################################\n# Por que \"least squares\" (\"cuadrados menores\"?)\n#######################################################\n\n# los betas estimados, minimizan la suma de los \"errores cuadrados\".\n", "meta": {"hexsha": "0359e5b94254db7ae9dac750f4c9f993d4185010", "size": 4344, "ext": "r", "lang": "R", "max_stars_repo_path": "Lectures/Clase8/Clase8.r", "max_stars_repo_name": "hbahamonde/OLS", "max_stars_repo_head_hexsha": "439cc5aac95a7fe1e57224732982a36d74a20f67", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Lectures/Clase8/Clase8.r", "max_issues_repo_name": "hbahamonde/OLS", "max_issues_repo_head_hexsha": "439cc5aac95a7fe1e57224732982a36d74a20f67", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Lectures/Clase8/Clase8.r", "max_forks_repo_name": "hbahamonde/OLS", "max_forks_repo_head_hexsha": "439cc5aac95a7fe1e57224732982a36d74a20f67", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 37.4482758621, "max_line_length": 396, "alphanum_fraction": 0.6300644567, "num_tokens": 1202, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9230391706552536, "lm_q2_score": 0.8418256432832333, "lm_q1q2_score": 0.7770380436124811}} {"text": "###################################################################\n# MDS and PCoA\n#\n# Reference: https://goo.gl/wUXSae\n# https://goo.gl/ckSGFW\n###################################################################\n\n#==============================================================================\n# LIBRARY DEPENDENCE\n#==============================================================================\nlibrary(ggplot2)\n\n# Load the data and add some whitenoise as control\ndata.matrix <- matrix(nrow=100, ncol=10)\ncolnames(data.matrix) <- c(\n paste(\"wt\", 1:5, sep=\"\"),\n paste(\"ko\", 1:5, sep=\"\"))\nrownames(data.matrix) <- paste(\"gene\", 1:100, sep=\"\")\nfor (i in 1:100) {\n wt.values <- rpois(5, lambda=sample(x=10:1000, size=1))\n ko.values <- rpois(5, lambda=sample(x=10:1000, size=1))\n \n data.matrix[i,] <- c(wt.values, ko.values)\n}\nhead(data.matrix)\ndim(data.matrix)\n \n#==============================================================================\n# Computing PCA as reference\n#==============================================================================\npca <- prcomp(t(data.matrix), scale=TRUE, center=TRUE) \n \n## calculate the percentage of variation that each PC accounts for...\npca.var <- pca$sdev^2\npca.var.per <- round(pca.var/sum(pca.var)*100, 1)\npca.var.per\n \n## now make a fancy looking plot that shows the PCs and the variation:\npca.data <- data.frame(Sample=rownames(pca$x),\n X=pca$x[,1],\n Y=pca$x[,2])\npca.data\n \nggplot(data=pca.data, aes(x=X, y=Y, label=Sample)) +\n geom_text() +\n xlab(paste(\"PC1 - \", pca.var.per[1], \"%\", sep=\"\")) +\n ylab(paste(\"PC2 - \", pca.var.per[2], \"%\", sep=\"\")) +\n theme_bw() +\n ggtitle(\"PCA Graph\")\n \n#==============================================================================\n# PCoA\n# \tPCA = PCoA if distance metric is Euclidean.\n# \tDifferent distance metrics produces diferent results\n#==============================================================================\ndistance.matrix <- dist(scale(t(data.matrix), center=TRUE, scale=TRUE), \n\t\t\t\t\tmethod=\"euclidean\")\n \n## do the MDS math (this is basically eigen value decomposition)\nmds.stuff <- cmdscale(distance.matrix, eig=TRUE, x.ret=TRUE)\n \n## calculate the percentage of variation that each MDS axis accounts for...\nmds.var.per <- round(mds.stuff$eig/sum(mds.stuff$eig)*100, 1)\nmds.var.per\n \n## now make a fancy looking plot that shows the MDS axes and the variation:\nmds.values <- mds.stuff$points\nmds.data <- data.frame(Sample=rownames(mds.values),\n\t\t\t\t\t\tX=mds.values[,1],\n\t\t\t\t\t\tY=mds.values[,2])\nmds.data\n \nggplot(data=mds.data, aes(x=X, y=Y, label=Sample)) +\n\tgeom_text() +\n\ttheme_bw() +\n\txlab(paste(\"MDS1 - \", mds.var.per[1], \"%\", sep=\"\")) +\n\tylab(paste(\"MDS2 - \", mds.var.per[2], \"%\", sep=\"\")) +\n\tggtitle(\"MDS plot using Euclidean distance\")\n \n#==============================================================================\n# Log scale\n#==============================================================================\nlog2.data.matrix <- log2(data.matrix)\n \n# empty distance matrix\nlog2.distance.matrix <- matrix(0,\n nrow=ncol(log2.data.matrix),\n ncol=ncol(log2.data.matrix),\n dimnames=list(colnames(log2.data.matrix),\n colnames(log2.data.matrix)))\n \nlog2.distance.matrix\n \n# now compute the distance matrix using avg(absolute value(log2(FC)))\nfor(i in 1:ncol(log2.distance.matrix)) {\n for(j in 1:i) {\n log2.distance.matrix[i, j] <-\n mean(abs(log2.data.matrix[,i] - log2.data.matrix[,j]))\n }\n}\nlog2.distance.matrix\n \n## do the MDS math (this is basically eigen value decomposition)\n## cmdscale() is the function for \"Classical Multi-Dimensional Scalign\"\nmds.stuff <- cmdscale(as.dist(log2.distance.matrix),\n eig=TRUE,\n x.ret=TRUE)\n \n## calculate the percentage of variation that each MDS axis accounts for...\nmds.var.per <- round(mds.stuff$eig/sum(mds.stuff$eig)*100, 1)\nmds.var.per\n \n## now make a fancy looking plot that shows the MDS axes and the variation:\nmds.values <- mds.stuff$points\nmds.data <- data.frame(Sample=rownames(mds.values),\n X=mds.values[,1],\n Y=mds.values[,2])\nmds.data\n \nggplot(data=mds.data, aes(x=X, y=Y, label=Sample)) +\n geom_text() +\n theme_bw() +\n xlab(paste(\"MDS1 - \", mds.var.per[1], \"%\", sep=\"\")) +\n ylab(paste(\"MDS2 - \", mds.var.per[2], \"%\", sep=\"\")) +\n ggtitle(\"MDS plot using avg(logFC) as the distance\")\n", "meta": {"hexsha": "674119520037c81cc7a1232b66b9c14075a921f6", "size": 4270, "ext": "r", "lang": "R", "max_stars_repo_path": "PCoA/PCoA.r", "max_stars_repo_name": "isix/R", "max_stars_repo_head_hexsha": "806e2a22e5abd93dc7933d3b9e8c3368562e1eaa", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "PCoA/PCoA.r", "max_issues_repo_name": "isix/R", "max_issues_repo_head_hexsha": "806e2a22e5abd93dc7933d3b9e8c3368562e1eaa", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "PCoA/PCoA.r", "max_forks_repo_name": "isix/R", "max_forks_repo_head_hexsha": "806e2a22e5abd93dc7933d3b9e8c3368562e1eaa", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 33.8888888889, "max_line_length": 79, "alphanum_fraction": 0.5484777518, "num_tokens": 1135, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9230391664210672, "lm_q2_score": 0.8418256432832333, "lm_q1q2_score": 0.7770380400480343}} {"text": "var.test <- function() { # var.test.r\r\n x <- c(21.6,20.8,17.6,20.1,20.1,21.9,20.6,19.4,21.5,26.1)\r\n y <- c(20.6,20.4,20.2,20.2,18.0,19.8,20.9,19.7,20.3,19.7,22.7)\r\n mm <- length(x); nn <- length(y)\r\n\r\n F0 <- sd(x)^2/sd(y)^2\r\n F0\r\n if (F0 >= 1) p.val <- 2*(1- pf(F0, mm-1, nn-1)) \r\n else p.val <- 2*pf(F0, mm-1, nn-1)\r\n p.val\r\n\r\n lbd <- 1/qf(0.975, mm-1, nn-1)*var(x)/var(y)\r\n ubd <- 1/qf(0.025, mm-1, nn-1)*var(x)/var(y)\r\n ci <- c(lbd, ubd)\r\n list(F0=F0, p.val=p.val, ci=ci)\r\n}\r\n", "meta": {"hexsha": "f35a8e1e24f4eaf023fd921a69b296118879f2e3", "size": 483, "ext": "r", "lang": "R", "max_stars_repo_path": "R.2019.2/advanced.R/Rcode/Chap3/var.test.r", "max_stars_repo_name": "tolkien/misc", "max_stars_repo_head_hexsha": "84651346a3a0053b6a2af31db26c227a34da33c8", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R.2019.2/advanced.R/Rcode/Chap3/var.test.r", "max_issues_repo_name": "tolkien/misc", "max_issues_repo_head_hexsha": "84651346a3a0053b6a2af31db26c227a34da33c8", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R.2019.2/advanced.R/Rcode/Chap3/var.test.r", "max_forks_repo_name": "tolkien/misc", "max_forks_repo_head_hexsha": "84651346a3a0053b6a2af31db26c227a34da33c8", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 28.4117647059, "max_line_length": 64, "alphanum_fraction": 0.4989648033, "num_tokens": 261, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9473810436809827, "lm_q2_score": 0.8198933337131076, "lm_q1q2_score": 0.7767514022002041}} {"text": "#03. 지수분포\n# 확률밀도함수: d~\n# 누적분포함수(점수): p~ 건수로 확률 추출\n# 누적분포함수(확률): q~ 확률로 건수(시간) 추출\n\n# 지수분포 누적확률계산\n# 이하 : P(X <= a) lower.tail = TRUE\n# 초과: P(X > a) lower.tail = FALSE\n# pexp(q=대기시간, rate=평균발생건수(λ))\n# 서비스센터 사례 - 평균발생건수: 5분에 1.5회\n# 1분 P(X<=1/5) 이내로 받을 확률\n\npexp(q=1/5, rate=1.5, lower.tail = TRUE)\n\n# 95%확률로 받을 수 있는 시간\nqexp(p=0.95, rate=1.5, lower.tail = TRUE) # 누적하면 95% 이하이므로 (10분에 1콜이 무조건 온다.)\n\n\n# 지수분포 누적확률 gra ph\nx <- seq(0, 3, length = 500) # 0부터 3까지 500로 쪼개서 넣어라. 여기서는 단위가 5분이니까 숫자 1 = 5분이 된다. \nplot(x, \n dexp(x, 1.5), # x 각각의 값을 y축에 뿌려주어라. \n type = \"l\", \n ylim = c(0,1.5))\n\n# 그래프의 의미 : 대기시간이 x에 도달 했을 때까지 전화를 못받을 확률을 알아보는 것. \n\nabline(h=0.2, # 그래프에 선을 그려주는 함수. h= 가로선이 그려짐\n col=\"red\", \n lty=1) # line 유형 \n \n# 10분에 평균 2회 전화, 3분 이내에 전화를 받을 확률 P(X<=3/10) 이하의 개념 이므로 lower.tail = TRUE\npexp(q=3/10, rate=2, lower.tail = TRUE)\n\n# 95%확률로 받을 수 있는 시간 : 15분 이내에 무조건 전화 한번은 받는다. (95% 확률로)\nqexp(p=0.95, rate=2, lower.tail = TRUE)\n\n\n# 부록 ggplot2 이용\nlibrary(ggplot2)\nggplot(data.frame(x=c(0,3)), aes(x=x)) + \n stat_function(fun=dexp, \n args=list(rate=1.5), \n colour=\"red\", size=1.5) + \n ggtitle(\"Exponential Distribution\") \n\n", "meta": {"hexsha": "c5de5f525614c42d0174e175b512ddefb2db465f", "size": 1171, "ext": "r", "lang": "R", "max_stars_repo_path": "ch06 - 확률분포/03.지수분포.r", "max_stars_repo_name": "Lee-changyul/Rstudy_Lee", "max_stars_repo_head_hexsha": "837a88d6cb4c0e223b42ca18dc5a469051b48533", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "ch06 - 확률분포/03.지수분포.r", "max_issues_repo_name": "Lee-changyul/Rstudy_Lee", "max_issues_repo_head_hexsha": "837a88d6cb4c0e223b42ca18dc5a469051b48533", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "ch06 - 확률분포/03.지수분포.r", "max_forks_repo_name": "Lee-changyul/Rstudy_Lee", "max_forks_repo_head_hexsha": "837a88d6cb4c0e223b42ca18dc5a469051b48533", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 24.914893617, "max_line_length": 83, "alphanum_fraction": 0.5789923143, "num_tokens": 750, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9441768588653855, "lm_q2_score": 0.8221891239865619, "lm_q1q2_score": 0.7762919444789149}} {"text": "############################\n# Visualization of Newton's and Halley's Method\n# demo of the Convergance Interval for both\n# https://www.youtube.com/OscarVeliz\n# @author Oscar Veliz\n############################\nhyperx <- a <- b <- c <- 0\ncenter <- 0\nrange <- 4\ncap <- 2000 #maximum value for hyperbola\nstepsize <- .001 #when generating points\neps <- 10^-7 #epsilon\nhyperbola <- function(x) (x - hyperx + c) / (a*(x - hyperx)+b)\nmax <- 5\ncolors <- rainbow(max)\ncolors[2] <- c('darkgoldenrod1')#otherwise you can't see it\ncolors[3] <- c('chartreuse3')#same here\t\n############################\n# Change the following functions\n############################\nname <- \"arctan(x)\"\nf <- function(x) atan(x)\nfp <- function(x) 1.0 / (x^2 + 1)\nfp2 <- function(x) (-2*x) / ((x^2+1)^2)\nnewtstep <- function(x) f(x) / fp(x)\nhalleystep <- function(x){\n\tfx = f(x)\n\tfpx = fp(x)\n\t(2*fx*fpx) / (2*fpx^2 - fx*fp2(x))\n}\n#####################\n# Plots Newton's or Halley's Method\n# @param xn starting x\n# @param gam gamma (damping value)\n# @param useNewt TRUE Newton, FALSE Halley\n##################################\nplotNewton <- function(xn = 1, gam = 1, useNewt = TRUE){\n\tif(useNewt)\n\t\tmethod = \"Newton\"\n\telse\n\t\tmethod = \"Halley\"\n\tprint(paste(method,\"Method\"))\n\tsvg(paste(method,\"Plot.svg\",sep = \"\"), bg = 'transparent')\n\tplot(f, center - range, center + range, xlab = paste(\"start =\", xn,\"gamma =\",gam, sep = \" \"), ylab = \" \", cex.lab = 1.4, cex.axis = 1.4, bg = 'transparent')\n\ttitle(main = \"\", sub = \"x\", cex.sub = 1.4, cex.main = 1.5 , xlab = \" \", ylab = name, cex.axis = 1.4, cex.lab = 1.4, line = 2)\n\ttitle(main = paste(method,\"'s Method\", sep = \"\"), cex.main = 1.5 , xlab = \"\", ylab = \"\", line = .7)\n\tabline(a = 0, b = 0)#x axis\n\tif(useNewt){#Newton Plot\n\t\tfor(n in 1:max){\n\t\t\tprint(paste(\"x\",n,\" = \",xn,sep=\"\"))\n\t\t\tsegments(xn, 0 , xn, f(xn), lty = \"dashed\", col = colors[n])#connect to axis\n\t\t\tpoints(xn, f(xn), col = colors[n])#draw point (xn, f(xn))\n\t\t\ttext(xn, y = 0.05, labels = bquote(x[.(n)]), col = colors[n])#label x's\n\t\t\tabline(a = (fp(xn) * (-xn) + f(xn)), b = fp(xn), col = colors[n])#y=a+bx\n\t\t\txn = xn - gam * newtstep(xn)#newton's method\n\t\t}\n\t}\n\telse{#Halley Plot\n\t\txpoints = seq(center - range, center + range, stepsize)\n\t\tfor(n in 1:max){\n\t\t\tprint(paste(\"x\",n,\" = \",xn,sep=\"\"))\n\t\t\tdenom = 2*fp(xn)^2-f(xn)*fp2(xn)\n\t\t\thyperx <<- xn\n\t\t\ta <<- (-fp2(xn)) / denom\n\t\t\tb <<- (2*fp(xn)) / denom\n\t\t\tc <<- (2*f(xn)*fp(xn)) / denom\n\t\t\tsegments(xn, 0 , xn, f(xn), lty = \"dashed\", col = colors[n])#connect to axis\n\t\t\tpoints(xn, f(xn), col = colors[n], pch = '.' )#draw point (xn, f(xn))\n\t\t\ttext(xn, y = 0.05, labels = bquote(x[.(n)]), col = colors[n])#label x's\n\t\t\typoints = hyperbola(xpoints)\n\t\t\t#sanitize to remove asymptote connection\n\t\t\tfor(i in 1:length(ypoints))\n\t\t\t\tif(abs(ypoints[i])>cap)\n\t\t\t\t\typoints[i] = NA\n\t\t\tlines(xpoints,ypoints,col = colors[n])\n\t\t\tpoints(xn, f(xn), col = colors[n])#draw point (xn, f(xn))\n\t\t\txn = xn - gam * halleystep(xn)#halley's method\n\t\t\tif(abs(f(xn))= eps || abs(rd - rc) >= eps){\n\t\tprint(paste(ld,\"[\",lc,\",\",rc,\"]\",rd))\n\t\tif(abs(lc - ld) >= eps){#left side\n\t\t\tconverging = FALSE\n\t\t\tx = (lc + ld) / 2.0 #midpoint between conv and div\n\t\t\tfor(n in 1:10){#test a few iterations to see if conv\n\t\t\t\tif(useNewt)\n\t\t\t\t\tx = x - gam * newtstep(x)\n\t\t\t\telse\n\t\t\t\t\tx = x - gam * halleystep(x)\n\t\t\t\tif(x >= lc && x <= rc)\n\t\t\t\t\tconverging = TRUE\n\t\t\t\tif(x < ld || x > rd)\n\t\t\t\t\tbreak\n\t\t\t}\n\t\t\tif (converging)\n\t\t\t\tlc = (lc + ld) / 2.0\n\t\t\telse\n\t\t\t\tld = (lc + ld) / 2.0\n\t\t}\n\t\tif(abs(rc - rd) >= eps){#repeat with right side\n\t\t\tconverging = FALSE\n\t\t\tx = (rc + rd) / 2.0\n\t\t\tfor(n in 1:10){\n\t\t\t\tif(useNewt)\n\t\t\t\t\tx = x - gam * newtstep(x)\n\t\t\t\telse\n\t\t\t\t\tx = x - gam * halleystep(x)\n\t\t\t\tif(x >= lc && x <= rc)\n\t\t\t\t\tconverging = TRUE\n\t\t\t\tif(x < ld || x > rd)\n\t\t\t\t\tbreak\n\t\t\t}\n\t\t\tif (converging)\n\t\t\t\trc = (rc + rd) / 2.0\n\t\t\telse\n\t\t\t\trd = (rc + rd) /2.0\n\t\t}\n\t}\n\tprint(paste(ld,\"[\",lc,\",\",rc,\"]\",rd))\n\t#plot the interval\n\tplot(f, center - range, center + range, xlab = paste(\"gamma =\", gam, \"[\", lc, \",\", rc,\"]\", sep = \" \"), ylab = \" \", cex.lab = 1.4, cex.axis = 1.4,)\n\ttitle(main = \"\", sub = \"x\", cex.sub = 1.4, cex.main = 1.5 , xlab = \" \", ylab = name, cex.axis = 1.4, cex.lab = 1.4, line = 2)\n\ttitle(main = paste(method, \"Convergence Interval\",sep = \" \"), cex.main = 1.5 , xlab = \"\", ylab = \"\", line = .7)\n\tabline(a = 0, b = 0)#x axis\n\tfor(x in seq(center - range + 0.1, center + range - 0.1, by = range/40))\n\t\tif(x >= lc && x <= rc)\n\t\t\tpoints(x, 0, col = c('chartreuse3'), pch = 15)\n\t\telse\n\t\t\tpoints(x, 0, col = c('firebrick3'), pch = 4)\n}\n\n### main\nstart <- 1.5\nplotNewton(start)\nplotHalley(start)\nplotInterval()\nplotInterval(useNewt = FALSE)\n", "meta": {"hexsha": "3b680d8b992282f44555466dcaf50c30c2e4f25c", "size": 5674, "ext": "r", "lang": "R", "max_stars_repo_path": "src/rootfinding/PlotNewtonHalley.r", "max_stars_repo_name": "deboradeben/numerical-veliz", "max_stars_repo_head_hexsha": "afd208d5198315642aab3e0dab20bf27b20ed61c", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 73, "max_stars_repo_stars_event_min_datetime": "2018-09-26T22:41:54.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-29T15:50:14.000Z", "max_issues_repo_path": "src/rootfinding/PlotNewtonHalley.r", "max_issues_repo_name": "KulakovaEA/numerical-veliz", "max_issues_repo_head_hexsha": "d2f3f80c4179ddc2793a19d334526ae84d6d7480", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 4, "max_issues_repo_issues_event_min_datetime": "2019-11-18T20:37:11.000Z", "max_issues_repo_issues_event_max_datetime": "2021-11-22T08:59:13.000Z", "max_forks_repo_path": "src/rootfinding/PlotNewtonHalley.r", "max_forks_repo_name": "KulakovaEA/numerical-veliz", "max_forks_repo_head_hexsha": "d2f3f80c4179ddc2793a19d334526ae84d6d7480", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 16, "max_forks_repo_forks_event_min_datetime": "2018-11-14T17:19:40.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-30T21:50:34.000Z", "avg_line_length": 33.7738095238, "max_line_length": 157, "alphanum_fraction": 0.5572788157, "num_tokens": 2008, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9111797051879431, "lm_q2_score": 0.851952809486198, "lm_q1q2_score": 0.7762821097816738}} {"text": "#' @title calcCwp\n#'\n#' @description Calculates the water plane area coefficient (\\code{Cwp})\n#' (dimensionless) using one of two methods (Kristensen or Schneekluth).\n#'\n#' @param Cbw Waterline block coefficient (vector of numericals, \n#' dimensionless) (see \\code{\\link{calcCbw}})\n#' @param CwpEquationType Indicates equation type:\n#' \\itemize{\\item\"kristensen\"\\item\"schneekluth\"}\n#' This argument is not vectorized, as it takes only a single string\n#'\n#' @details\n#'Kristensen:\n#'\\deqn{Cwp = 0.55+0.45Cbw}\n#'\n#'Schneekluth:\n#'\\deqn{Cwp = \\frac{1+2Cbw}{3}}{Cwp = (1+2Cbw)/3}\n#'\n#' @return \\code{Cwp} (vector of numericals, dimensionless)\n#'\n#' @references\n#'Kristensen, H. O. and Lutzen, M. 2012. \"Prediction of Resistance and Propulsion\n#'Power of Ships. Clean Shipping Currents, 1 (6).\n#'\n#'Schneekluth, H. and Bertram, V. 1998. \"Ship Design for Efficiency and Economy.\"\n#'2nd ed. Oxford, Boston: Butterworth-Heinemann.\n#'\n#' @seealso \\code{\\link{calcCbw}}\n#'\n#' @examples\n#' calcCwp(c(0.81,0.65),\"kristensen\")\n#'\n#' @export\n\ncalcCwp <- function(Cbw, CwpEquationType){\n\n if(grepl(\"kristensen\", tolower(CwpEquationType))){\n Cwp<-0.55+0.45*Cbw\n }else{\n Cwp<-(1+2*Cbw)/3\n }\n\n\n return(Cwp)\n\n}\n", "meta": {"hexsha": "f13d7cb3546706be52d077e23f53b9c388ea63b4", "size": 1202, "ext": "r", "lang": "R", "max_stars_repo_path": "ShipPowerModel/R/calcCwp.r", "max_stars_repo_name": "USEPA/Marine_Emissions_Tools", "max_stars_repo_head_hexsha": "28e12dc51acb5baafc460b1a9de35d355f3cc64f", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 7, "max_stars_repo_stars_event_min_datetime": "2020-05-13T17:14:11.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-26T18:47:39.000Z", "max_issues_repo_path": "ShipPowerModel/R/calcCwp.r", "max_issues_repo_name": "USEPA/Marine_Emissions_Tools", "max_issues_repo_head_hexsha": "28e12dc51acb5baafc460b1a9de35d355f3cc64f", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "ShipPowerModel/R/calcCwp.r", "max_forks_repo_name": "USEPA/Marine_Emissions_Tools", "max_forks_repo_head_hexsha": "28e12dc51acb5baafc460b1a9de35d355f3cc64f", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-09-08T15:55:06.000Z", "max_forks_repo_forks_event_max_datetime": "2021-09-08T15:55:06.000Z", "avg_line_length": 25.5744680851, "max_line_length": 81, "alphanum_fraction": 0.6813643927, "num_tokens": 421, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9173026663679976, "lm_q2_score": 0.8459424334245618, "lm_q1q2_score": 0.7759852497741828}} {"text": "#!/usr/bin/env Rscript\n\n\na = c(1,2,3)\n# 显示是column vector\nprint(a)\n\n# 显示的是行向量 [, x] \nb = t(a)\n\n7*a\n\n# a列向量 b行向量, 为啥能相加\n# 1 2 3 \n# 1\n# 2\n# 3\nc1 = a + b\n\n# 列向量相加\nc2 = t(b) + a\n\n# 行向量相加 == c1\nc3 = b + t(a)\n\na = c(1,3,2)\na\nb = c(2,8,9)\nb\na + b\n# 这个不是内积, 只是相乘\na*b\n# 做求和运算(内积)\nsum(a*b)\n\n# 向量的length\nsqrt(sum(a*a))\n\n# 0-vector\nrep(0, 5)\n\n# 1-vector\nrep(1, 3)\n\n# (1,3) (2,2), (8,9) col by col\na = c(1,3)\nb = c(2,2)\nc = c(8,9)\nA = matrix(c(a, b, c), ncol = 3)\nA\nA = matrix(c(a, b, c), ncol =3, byrow=T)\nA\n\nA1 = rbind(c(1, 3, 2), c(2, 8, 9))\nA1\n\n7*A1\nt(A1)\n\nB = matrix(c(5,8,3,4,2,7),ncol=3,byrow=T)\nB\nA+B\n\n# A: 2x3 a:3x1\na = c(1, 3, 2)\n# 注意形式: Aa\nprint(A)\nprint(A%*%a)\n# ?????\nprint(A*a)\n", "meta": {"hexsha": "9e0479653082ea042b6b8dbe34a59101ea0affb2", "size": 686, "ext": "r", "lang": "R", "max_stars_repo_path": "R/learn/ILAR/class1.r", "max_stars_repo_name": "qrsforever/workspace", "max_stars_repo_head_hexsha": "53c7ce7ca7da62c9fbb3d991ae9e4e34d07ece5f", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2017-06-07T03:20:42.000Z", "max_stars_repo_stars_event_max_datetime": "2020-01-07T09:14:26.000Z", "max_issues_repo_path": "R/learn/ILAR/class1.r", "max_issues_repo_name": "qrsforever/workspace", "max_issues_repo_head_hexsha": "53c7ce7ca7da62c9fbb3d991ae9e4e34d07ece5f", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/learn/ILAR/class1.r", "max_forks_repo_name": "qrsforever/workspace", "max_forks_repo_head_hexsha": "53c7ce7ca7da62c9fbb3d991ae9e4e34d07ece5f", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 9.661971831, "max_line_length": 41, "alphanum_fraction": 0.4897959184, "num_tokens": 435, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.900529786117893, "lm_q2_score": 0.8615382147637195, "lm_q1q2_score": 0.7758408242735637}} {"text": "## The Heston Stochastic Volatility model\n##\n## - Closed form solution for a European call option\n## - Monte Carlo solution (Absorbing at zero)\n## - Monte Carlo solution (Reflecting at zero)\n## - Monte Carlo solution (Reflecting at zero + Milstein method)\n## - Monte Carlo solution (Alfonsi)\n## - Plot implied volality surface\n##\n## Dale Roberts \n##\n## PARAMETERS\n##\n## lambda: mean-reversion speed\n## vbar: long-term average volatility\n## eta: volatility of vol process\n## rho: correlation between stock and vol\n## v0: initial volatility\n## r: risk-free interest rate\n## tau: time to maturity\n## S0: initial share price\n## K: strike price\n##\n## MODEL\n## \n## dS_t = S_t r dt + S_t sqrt(V_t)dW_t^S\n## dV_t = \\lambda (\\vbar - V_t)dt - eta sqrt(V_t)dW_t^V\n## with d_t = \\rho dt\n\nONEYEAR <- 250\n\nMoneyness <- function(S, K, tau, r) {\n K*exp(-r*tau)/S\n}\n\nBlackScholesCall <- function(S0, K, tau, r, sigma, EPS=0.01) {\n d1 <- (log(S0/K) + (r + 0.5*sigma^2)*tau)/(sigma*sqrt(tau))\n d2 <- d1 - sigma*sqrt(tau)\n if (T < EPS) {\n return(max(S0-K,0))\n } else {\n return(S0*pnorm(d1) - K*exp(-r*(tau))*pnorm(d2))\n }\n}\n\nImpliedVolCall <- function(S0, K, tau, r, price) {\n f <- function(x) BlackScholesCall(S0,K,tau,r,x) - price\n if (f(-1) * f(1) > 0)\n return(NA)\n uniroot(f,c(-1,1))$root\n}\n\nHestonCallClosedForm <-\n function(lambda, vbar, eta, rho, v0, r, tau, S0, K) {\n\tPIntegrand <- function(u, lambda, vbar, eta, rho, v0, r, tau, S0, K, j) {\n F <- S0*exp(r*tau)\n x <- log(F/K)\n a <- lambda * vbar\n \n if (j == 1) {\n b <- lambda - rho* eta\n alpha <- - u^2/2 - u/2 * 1i + 1i * u\n beta <- lambda - rho * eta - rho * eta * 1i * u\n } else {\n b <- lambda\n alpha <- - u^2/2 - u/2 * 1i\n beta <- lambda - rho * eta * 1i * u\n }\n \n gamma <- eta^2/2\n d <- sqrt(beta^2 - 4*alpha*gamma)\n rplus <- (beta + d)/(2*gamma)\n rminus <- (beta - d)/(2*gamma)\n g <- rminus / rplus\n \n D <- rminus * (1 - exp(-d*tau))/(1-g*exp(-d*tau))\n C <- lambda * (rminus * tau - 2/(eta^2) * log( (1-g*exp(-d*tau))/(1-g) ) )\n \n top <- exp(C*vbar + D*v0 + 1i*u*x)\n bottom <- (1i * u)\n Re(top/bottom)\n\t}\n\t\n\tP <- function(lambda, vbar, eta, rho, v0, r, tau, S0, K, j) {\n value <- integrate(PIntegrand, lower = 0, upper = Inf,\n lambda, vbar, eta, rho, v0, r, tau,\n S0, K, j, subdivisions=1000)$value\n 0.5 + 1/pi * value\n\t}\n\n A <- S0*P(lambda, vbar, eta, rho, v0, r, tau, S0, K, 1)\n B <- K*exp(-r*tau)*P(lambda, vbar, eta, rho, v0, r, tau, S0, K, 0)\n A-B\n }\n\nHestonCallMonteCarlo <-\n function(lambda, vbar, eta, rho, v0, r, tau, S0, K, nSteps=2000, nPaths=3000, vneg=2) {\n\n n <- nSteps\n N <- nPaths\n \n dt <- tau / n\n \n negCount <- 0\n \n S <- rep(S0,N)\n v <- rep(v0,N)\n \n for (i in 1:n)\n {\n W1 <- rnorm(N);\n W2 <- rnorm(N);\n W2 <- rho*W1 + sqrt(1 - rho^2)*W2;\n\n sqvdt <- sqrt(v*dt)\n S <- S*exp((r-v/2)*dt + sqrt(v * dt) * W1)\n \n if ((vneg == 3) & (2*lambda*vbar/(eta^2) <= 1)) {\n cat(\"Variance not guaranteed to be positive with choice of lambda, vbar, and eta\\n\")\n cat(\"Defaulting to Reflection + Milstein method\\n\")\n vneg = 2\n }\n\n if (vneg == 0){\n ## Absorbing condition\n v <- v + lambda*(vbar - v)* dt + eta * sqvdt * W2\n negCount <- negCount + length(v[v < 0])\n v[v < 0] <- 0\n }\n if (vneg == 1){\n ## Reflecting condition\n sqvdt <- sqrt(v*dt)\n v <- v + lambda*(vbar - v)* dt + eta * sqvdt * W2\n negCount <- negCount + length(v[v < 0])\n v <- ifelse(v<0, -v, v)\n }\n if (vneg == 2) {\n ## Reflecting condition + Milstein\n v <- (sqrt(v) + eta/2*sqrt(dt)*W2)^2 - lambda*(v-vbar)*dt - eta^2/4*dt\n negCount <- negCount + length(v[v < 0])\n v <- ifelse(v<0, -v, v) \n }\n if (vneg == 3) {\n ## Alfonsi - See Gatheral p.23\n v <- v -lambda*(v-vbar)*dt +eta*sqrt(v*dt)*W2 - eta^2/2*dt \n }\n }\n \n negCount <- negCount / (n*N);\n\n ## Evaluate mean call value for each path\n V <- exp(-r*tau)*(S>K)*(S - K); # Boundary condition for European call\n AV <- mean(V);\n AVdev <- 2 * sd(V) / sqrt(N);\n\n list(value=AV, lower = AV-AVdev, upper = AV+AVdev, zerohits = negCount)\n }\n\nHestonSurface <- function(lambda, vbar, eta, rho, v0, r, tau, S0, K, N=5, min.tau = 1/ONEYEAR) {\n LogStrikes <- seq(-0.5, 0.5, length=N)\n Ks <- rep(0.0,N)\n taus <- seq(min.tau, tau, length=N)\n vols <- matrix(0,N,N)\n\n TTM <- Money <- Vol <- rep(0,N*N)\n \n HestonPrice <- function(K, tau) {\n HestonCallClosedForm(lambda, vbar, eta, rho, v0, r, tau, S0, K)\n }\n\n n <- 1\n for (i in 1:N) {\n for (j in 1:N) {\n Ks[i] <- exp(r * taus[j]+LogStrikes[i]) * S0\n price <- HestonPrice(Ks[i],taus[j])\n iv <- ImpliedVolCall(S0, Ks[i], taus[j], r, price)\n TTM[n] <- taus[j] * ONEYEAR # in days\n Money[n] <- Moneyness(S0,Ks[i],taus[j],r)\n Vol[n] <- iv\n n <- n+1\n }\n }\n\n data.frame(TTM=TTM, Moneyness=Money, ImpliedVol=Vol)\n}\n\nPlotHestonSurface <-\n function(lambda=6.21, vbar=0.019, eta=0.61, rho=-0.7, v0=0.010201, r=0.0319,\n tau=1.0, S0=100, K=100, N=30, min.tau = 1/ONEYEAR, ...) {\n \n Ks <- seq(0.8*K, 1.25 * K, length=N) \n taus <- seq(0.21, tau, length=N)\n \n HestonPrice <- Vectorize(function(k, t) {\n HestonCallClosedForm(lambda, vbar, eta, rho, v0, r, t, S0, k)})\n \n IVHeston <- Vectorize(function(k,t) { ImpliedVolCall(S0, k, t, r, HestonPrice(k,t))})\n \n z <- outer(Ks, taus, IVHeston)\n \n nrz <- nrow(z)\n ncz <- ncol(z)\n nb.col <- 256\n color <- heat.colors(nb.col)\n facet <- - (z[-1, -1] + z[-1, -ncz] + z[-nrz, -1] + z[-nrz, -ncz])\n facetcol <- cut(facet, nb.col)\n \n persp(x=Ks, y=taus, z, theta = 40, phi = 20, expand = 0.5, col=color[facetcol],\n xlab=\"Strikes\", ylab=\"Time to maturity\", zlab=\"Implied Volatility\",\n ticktype=\"detailed\", ...) -> res\n\n return(invisible(z))\n }\n", "meta": {"hexsha": "7c592f4b6501f36664a7d2fe95e08cef0e5bd7a0", "size": 7026, "ext": "r", "lang": "R", "max_stars_repo_path": "heston.r", "max_stars_repo_name": "dendisuhubdy/heston", "max_stars_repo_head_hexsha": "ede095c1298ab2eaae89966e1cabfa43bfe86cee", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 18, "max_stars_repo_stars_event_min_datetime": "2015-03-12T00:46:32.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-23T11:28:39.000Z", "max_issues_repo_path": "heston.r", "max_issues_repo_name": "dendisuhubdy/heston", "max_issues_repo_head_hexsha": "ede095c1298ab2eaae89966e1cabfa43bfe86cee", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "heston.r", "max_forks_repo_name": "dendisuhubdy/heston", "max_forks_repo_head_hexsha": "ede095c1298ab2eaae89966e1cabfa43bfe86cee", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 13, "max_forks_repo_forks_event_min_datetime": "2015-07-01T19:41:24.000Z", "max_forks_repo_forks_event_max_datetime": "2020-08-19T16:00:33.000Z", "avg_line_length": 32.8317757009, "max_line_length": 104, "alphanum_fraction": 0.4570167948, "num_tokens": 2295, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9334308184368928, "lm_q2_score": 0.8311430478583169, "lm_q1q2_score": 0.7758145354005224}} {"text": "## 1. Multiple Random Experiments ##\n\np_a <- 12/100\np_b <- 17/100\np_a_and_b <- 3/100\np_a_or_b <- p_a + p_b - p_a_and_b\n\n## 2. The Multiplication Rule ##\n\np_6_6 <- 1/6 * 1/6\np_3_2 <- 1/6 * 1/6\np_even_even <- 3/6 * 3/6\np_1_even <- 1/6 * 3/6\n\n## 3. Independent Events ##\n\nsql_and_ml <- 0.2 * 0.3\nml_or_viz <- 0.3 + 0.4 - (0.3 * 0.4)\nat_least_one_skill <- 0.2 + 0.3 + 0.4 - (0.2 * 0.3) - (0.2 * 0.4) - (0.3 * 0.4) - (0.2 * 0.3 * 0.4)\n\n## 4. Independence vs Mutual Exclusivity ##\n\nsql_and_ml_me <- 0\nml_or_viz_me <- 0.3 + 0.4\nat_least_one_skill_me <- 0.2 + 0.3 + 0.4\n\n## 5. Complements ##\n\np_complement_even <- 1/2\np_complement_ace <- 48/52\n\n## 6. Using Complements With Probability ##\n\np_one_double_6 <- 1 - (35/36)**24\n\n## 7. Another Application: Detecting Dependence ##\n\np_intersection <- (0.1 * 0.17)\nis_independent <- p_intersection == 0.08", "meta": {"hexsha": "e72434e6ba84b5a9383b64ea23464e65a3d8801c", "size": 840, "ext": "r", "lang": "R", "max_stars_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/3. Probability Fundamentals in R/3. Probabilities of Multiple Random Experiments.r", "max_stars_repo_name": "MyArist/Dataquest", "max_stars_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 8, "max_stars_repo_stars_event_min_datetime": "2020-07-27T12:04:54.000Z", "max_stars_repo_stars_event_max_datetime": "2021-03-01T04:39:33.000Z", "max_issues_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/3. Probability Fundamentals in R/3. Probabilities of Multiple Random Experiments.r", "max_issues_repo_name": "myarist/Dataquest", "max_issues_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/3. Probability Fundamentals in R/3. Probabilities of Multiple Random Experiments.r", "max_forks_repo_name": "myarist/Dataquest", "max_forks_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 15, "max_forks_repo_forks_event_min_datetime": "2021-03-30T06:45:19.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-17T03:55:02.000Z", "avg_line_length": 21.5384615385, "max_line_length": 99, "alphanum_fraction": 0.6154761905, "num_tokens": 388, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9688561694652215, "lm_q2_score": 0.8006920020959544, "lm_q1q2_score": 0.7757553860721255}} {"text": "#задание 2\nprint (\"task 2\")\nA <- matrix (c(-1,-3,-6,0,-3,3,-11,0,-8,-5,-5,-1,4,-7,-7,-5,-9,-7,-1,-8,11,-7,2,4,3,-4,7,10,4,8,-10,3,-5,-11,7,9),6,6)\nA\n#определитель\ndet(A) # Определитель A\n#обратная\nsolve(A)\n#транспон\nt(A)\n#задание 3\nprint (\"task 3\")\na <- c(2,-3,3,5,1) #\nprint (\"Answer on the second task\")\npolyroot(a)\n\n#задание 4\nprint (\"task 4\")\nQ <- cbind(c(1,2,1),c(1,3,2),c(7,0,-1)) # Составить матрицу из трех столбцов-векторов\nQ\nd <- eigen(Q)$values;d\nd1 <- round(d, 3); d1\nD <- diag(d1); D\n\n\n\n#задание 5\nprint (\"5 task\")\na <- c(1,5,-1,2,0,6,-2,1,1,-3,5,1)\nb <- c(0,2,3,1,-4,-1,0,2,1,4,1,3)\np <- c(-3,0,-1,-1,0,4,3,2,-5,1,1,-6)\n\nfir <- ((3)*a)-(4*b)\nprint (\"first answer\")\nfir\nsec <- ((2)*as.numeric(a%*%b))*p+2*(norm(p, type=\"2\"))*a\nprint (\"second answer\")\nsec\nthr <- 3*as.numeric(a%*%p)*b+2*as.numeric(b%*%p)*a-2*(norm(p, type=\"2\"))*p\nprint (\"third answer\")\nthr\n\n#6 задание\nprint (\"sixth task\")\ninstall.packages(\"lpSolveAPI\") # Загружаем библиотеку\nlibrary(lpSolveAPI) # Активируем библиотеку линейного программирования\nM <- make.lp(ncol= 2) # Объявляем количество неотрицательных переменных в M\nname.lp(M, \"Example\") # Объявляем название \"Example\"для задачи(модели) М\ncolnames(M) <- c(\"X1\", \"X2\") # Объявляем названия переменных в модели М\nlp.control(M, sense = \"min\")$sense# Объявляем задачу на минимум модели М\nset.objfn(M, c(22,25)) # Задаем целевую функцию:\nadd.constraint(M, c(6,8), \"<=\", 80) # Задаем ограничение:\nadd.constraint(M, c(4, 6), \"<=\",120) #\nadd.constraint(M, c(4, 5), \"<=\",70) #\nadd.constraint(M, c(1, 0), \"<=\",12)\nadd.constraint(M, c(0, 1), \"<=\",14)\n\nrownames(M) <- c(\"A\", \"B\",\"C\",\"D\",\"E\") # Называем ограничения в модели М\nM # Выводим модель M на экран\nsolve.lpExtPtr(M)\nget.variables(M) # Оптимальный план\nget.objective(M) # Достигнутый min\nX1.opt<- get.variables(M)[1]; X1.opt # Оптимальное значение для X1\nX2.opt<- get.variables(M)[2]; X2.opt # Оптимальное значение для X2\nf.max<- get.objective(M); f.max# Значение целевой функции на оптимальном решении\n", "meta": {"hexsha": "91b04d6d0e80d26802299f9390dc3a3dd00a2042", "size": 1986, "ext": "r", "lang": "R", "max_stars_repo_path": "Tasks/Task 3/solution.r", "max_stars_repo_name": "Master-sniffer/Doing-some-tasks-with-R", "max_stars_repo_head_hexsha": "629e7add02437ea22c079ecd7a4279e46028b69c", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Tasks/Task 3/solution.r", "max_issues_repo_name": "Master-sniffer/Doing-some-tasks-with-R", "max_issues_repo_head_hexsha": "629e7add02437ea22c079ecd7a4279e46028b69c", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Tasks/Task 3/solution.r", "max_forks_repo_name": "Master-sniffer/Doing-some-tasks-with-R", "max_forks_repo_head_hexsha": "629e7add02437ea22c079ecd7a4279e46028b69c", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 30.0909090909, "max_line_length": 118, "alphanum_fraction": 0.6379657603, "num_tokens": 904, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9433475699138559, "lm_q2_score": 0.8221891392358015, "lm_q1q2_score": 0.7756101265076583}} {"text": "# Logistic model.\nN <- function(t, r, K, N0) { K / (1 + ((K-N0)/N0)*exp(-r*t)) }\n\n# Params.\nk = 2000 # carrying capacity\nn0 = 100 # initial population\nR = 0.1 # rate of increase\n\nplot(N(1:100, R, k, n0), t='l', lwd=2, col='blue', ylim=c(0, k),\n main='Logistic model for population growth in an environment')\nabline(h=k)\nabline(h=0)", "meta": {"hexsha": "94ec6b866a006f9f4d71f863a273a8555a3d0b07", "size": 354, "ext": "r", "lang": "R", "max_stars_repo_path": "population-growth-models/population-growth-logistic.r", "max_stars_repo_name": "cassiopagnoncelli/applied-mathematics-problems", "max_stars_repo_head_hexsha": "c7b155bb7c97fb30b4c235425d206d154294095d", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "population-growth-models/population-growth-logistic.r", "max_issues_repo_name": "cassiopagnoncelli/applied-mathematics-problems", "max_issues_repo_head_hexsha": "c7b155bb7c97fb30b4c235425d206d154294095d", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "population-growth-models/population-growth-logistic.r", "max_forks_repo_name": "cassiopagnoncelli/applied-mathematics-problems", "max_forks_repo_head_hexsha": "c7b155bb7c97fb30b4c235425d206d154294095d", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 29.5, "max_line_length": 67, "alphanum_fraction": 0.5790960452, "num_tokens": 129, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9433475715065793, "lm_q2_score": 0.8221891305219504, "lm_q1q2_score": 0.7756101195969879}} {"text": "# Function to propagate errors on individual aliquots through the D47 averages\r\n# Based on: \"Combining Multiple Averaged Data Points And Their Errors\" by Ken Tatebe\r\n# Iterative approach adding datapoints and propagating uncertainty\r\n\r\naverage_p <- function(x, x_sd, n = NA, verbose = FALSE, output = \"SD\"){\r\n if(is.na(n)){\r\n n = rep(1, length(x))\r\n }\r\n N <- n[1] + n[2] # Calculate sample size for first 2 samples\r\n average <- (x[1] * n[1] + x[2] * n[2]) / N # Calculate weighted average for first 2 samples\r\n sd_p <- sqrt(n[1]) # Calculate weighted standard deviation for first 2 samples\r\n for(i in 3:length(x)){ # Loop over x and their uncertainties x_sd\r\n sd_p <- sqrt(\r\n (N ^ 2 - N) / ((N + n[i]) ^ 2 - (N + n[i])) * sd_p ^ 2 + # Existing error term\r\n (n[i] ^ 2 - n[i]) / ((N + n[i]) ^ 2 - (N + n[i])) * x_sd[i] ^ 2 + # Error term of new datapoint\r\n N * n[i] * (average - x[i]) ^ 2 / ((N + n[i]) * ((N + n[i]) ^ 2 - (N + n[i]))) # Term resulting from distance between points\r\n )\r\n average <- (average * N + x[i] * n[i]) / (N + n[i]) # Increment total average\r\n N <- N + n[i] # Increment total sample size\r\n }\r\n resultvec <- c(average, sd_p, N)\r\n names(resultvec) <- c(\"average\", \"sd\", \"N\")\r\n if(output == \"SD\"){\r\n return(resultvec[2])\r\n } else if(output == \"All\"){\r\n return(resultvec)\r\n } else{\r\n return(\"Error: output string not recognized\")\r\n }\r\n}\r\n\r\n# Repeat calculations based on Monte Carlo simulations\r\n\r\npropagate_MC <- function(x, x_sd, n = NA, Nsim = 10 ^ 4, verbose = FALSE, na.rm = TRUE, output = \"SD\"){ # Monte Carlo approach to estimate same errors\r\n if(is.na(n)){\r\n n = rep(1, length(x))\r\n }\r\n\r\n sims <- rep(NA, sum(Nsim * n)) # Vector to store simulated values\r\n for(i in 1:length(x)){\r\n sims[which(is.na(sims))[1]:(which(is.na(sims))[1] + Nsim * n[i] - 1)] <- rnorm(Nsim * n[i], x[i], x_sd[i]) # Add simulated values to vector\r\n }\r\n\r\n if(na.rm == TRUE){\r\n if(length(which(is.na(sims))) > 0){\r\n sims <- sims[-which(is.na(sims))] # Remove NA's from sims if called for\r\n }\r\n }\r\n\r\n average <- mean(sims) # Calculate average\r\n sd_p <- sd(sims) # Calculate standard deviation\r\n N <- length(sims) / Nsim # Calculate effective sample size\r\n\r\n resultvec <- c(average, sd_p, N)\r\n names(resultvec) <- c(\"average\", \"sd\", \"N\")\r\n\r\n if(verbose == TRUE){\r\n print(resultvec)\r\n }\r\n if(output == \"SD\"){\r\n return(resultvec[2])\r\n } else if(output == \"average\"){\r\n return(resultvec[1])\r\n } else if(output == \"All\"){\r\n return(resultvec)\r\n } else if(output == \"sims\"){\r\n return(sims)\r\n } else{\r\n return(\"Error: output string not recognized\")\r\n }\r\n}\r\n", "meta": {"hexsha": "fabacc509540a043145601f680cb9d4b7e98a803", "size": 2816, "ext": "r", "lang": "R", "max_stars_repo_path": "03_Average_error_propagation.r", "max_stars_repo_name": "japhir/Aragonite_clumped", "max_stars_repo_head_hexsha": "498ccff398279b18ed176aaeac1faa0415659419", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "03_Average_error_propagation.r", "max_issues_repo_name": "japhir/Aragonite_clumped", "max_issues_repo_head_hexsha": "498ccff398279b18ed176aaeac1faa0415659419", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "03_Average_error_propagation.r", "max_forks_repo_name": "japhir/Aragonite_clumped", "max_forks_repo_head_hexsha": "498ccff398279b18ed176aaeac1faa0415659419", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 39.1111111111, "max_line_length": 151, "alphanum_fraction": 0.5486505682, "num_tokens": 810, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9381240073565738, "lm_q2_score": 0.8267117855317474, "lm_q1q2_score": 0.7755581731719512}} {"text": "rm(list=ls())\n\n# [1]\n# a) Unfair coin and you flip 8 times. Probability heads is 0.4. What's the probability to have 2 heads?\n# b) 8 athletes to compete in Olympic Games. Probability of making the final race is 0.4. What's the probability that 2 athletes make it into the final race?\ndbinom(2,8,0.4)\n\n# [2]\n# a) Expectation number of heads\n# b) Expectation number of athletes that make it into the finals\n\n# E[Successes|N = 8] = n*p\nE_successes_n_8 = 8*0.4\n\n# [3]\n# Supose E[N]=2 and var(N)=1.5\nE_n = 2\nVar_n = 1.5\n\n# a) What is the expectation of the number of heads?\n# b) What is the expectation of the number of swimmers that make it to the final?\n\n# E[successes] = E[E[successes|N]] -> expectation of expectation of conditional\n# E[E[successes|N = n]] = E[N*p] = 0.4*E[N] =>\nE_successes = 0.4*E_n\n\n# a) What is the variance of the number of heads?\n# b) What is the variance of the number of swimmers that make it to the final?\n\n# Var(success) = Var(E[successes|N]) + E[Var(successes|N)]\n# we know of binomial:\n# E[successes|N] = n*p\n# Var(sucesses|N) = n*p*(1-p)\n#\n# so we get => Var(N*p) + E[N*p*(1-p)] => p^2*Var(N) + p*(1-p)*E[N]\nVar_successes = 0.4^2*Var_n + 0.4*(1 - 0.4)*E_n\n", "meta": {"hexsha": "ceb4a7de5cf64c84ef93ecce1eb9dd8ef08cb665", "size": 1197, "ext": "r", "lang": "R", "max_stars_repo_path": "problem.r", "max_stars_repo_name": "samuxiii/r-projects", "max_stars_repo_head_hexsha": "13a17bdf5a3db2efcf785c4810bb55c86459bfb3", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "problem.r", "max_issues_repo_name": "samuxiii/r-projects", "max_issues_repo_head_hexsha": "13a17bdf5a3db2efcf785c4810bb55c86459bfb3", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "problem.r", "max_forks_repo_name": "samuxiii/r-projects", "max_forks_repo_head_hexsha": "13a17bdf5a3db2efcf785c4810bb55c86459bfb3", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 5, "max_forks_repo_forks_event_min_datetime": "2019-06-24T17:18:38.000Z", "max_forks_repo_forks_event_max_datetime": "2020-07-22T03:39:37.000Z", "avg_line_length": 32.3513513514, "max_line_length": 157, "alphanum_fraction": 0.6591478697, "num_tokens": 430, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9653811621568289, "lm_q2_score": 0.8031737940012418, "lm_q1q2_score": 0.7753688506668283}} {"text": "library(lpSolve)\n\n\n#Linear Programing (LP)\n\nf.Obj<-c(2,3)\n\n##set constraint matrix coefficient\nf.con<-matrix(c(1,3,\n 2.5,1),nrow=2,byrow=TRUE)\n\n## equality signs\n\nf.dir <- c(\"<=\",\n \"<=\")\n\n## set right hand side coefficient\n\nf.rhs <- c(8.25,\n 8.75)\n\n##Final value of obj\n\nZ1 <- lp(\"max\", f.Obj,f.con, f.dir, f.rhs)\n\nZ1$solution\nZ1\n\n##### Mixed Linear Integer Programming (MIP)\n\nZ2 <- lp(\"max\", f.Obj,f.con, f.dir, f.rhs,int.vec = 1:2)\nZ2$solution\nZ2\n\n\n", "meta": {"hexsha": "f5785a41d66cfa4dd37ed3e72c03f930321f1cb9", "size": 486, "ext": "r", "lang": "R", "max_stars_repo_path": "notes/week6-examples/optimization.r", "max_stars_repo_name": "namkyodai/2022-UrbanComputation-SUTD", "max_stars_repo_head_hexsha": "fc3921ec4ea8719ebfb04f2646f00c90d886721f", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 4, "max_stars_repo_stars_event_min_datetime": "2022-03-16T10:46:46.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-30T02:48:39.000Z", "max_issues_repo_path": "notes/week6-examples/optimization.r", "max_issues_repo_name": "namkyodai/2022-UrbanComputation-SUTD", "max_issues_repo_head_hexsha": "fc3921ec4ea8719ebfb04f2646f00c90d886721f", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 3, "max_issues_repo_issues_event_min_datetime": "2022-03-16T06:48:23.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T16:39:15.000Z", "max_forks_repo_path": "notes/week6-examples/optimization.r", "max_forks_repo_name": "namkyodai/2022-UrbanComputation-SUTD", "max_forks_repo_head_hexsha": "fc3921ec4ea8719ebfb04f2646f00c90d886721f", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 6, "max_forks_repo_forks_event_min_datetime": "2022-03-16T10:35:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-30T11:12:09.000Z", "avg_line_length": 13.5, "max_line_length": 56, "alphanum_fraction": 0.5761316872, "num_tokens": 169, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9481545333502203, "lm_q2_score": 0.817574478416099, "lm_q1q2_score": 0.7751869480616661}} {"text": "# confidence interval for indpendent sample\r\nfresh=c(10.2, 10.6,10.5 ,10.7,10.3, 10.2,10.8, 10.0,9.8 ,10.6 )\r\nstored=c( 9.8, 9.7,\r\n 9.6, 9.5,\r\n 10.1, 9.6,\r\n 10.2, 9.8,\r\n 10.1 ,9.9)\r\nn1=length(fresh)\r\nn2= length(stored)\r\ny1bar = mean(fresh)\r\ny2bar=mean(stored)\r\ns1=sd(fresh)\r\ns2=sd(stored)\r\n# common standard deviation \r\nsp=sqrt(((n1-1)*s1*s1+(n2-1)*s2*s2)/(n1+n2-2))\r\n \r\n# the t-percentile based on df for 95% confidence interval\r\ntstar=qt( .975, df=18)\r\n margin=tstar*sp*sqrt((1/n1)+(1/n2))\r\n left_i=(y1bar-y2bar)-margin\r\n right_i=(y1bar-y2bar)+margin\r\n print(\"confidence interval is\")\r\n print(left_i)\r\n print(right_i)\r\n", "meta": {"hexsha": "56e54ea82233209ac6572a8d9473b5f9944e7884", "size": 657, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH6/EX6.1/Ex6_1.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH6/EX6.1/Ex6_1.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH6/EX6.1/Ex6_1.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 26.28, "max_line_length": 64, "alphanum_fraction": 0.6103500761, "num_tokens": 271, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9648551566309688, "lm_q2_score": 0.8031738010682209, "lm_q1q2_score": 0.7749463836315689}} {"text": "#задание 2\nprint (\"task 2\")\nA <- matrix (c(0,-12,-11,13,11,11,-3,12,9,-11,12,-13,0,-8,11,14,14,-13,7,8,-1,-10,14,-6,-2,-14,-7,8,1,14,13,9,-6,7,-3,2),6,6)\nA\n#определитель\ndet(A) # Определитель A\n\n#задание 4\nprint (\"task 4\")\nA <- matrix (c(-1,3,-5,0,0,-7,-1,-3,10,-6,-1,6,-3,4,-9,1,7,-8,5,12,4,-12,10,5,-2,-12,-7,-5,-6,-4,7,-9,11,-2,5,5),6,6)\nA\nB <- matrix (c(-6,1,8,6,5,2,6,3,-6,-6,9,-2,3,5,2,0,-3,9,4,-1,-6,4,-1,1,6,-9,0,6,5,1,8,-6,8,-4,-1,0),6,6)\nB\nx <- solve(B,A)\nprint (\"x равен\")\nx\n\n#задание 5\nprint (\"5 task\")\na <- c(0,-4,2,3,1,1,1,0,-5,-2,-1,3)\nb <- c(-4,-4,0,3,-2,-1,-2,3,3,1,1,5)\np <- c(1,5,2,4,3,0,-4,-5,1,2,2,1)\n\nfir <- ((7)*a)+(4*b)\nprint (\"first answer\")\nfir\nsec <- ((9)*as.numeric(a%*%b))*p-2*(norm(p, type=\"2\"))*a\nprint (\"second answer\")\nsec\nthr <- 1*as.numeric(a%*%p)*b-2*as.numeric(b%*%p)*a-2*(norm(p, type=\"2\"))*p\nprint (\"third answer\")\nthr\n\n#6 задание\nprint (\"sixth task\")\ninstall.packages(\"lpSolveAPI\") # Загружаем библиотеку\nlibrary(lpSolveAPI) # Активируем библиотеку линейного программирования\nM <- make.lp(ncol= 2) # Объявляем количество неотрицательных переменных в M\nname.lp(M, \"Example\") # Объявляем название \"Example\"для задачи(модели) М\ncolnames(M) <- c(\"X1\", \"X2\") # Объявляем названия переменных в модели М\nlp.control(M, sense = \"max\")$sense# Объявляем задачу на минимум модели М\nset.objfn(M, c(2,1)) # Задаем целевую функцию:\nadd.constraint(M, c(4,3), \"<=\", 1) # Задаем ограничение:\nadd.constraint(M, c(-0.2, -0.6), \">=\",-1.5) #\n\nrownames(M) <- c(\"A\", \"B\") # Называем ограничения в модели М\nM # Выводим модель M на экран\nsolve.lpExtPtr(M)\nget.variables(M) # Оптимальный план\nget.objective(M) # Достигнутый min\nX1.opt<- get.variables(M)[1]; X1.opt # Оптимальное значение для X1\nX2.opt<- get.variables(M)[2]; X2.opt # Оптимальное значение для X2\nf.max<- get.objective(M); f.max# Значение целевой функции на оптимальном решении\n", "meta": {"hexsha": "baf56d4d9fd971485a1ee02dba4dcfea4bc5d2e1", "size": 1856, "ext": "r", "lang": "R", "max_stars_repo_path": "Tasks/Task 4/solution.r", "max_stars_repo_name": "Master-sniffer/Doing-some-tasks-with-R", "max_stars_repo_head_hexsha": "629e7add02437ea22c079ecd7a4279e46028b69c", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Tasks/Task 4/solution.r", "max_issues_repo_name": "Master-sniffer/Doing-some-tasks-with-R", "max_issues_repo_head_hexsha": "629e7add02437ea22c079ecd7a4279e46028b69c", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Tasks/Task 4/solution.r", "max_forks_repo_name": "Master-sniffer/Doing-some-tasks-with-R", "max_forks_repo_head_hexsha": "629e7add02437ea22c079ecd7a4279e46028b69c", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 34.3703703704, "max_line_length": 125, "alphanum_fraction": 0.6271551724, "num_tokens": 904, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9399133565584851, "lm_q2_score": 0.8244619220634457, "lm_q1q2_score": 0.7749227725213134}} {"text": "check_mod <- function(num,base){\n return(ifelse(num%%base == 0,num,0))\n}\n\nsum_sequence <- function(max,base){\n val <- 1:max\n ret_val <- sum(sapply(X = val,FUN = function(x){check_mod(num = x,base = base)}))\n return(ret_val)}\n\n\nsum_sequence(1000,3)+sum_sequence(1000,5)-sum_sequence(1000,15)", "meta": {"hexsha": "e7e57e7e2ce1c43ac22022ea26c5d57609e6bb47", "size": 294, "ext": "r", "lang": "R", "max_stars_repo_path": "R/Euler 1.r", "max_stars_repo_name": "poc1673/Project-Euler-Exercises", "max_stars_repo_head_hexsha": "80044be236f56dd29d5db41296e0e3d683085a03", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/Euler 1.r", "max_issues_repo_name": "poc1673/Project-Euler-Exercises", "max_issues_repo_head_hexsha": "80044be236f56dd29d5db41296e0e3d683085a03", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/Euler 1.r", "max_forks_repo_name": "poc1673/Project-Euler-Exercises", "max_forks_repo_head_hexsha": "80044be236f56dd29d5db41296e0e3d683085a03", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.7272727273, "max_line_length": 83, "alphanum_fraction": 0.6802721088, "num_tokens": 95, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9372107861416413, "lm_q2_score": 0.8267117940706734, "lm_q1q2_score": 0.7748032104335425}} {"text": "#' @export\n#'\n#' @title Baysian estimation of a multinomial\n#' proportion vector assuming a conjugate\n#' prior.\n#'\n#' @description This routine assumes you have an observation\n#' from a multinomial distribution with k classes (k >= 2, parameter\n#' \\code{x}) and have assumed that the multinomial distribution's\n#' proportion vector (\"pi vector\") follows a Dirichelet distribution.\n#' If so, this routine estimates the proportion vector's\n#' posterior distribution mean, variance, and mode.\n#'\n#' @param x An integer vector\n#' containing the number of observed 'successes' in\n#' each catagory of the multinomial. Total number of trials is \\code{sum(x)}.\n#' The number of catagories is K = \\code{length(x)}.\n#'\n#' @param pseudoCounts A vector of real-valued \"pseudo counts\"\n#' for the K catagories in the problem. This is sometimes called\n#' the \"concentration\" parameter.\n#'\n#'\n#' @details\n#'\n#' Computations are elementary because the Dirichlet(a1, a2, ..., aK) prior is\n#' conjugate for the multinomial. Nearly every text on Bayesian\n#' estimation shows that given values for \\code{x} and \\code{pseudoCounts},\n#' the posterior distribution of the mulitinomial's p vector\n#' is,\n#' \\deqn{Dirichlet(x1+a1, x2+a2, ..., xk+ak).}\n#' Hence, the Bayes point estimator of the multinomial's proportions is,\n#' \\deqn{phat_i = (xi+ai) / sum(xi + ai),}\n#' which is the mean of the posterior. Standard error of the\n#' posterior is,\n#' \\deqn{se.phat_i=sqrt((xi+ai)*(A-ai)/(A^2*(A+1))).}\n#' where A = sum(xi + ai). If \\code{(xi+ai)>1} for all i, mode of the\n#' posterior for the proportion vector is,\n#' \\deqn{(xi+ai-1)/(A-K).}\n#'\n#'\n#' The default value for \\code{pseudoCounts}\n#' corresponds to the Jeffery's prior. The Jeffery's prior is\n#' proportional to the root of Fisher's information and\n#' is equal to Dirichlet(1/K,1/K, ..., 1/K).\n#'\n#' @return A data frame with number of rows equal to\n#' \\code{length(x)}\n#' containing the Baysian point estimates for the proportion\n#' in each catagory.\n#' The data frame has the\n#' following columns:\n#' \\enumerate{\n#' \\item \\code{phat} : the Bayes point estimates equal to the\n#' mean vector of the posterior distribution. This column sums to 1.0\n#' \\item \\code{phat.mode} : if \\code{xi+ai} > 1 for all i, this\n#' column contains the mode vector of the posterior. Mode vector\n#' is the most vector of proportions with maximum likelihood.\n#' If any \\code{xi+ai} < 1, \\code{phat.mode = NA}.\n#' \\item \\code{se.phat} : the standard\n#' error vector of the posterior distribution.\n#' \\item \\code{psuedoCounts} : the vector of pseudoCounts\n#' associated with the Dirichlet posterior. This vector\n#' can be used to accumulate counts over muliple calls.\n#' }\n#'\n#' @author Trent McDonald\n#'\n#'\n#' @seealso \\code{\\link{agrestiCoullPhat}}\n#'\n#' @examples\n#' bayesPiVector(c(1,5), c(.5,.5)) # Jeffery's prior\n#' bayesPiVector(c(1,5), c(1, 1)) # flat prior\n#'\n#' # When prior data is available:\n#' x.prior <- 5\n#' n.prior <- 100\n#' bayesPiVector(c(1,5), c(x.prior+0.5, n.prior-x.prior+0.5))\n#'\n#' # Simulation: point est bias and ci coverage\n#' trueP <- c(0.01, 0.04, 0.95)\n#' n <- 20\n#' x <- rbinom( 1000, n, trueP)\n#' baPhat <- apply(x, 1, bayesPiVector, pseudoCounts=rep(1,3)/3 )\n#' muBA <- mean(baPhat$phat)\n#'\nbayesPiVector <- function(x, pseudoCounts=rep(1,length(x))/length(x)){\n aPost <- x + pseudoCounts\n A <- sum(aPost)\n phat <- aPost / A\n\n se <- sqrt(aPost*(A-aPost) / (A^2*(A+1)))\n\n if( all(aPost>1) ){\n phat.mode <- (aPost-1) / (A - length(aPost))\n } else {\n phat.mode <- NA\n }\n\n data.frame(phat=phat, se.phat=se, phat.mode=phat.mode, pseudoCounts=aPost)\n}\n", "meta": {"hexsha": "a2dc2ce85b34161b2230f728b5ea3902d03056ea", "size": 3631, "ext": "r", "lang": "R", "max_stars_repo_path": "R/bayesPiVector.r", "max_stars_repo_name": "tmcd82070/EoAR", "max_stars_repo_head_hexsha": "30bdd48e88046332fdb1c97d55fb9a6a1a983e06", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/bayesPiVector.r", "max_issues_repo_name": "tmcd82070/EoAR", "max_issues_repo_head_hexsha": "30bdd48e88046332fdb1c97d55fb9a6a1a983e06", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/bayesPiVector.r", "max_forks_repo_name": "tmcd82070/EoAR", "max_forks_repo_head_hexsha": "30bdd48e88046332fdb1c97d55fb9a6a1a983e06", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 35.2524271845, "max_line_length": 78, "alphanum_fraction": 0.6747452492, "num_tokens": 1131, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9273632976542185, "lm_q2_score": 0.8354835371034368, "lm_q1q2_score": 0.7747967681040538}} {"text": "N <- 1000\nc <- c(0.2, 0.15, 0.25, 0.4)\nu <- runif(N)\nr <- 1:N * 0\nr2 <- 1:N * 0\n\n# Varianta 1\ncount1 <- 0\nfor(i in 1:N){\n if(u[i] < c[1]){\n r[i] <- 1\n count1 <- count1 + 1\n }else\n if(u[i] < c[1] + c[2]) {\n r[i] <- 2\n count1 <- count1 + 2\n }else\n if(u[i] < c[1] + c[2] + c[3]) {\n r[i] <- 3\n count1 <- count1 + 3\n }else {\n r[i] <- 4\n count1 <- count1 + 3\n }\n}\ncount1\n\n# Varianta 2\ncount2 <- 0\nfor(i in 1:N){\n if(u[i] < c[4]){\n r2[i] <- 4\n count2 <- count2 + 1\n }else\n if(u[i] < c[4] + c[3]) {\n r2[i] <- 3\n count2 <- count2 + 2\n }else\n if(u[i] < c[4] + c[3] + c[1]) {\n r2[i] <- 1\n count2 <- count2 + 3\n }else {\n r2[i] <- 2\n count2 <- count2 + 3\n }\n}\ncount2\n\nlength(r[r == 1]) / length(r)\nlength(r[r == 2]) / length(r)\nlength(r[r == 3]) / length(r)\nlength(r[r == 4]) / length(r)\nrr <- sample(1:4, size=N, prob = c, replace=TRUE)\nlength(rr[rr == 1]) / length(rr)\nlength(rr[rr == 2]) / length(rr)\nlength(rr[rr == 3]) / length(rr)\nlength(rr[rr == 4]) / length(rr)\n\nlength(r2[r2 == 1]) / length(r2)\nlength(r2[r2 == 2]) / length(r2)\nlength(r2[r2 == 3]) / length(r2)\nlength(r2[r2 == 4]) / length(r2)\nlength(rr[rr == 1]) / length(rr)\nlength(rr[rr == 2]) / length(rr)\nlength(rr[rr == 3]) / length(rr)\nlength(rr[rr == 4]) / length(rr)\n\nsample(1:4) \ny <- c(1:5, 3:6)\nsample(y)\nsample(1:4, size=3)\nsample(1:4, size=3, replace=TRUE)\ns <- sample(y, size=900, replace=TRUE) # doar 1, 2 si 6 au prob 1/9, in timp ce 2,4 si 5 au 2/9\nlength(s[s == 1]) / length(s)\nlength(s[s == 2]) / length(s)\nlength(s[s == 3]) / length(s)\nlength(s[s == 4]) / length(s)\nlength(s[s == 5]) / length(s)\nlength(s[s == 6]) / length(s)\n\nt <- sample(1:4, size=100, prob=c(0.2, 0.15, 0.25, 0.4), replace=TRUE)\nlength(t[t == 1]) / length(t)\nlength(t[t == 2]) / length(t)\nlength(t[t == 3]) / length(t)\nlength(t[t == 4]) / length(t)\n", "meta": {"hexsha": "9205606fc65ad8acd686504d46debbc7cf76c81c", "size": 1919, "ext": "r", "lang": "R", "max_stars_repo_path": "Bachelors Year 3/Simulation techniques/Simulation of discrete distributions.r", "max_stars_repo_name": "marianlupascu/School-Projects", "max_stars_repo_head_hexsha": "3da91ac0a5a996028ed3ff9207cc89b1e7f8c20e", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2019-11-26T14:54:52.000Z", "max_stars_repo_stars_event_max_datetime": "2019-11-26T14:54:52.000Z", "max_issues_repo_path": "Bachelors Year 3/Simulation techniques/Simulation of discrete distributions.r", "max_issues_repo_name": "marianlupascu/Bachelors-Projects", "max_issues_repo_head_hexsha": "3da91ac0a5a996028ed3ff9207cc89b1e7f8c20e", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Bachelors Year 3/Simulation techniques/Simulation of discrete distributions.r", "max_forks_repo_name": "marianlupascu/Bachelors-Projects", "max_forks_repo_head_hexsha": "3da91ac0a5a996028ed3ff9207cc89b1e7f8c20e", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-05-21T09:55:24.000Z", "max_forks_repo_forks_event_max_datetime": "2018-05-21T09:55:24.000Z", "avg_line_length": 22.3139534884, "max_line_length": 95, "alphanum_fraction": 0.4898384575, "num_tokens": 827, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9273632856092016, "lm_q2_score": 0.8354835452961425, "lm_q1q2_score": 0.774796765638255}} {"text": "## calculate beta (1st moment of inertia) for piecewise linear function y = f(x)\r\nbeta <- function(x, y) {\r\n\r\n beta <- 0\r\n for (i in 2:length(x)) {\r\n ## for each segment\r\n\r\n if (x[i] != x[i-1]) {\r\n ## not a step change so segment will add to beta for segment of length base\r\n base <- x[i] - x[i-1]\r\n\r\n ## calculate beta for rectangular part\r\n rheight <- min(y[i], y[i-1])\r\n rarea <- base * rheight\r\n rcentroid <- (x[i] + x[i-1]) / 2\r\n beta <- beta + rarea * rcentroid\r\n\r\n ## calculate additional beta for triangular part, if any\r\n if (y[i-1] != y[i]) {\r\n ## there is additional area to consider\r\n theight <- max(y[i], y[i-1]) - rheight\r\n tarea <- base * theight / 2\r\n if (y[i-1] < y[i]) {\r\n ## triangle height increasing with distance\r\n tcentroid <- x[i-1] + base * 2 / 3\r\n } else {\r\n ## triangle height decreases with distance\r\n tcentroid <- x[i-1] + base * 1 / 3\r\n }\r\n beta <- beta + tarea * tcentroid\r\n }\r\n }\r\n }\r\n return(beta)\r\n} \r\n\r\n## x <- c(0, 10, 10, 15, 20)\r\n## y <- c(5, 5, 10, 10, 5)\r\n## beta(x,y)\r\n", "meta": {"hexsha": "ec4103db261bf7f23e8fda09599852abdedcba8f", "size": 1358, "ext": "r", "lang": "R", "max_stars_repo_path": "modules/beta.r", "max_stars_repo_name": "TECComputing/R-setup", "max_stars_repo_head_hexsha": "f4b5e45c6e2e55fcc6f58f804bb50cea3a697fe0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "modules/beta.r", "max_issues_repo_name": "TECComputing/R-setup", "max_issues_repo_head_hexsha": "f4b5e45c6e2e55fcc6f58f804bb50cea3a697fe0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "modules/beta.r", "max_forks_repo_name": "TECComputing/R-setup", "max_forks_repo_head_hexsha": "f4b5e45c6e2e55fcc6f58f804bb50cea3a697fe0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-06-16T12:06:21.000Z", "max_forks_repo_forks_event_max_datetime": "2021-06-16T12:06:21.000Z", "avg_line_length": 33.95, "max_line_length": 88, "alphanum_fraction": 0.4256259205, "num_tokens": 359, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9343951588871157, "lm_q2_score": 0.8289388083214156, "lm_q1q2_score": 0.7745564095091855}} {"text": "newton.raphson <- function(f, ..., xguess=0, tol = 1e-5, n = 1000, plot='no') {\n ## use newton raphson to find x where f(x, ...) = 0\n ## where \"...\" is a list of additional arguments needed by f, if any\n ## starts search from xguess\n\n args <- unlist( list(...) )\n \n ## following modified from https://rpubs.com/aaronsc32/newton-raphson-method\n library(numDeriv) # Package for computing f'(x)\n\n x0 <- xguess # Set start value to supplied guess\n xvalue <- n # Initialize for iteration results\n yvalue <- n # Initialize for iteration results\n\n ## Check to see if xguess result in 0\n ## if (f(x0, ...) == 0.0) return(x0)\n if (length(args) == 1) {\n if (f(x0) == 0.0) return(x0)\n } else {\n if (f(x0, ...) == 0.0) return(x0)\n }\n \n ## iterate to find where f(x, ...) = 0\n xvalue[1] <- x0 # store x values\n yvalue[1] <- f(x0, ...) # store y values\n for (i in 2:(n+1)) {\n dx <- genD(func = f, ..., x = x0)$D[1] # First-order derivative f'(x0)\n x1 <- x0 - (f(x0, ...) / dx) # Calculate next guess x1\n ## Once the difference between x0 and x1 becomes sufficiently small, output the results.\n if (abs(x1 - x0) < tol) {\n root.approx <- tail(xvalue, n=1)\n res <- list('root' = root.approx, 'iterations' = xvalue)\n if (plot != 'no') {\n main <- 'Solution found within tolerance'\n plot(xvalue, yvalue, col='red', main=main)\n points(xvalue[1], yvalue[1], col='black', pch=19) # solid black initial guess\n last <- length(xvalue)\n points(xvalue[last], yvalue[last], col='red', pch=19) # solid red final result\n x <- seq(min(xvalue), max(xvalue), (max(xvalue)-min(xvalue))/100)\n y <- f(x, ...)\n points(x,y,type='l')\n legend('bottomright',\n legend=c('initial guess', 'intermediate steps', 'final result'),\n col =c('black', 'red', 'red'),\n pch =c(19, 1, 19))\n }\n return(res)\n }\n \n ## save new valeus of x and y\n xvalue[i] <- x1\n yvalue[i] <- f(x1, ...)\n \n ## If search has not yet reached convergence, set new x0 guess\n ## check whether solution is bracketed\n if (yvalue[i] / yvalue[i-1] < 0) {\n ## bracketed solution since successive y values have opposite sign\n ## use bisection to keep solution from diverging\n x0 <- (x0 + x1)/2\n } else {\n ## have not bracketed solution so use X1 as next guess\n x0 <- x1\n }\n }\n main <- 'Too many iterations in method'\n plot(xvalue, yvalue, col='red', main=main)\n points(xvalue[1], yvalue[1], col='black', pch=19) # solid black initial guess\n last <- length(xvalue)\n points(xvalue[last], yvalue[last], col='red', pch=19) # solid red final result\n x <- seq(min(xvalue), max(xvalue), (max(xvalue)-min(xvalue))/100)\n y <- f(x, ...)\n points(x,y,type='l')\n legend('bottomright',\n legend=c('initial guess', 'intermediate steps', 'final result'),\n col =c('black', 'red', 'red'),\n pch =c(19, 1, 19))\n}\n\ntest_newton.raphson <- function() {\n set.seed(1)\n \n ## example: this works\n x <- rnorm(1000)\n jparms <- SuppDists::JohnsonFit(x)\n zero <- function(x, parms, z) john_z(x, parms) - z\n x.out <- newton.raphson(\n zero,\n parms = jparms,\n z=2.4,\n xguess = mean(x),\n tol=1E-10,\n plot='yes'\n )\n x.out$root\n \n ## example: this works\n set.seed(1)\n x <- rnorm(1000)\n zero <- function(x, parm1, parm2, z) (x^2 + parm1 + parm2) - z\n plotspace(2,1)\n x.out <- newton.raphson(\n zero,\n parm1 = 11,\n parm2 = mean(x),\n z=30,\n xguess = 30,\n tol=1E-10,\n plot='yes'\n )\n x.out$root\n plot(x, y = x^2 + 11 + mean(x), main='wider view of function')\n \n ## example: this works\n x <- rnorm(1000)\n zero <- function(x, mean, sd, z) (x - mean)/sd - z\n x.out <- newton.raphson(\n zero,\n mean=mean(x),\n sd=sd(x),\n z=2.4,\n xguess = mean(x),\n tol=1E-10,\n plot='yes'\n )\n x.out$root\n\n ## example: This fails because only 1 xguess is passed into the function so sd(xguess) is NA\n ## It aborts when the newton.raphson function tries using the zero function\n ## e.g., zero(x=2, z=3) returns NA\n ## zero(x=c(2,4), z=3) returns -3.71 and -2.29\n ## Note that mean(x) = x also does not make much sense for a single x value, \n ## but that does not make the function abort\n x <- rnorm(1000)\n zero <- function(x, z) (x - mean(x))/sd(x) - z\n x.out <- newton.raphson(\n zero,\n z=2.4,\n xguess = mean(x),\n tol=1E-10,\n plot='yes'\n )\n x.out$root\n}\n", "meta": {"hexsha": "6c2107341a98967e2be4bfa732900d78404f7a1f", "size": 5133, "ext": "r", "lang": "R", "max_stars_repo_path": "modules/newton.raphson.r", "max_stars_repo_name": "dhjelmar/R-setup", "max_stars_repo_head_hexsha": "42436ac2389512261da87dfb0257d34b7ad33b14", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "modules/newton.raphson.r", "max_issues_repo_name": "dhjelmar/R-setup", "max_issues_repo_head_hexsha": "42436ac2389512261da87dfb0257d34b7ad33b14", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "modules/newton.raphson.r", "max_forks_repo_name": "dhjelmar/R-setup", "max_forks_repo_head_hexsha": "42436ac2389512261da87dfb0257d34b7ad33b14", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-06-16T12:06:21.000Z", "max_forks_repo_forks_event_max_datetime": "2021-06-16T12:06:21.000Z", "avg_line_length": 35.6458333333, "max_line_length": 96, "alphanum_fraction": 0.5004870446, "num_tokens": 1517, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8947894604912848, "lm_q2_score": 0.8652240773641087, "lm_q1q2_score": 0.7741933853887005}} {"text": "### Distribuição a priori\n## ! Dica: brinque com os hiperparâmetros da priori e olhe o que acontece com o segundo gráfico.\nalpha <- 1\nbeta <- 2\ntheta <- rgamma(1e6, shape = alpha, rate = beta)\n\ncurve(dgamma(x, shape = alpha, rate = beta), min(theta), max(theta), \n xlab = expression(theta), ylab = expression(xi(theta)), lwd = 3, cex.lab=1.5)\n\n## Gerando alguns dados\n\nn <- 10\n## ! Dica: mude o número de observações e veja o que acontece com a posteriori no segundo gráfico.\n\ntheta.vdd <- 0.65 # theta \"verdadeiro\"\n\nX <- rexp(n = n, rate = theta.vdd)\nmean(X); sd(X)\n\nS <- sum(X)\n\ncurve(dgamma(x, shape = alpha, rate = beta), min(theta), max(theta), \n xlab = expression(theta), ylab = \"Densidade\", lwd = 3, cex.lab = 1.5)\ncurve(dgamma(x, shape = alpha + n + 1, rate = beta + S), min(theta), max(theta), \n lwd = 3, lty = 2, col = \"grey50\", add = TRUE)\nlegend(x = \"topright\", legend = c(\"Priori\", \"Posteriori\"), bty = 'n', lwd = 2, lty = 1:2, col = c(\"black\", \"grey50\"))\n\n## Agora, o aprendizado sequencial\n\ncurve(dgamma(x, shape = alpha, rate = beta), min(theta), max(theta), \n xlab = expression(theta), ylab = \"Densidade\", lwd = 4, cex.lab = 1.5)\nfor(i in 1:n){\n curve(dgamma(x, shape = alpha + n + 1, rate = beta + sum(X[1:i])), min(theta), max(theta), \n lwd = 4, lty = 2, col = rev(heat.colors(n))[i], add = TRUE)\n}\nlegend(x = \"topright\",\n legend = c(\"Priori\", paste(\"Posteriori até x_\", 1:n, sep = \"\")), bty = 'n', lwd = 3, lty = c(1, rep(2, n)),\n col = c(\"black\", rev(heat.colors(n)[1:n])))\n", "meta": {"hexsha": "6f05b1da5c793196a37e1137ba80f362d372192f", "size": 1538, "ext": "r", "lang": "R", "max_stars_repo_path": "code/exemplo_componentes_eletronicos.r", "max_stars_repo_name": "jlduim/Statistical_Inference_BSc", "max_stars_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 33, "max_stars_repo_stars_event_min_datetime": "2020-08-03T15:42:28.000Z", "max_stars_repo_stars_event_max_datetime": "2021-11-30T15:43:10.000Z", "max_issues_repo_path": "code/exemplo_componentes_eletronicos.r", "max_issues_repo_name": "jlduim/Statistical_Inference_BSc", "max_issues_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 23, "max_issues_repo_issues_event_min_datetime": "2020-08-16T23:02:47.000Z", "max_issues_repo_issues_event_max_datetime": "2021-11-07T14:34:43.000Z", "max_forks_repo_path": "code/exemplo_componentes_eletronicos.r", "max_forks_repo_name": "jlduim/Statistical_Inference_BSc", "max_forks_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 10, "max_forks_repo_forks_event_min_datetime": "2020-08-13T00:53:42.000Z", "max_forks_repo_forks_event_max_datetime": "2021-12-10T07:35:56.000Z", "avg_line_length": 39.4358974359, "max_line_length": 117, "alphanum_fraction": 0.6014304291, "num_tokens": 544, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9390248157222395, "lm_q2_score": 0.8244619263765707, "lm_q1q2_score": 0.7741902084857619}} {"text": "### Code skeleton for Series 8, task 2\n\n## read in data\n## data(ozone, package = \"gss\")\n\n## alternative\nozone <- read.table(\"http://stat.ethz.ch/Teaching/Datasets/ozone.dat\", header = TRUE)\n\n###################################################\n### TASK a)\n###################################################\n\nozone$logupo3 <- log(ozone$upo3)\nd.ozone <- subset(ozone, select = -upo3)\npairs(ozone, pch = \".\", gap = 0.1)\n\n## delete outlier\nout <- 92\nd.ozone.e <- d.ozone[-out,]\n\n\n\n###################################################\n### TASK b)\n###################################################\n\n## package for wrapFormula() [sfsmisc := miscellaneous from SfS\n## --- SfS = Seminar für Statistik, ETH Z ]\nrequire(sfsmisc)\n\n## Linear models\n## fit 1 (polynomial of degree 1)\n# write a formula as you know it from lm()\nform1 <- as.formula(logupo3 ~ .)\nfit1 <- lm(form1, d.ozone.e)\n\n\n\n## fits of degree 2 to 5\nform2 <- wrapFormula(f = form1, data = d.ozone.e, wrapString = \"poly(*, degree = 2)\")\nfit2 <- lm(form2, d.ozone.e)\n\nform3 <- wrapFormula(f = form1, data = d.ozone.e, wrapString = \"poly(*, degree = 3)\")\nfit3 <- lm(form3, d.ozone.e)\n\nform4 <- wrapFormula(f = form1, data = d.ozone.e, wrapString = \"poly(*, degree = 4)\")\nfit4 <- lm(form4, d.ozone.e)\n\nform5 <- wrapFormula(f = form1, data = d.ozone.e, wrapString = \"poly(*, degree = 5)\")\nfit5 <- lm(form5, d.ozone.e)\n\n\n## GAM\nrequire(mgcv)\ngamForm <- wrapFormula(form1, data=d.ozone.e, wrapString = \"s(*)\")\ng1 <- gam(formula = gamForm, data = d.ozone.e)\nsummary(g1)\n\n###################################################\n### TASK c)\n###################################################\n\n## plot the fits\n\n## for the linear models\npar(mfrow=c(3, 3))\ntermplot(fit1, partial.resid = TRUE, rug = TRUE, se = TRUE, pch = 19)\n\n\npar(mfrow=c(3, 3))\ntermplot(fit2, partial.resid = TRUE, rug = TRUE, se = TRUE, pch = 19)\n\npar(mfrow=c(3, 3))\ntermplot(fit3, partial.resid = TRUE, rug = TRUE, se = TRUE, pch = 19)\n\npar(mfrow=c(3, 3))\ntermplot(fit4, partial.resid = TRUE, rug = TRUE, se = TRUE, pch = 19)\n\npar(mfrow=c(3, 3))\ntermplot(fit5, partial.resid = TRUE, rug = TRUE, se = TRUE, pch = 19)\n\n\n## for the additive model\nmult.fig(nr.plots = 9, main = \"gam(gamForm, data = d.ozone.e)\")\nplot(g1, shade = TRUE)\n\n\n###################################################\n### TASK d)\n###################################################\n\n\n## Mallows Cp function\n\nCp <- function(object, sigma){\n res <- residuals(object)\n n <- length(res)\n p <- n - object$df.residual\n SSE <- sum(res^2)\n SSE / sigma^2 - n + 2 * p\n}\n\n## set sigma (use estimated sigma from fit5)\nsigma <- sigma(fit5)\n\n## Calculate Mallows's Cp statistic for all 6 models\nCp1 = Cp(fit1, sigma)\nCp2 = Cp(fit2, sigma)\nCp3 = Cp(fit3, sigma)\nCp4 = Cp(fit4, sigma)\nCp5 = Cp(fit5, sigma)\nCpg1 = Cp(g1, sigma)\n \n \n###################################################\n### TASK e)\n###################################################\nrequire(earth)\nm1 <- earth(form1, d.ozone.e, degree = 1)\nsummary(m1)\n\n\n###################################################\n### TASK f)\n###################################################\nset.seed(1)\nn <- nrow(d.ozone.e)\nK <- 10\nfolds <- sample(cut(seq(1, n), breaks = K, labels = FALSE), replace = FALSE)\n\nfold.error.m1 <- numeric(K)\nfold.error.m2 <- numeric(K)\nfold.error.m3 <- numeric(K)\nfold.error.g1 <- numeric(K)\n\nfor (i in 1:K) {\n test.ind <- which(folds == i)\n df.train <- d.ozone.e[-test.ind, ]\n df.test <- d.ozone.e[test.ind, ]\n \n m1i <- earth(formula = form1, data = df.train, degree = 1)\n\n yhat.m1 <- predict(m1i, newdata = df.test, type = \"response\")\n\n fold.error.m1[i] <- mean((yhat.m1 - df.test$logupo3) ** 2)\n\n m2i <- earth(formula = form1, data = df.train, degree = 2)\n\n yhat.m2 <- predict(m2i, newdata = df.test, type = \"response\")\n\n fold.error.m2[i] <- mean((yhat.m2 - df.test$logupo3) ** 2)\n\n m3i <- earth(formula = form1, data = df.train, degree = 3)\n\n yhat.m3 <- predict(m3i, newdata = df.test, type = \"response\")\n\n fold.error.m3[i] <- mean((yhat.m3 - df.test$logupo3) ** 2)\n\n g1i <- gam(formula = gamForm, data = df.train)\n\n yhat.g1 <- predict(g1i, newdata = df.test, type = \"response\")\n\n fold.error.g1[i] <- mean((yhat.g1 - df.test$logupo3) ** 2)\n}\n\nc(m1 = mean(fold.error.m1), m2 = mean(fold.error.m2), m3 = mean(fold.error.m3),\n g1 = mean(fold.error.g1))", "meta": {"hexsha": "9c44641731b5376307a62f602529df6e74d63632", "size": 4349, "ext": "r", "lang": "R", "max_stars_repo_path": "Computational_Statistics/Exercices/8_2.r", "max_stars_repo_name": "DanDoge/course_ethz", "max_stars_repo_head_hexsha": "73e5f77e3694d6134169127c0500898402683c32", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Computational_Statistics/Exercices/8_2.r", "max_issues_repo_name": "DanDoge/course_ethz", "max_issues_repo_head_hexsha": "73e5f77e3694d6134169127c0500898402683c32", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Computational_Statistics/Exercices/8_2.r", "max_forks_repo_name": "DanDoge/course_ethz", "max_forks_repo_head_hexsha": "73e5f77e3694d6134169127c0500898402683c32", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.0419161677, "max_line_length": 85, "alphanum_fraction": 0.5300068981, "num_tokens": 1333, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9219218434359676, "lm_q2_score": 0.8397339736884712, "lm_q1q2_score": 0.7741690930186857}} {"text": "# Group members (Name, Student ID, E-Mail):\n# 1. Baldomero Valdez, Valenzuela, 2905175, baldmer.w@gmail.com\n# 2. Omar Trinidad Gutierrez Mendez, 2850441, omar.vpa@gmail.com\n# 3. Shinho Kang, 2890169, wis.shinho.kang@gmail.com\n\n#=========================================\n# TASK 3\n#=========================================\n# original data\nspecies.richness <- c(32, 29, 35, 36, 41)\nlake.area <- c(2.0, 0.9, 3.1, 3.0, 3.0)\n\n# pearson's correlation - original\ncor.original <- cor(species.richness, lake.area)\n\n# 1000 times of permutations\nN <- 1000\ncnt <- 0\nfor (i in 1:N) {\n # randomly sampling vectors\n species.richness.random <- sample(species.richness)\n lake.area.random <- sample(lake.area)\n \n # pearson's correlation - random\n cor.random <- cor(species.richness.random, lake.area.random)\n \n # if cor.random is greater than or equal to cor.original\n # count variable + 1\n if (cor.random >= cor.original) {\n cnt <- cnt+1\n }\n}\nprint (\"===============\")\nprint (paste(\"P-Value: \", cnt/N))\n\n", "meta": {"hexsha": "f5d939d00c6551995a2e15d856753cbdbeb19138", "size": 1002, "ext": "r", "lang": "R", "max_stars_repo_path": "Ex4/Ex4_3.r", "max_stars_repo_name": "omartrinidad/ml_bioinformatics", "max_stars_repo_head_hexsha": "2ff4962767a9cfe206620f1fc870839e249dde96", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Ex4/Ex4_3.r", "max_issues_repo_name": "omartrinidad/ml_bioinformatics", "max_issues_repo_head_hexsha": "2ff4962767a9cfe206620f1fc870839e249dde96", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Ex4/Ex4_3.r", "max_forks_repo_name": "omartrinidad/ml_bioinformatics", "max_forks_repo_head_hexsha": "2ff4962767a9cfe206620f1fc870839e249dde96", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2019-05-15T02:23:47.000Z", "max_forks_repo_forks_event_max_datetime": "2019-05-15T02:23:47.000Z", "avg_line_length": 27.8333333333, "max_line_length": 64, "alphanum_fraction": 0.6097804391, "num_tokens": 312, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9362850039701655, "lm_q2_score": 0.8267117983401363, "lm_q1q2_score": 0.7740378593910772}} {"text": "train <- function(df, n) {\t# df - input dataframe, n - learning rate\n\tl <- length(df$X1)\t# records in dataframe\n#\tw <- c(0.001,0.001)\n\tw <- c(5.0,5.0)\n\tb <- 0\n\tR <- max(sqrt(df$X1^2 + df$X2^2))\n\t\n\t\n\trepeat {\n\t\tmistake <- FALSE\n\t\tfor (i in 1:l) {\n\t\t\txi <- c(df$X1[i],df$X2[i])\n\t\t\tyi <- df$Y[i]\n\t\t\tif (sign(sum(w*xi) - b) != yi) {\n\t\t\t\tmistake <- TRUE\n\t\t\t\tw <- w + n*yi*xi\n\t\t\t\tb <- b - n*yi*R^2\n\t\t\t}\n\t\t}\n\t\tsurface(list(\"w\"=w,\"b\"=b)) # keep plotting the evolving decision surface\n\t\tif (interactive)\n\t\t\treadline(prompt=\"Paused\")\n\t\tif (!mistake) \n\t\t\tbreak\n\t}\n\n\tfinalsurface(list(\"w\"=w,\"b\"=b)) \t\n\tslope = -(w[1]/w[2])\n#\toffset = - (b/w[2])\n\toffset = (b/w[2])\n\tlist(\"slope\"=slope,\"offset\"=offset)\n\n}\n\nsurface <- function(m) {\n\tw <- m$w\n\tb <- m$b\n\t\n\tslope = -(w[1]/w[2])\n#\toffset = - (b/w[2])\n\toffset = (b/w[2])\n\t\n\t# assumes that there was something like this, plot(0:9,0:9,type=\"n\"), before\n\tabline(offset,slope,lty=\"dashed\")\n}\n\nfinalsurface <- function(m) {\n\tw <- m$w\n\tb <- m$b\n\t\n\tslope = -(w[1]/w[2])\n#\toffset = - (b/w[2])\n\toffset = (b/w[2])\n\t\n\t# assumes that there was something like this, plot(0:9,0:9,type=\"n\"), before\n\tabline(offset,slope,lty=\"solid\",lwd=2,col=\"green\")\n}\n\ndataset <- function(df) {\n\tquartz(width=8,height=8)\n\t# setup the plot\n\tplot(-20:20,-20:20,type=\"n\",main=\"Perceptron Learning\",xlab=\"X1\",ylab=\"X2\")\n\tabline(h=0)\n\tabline(v=0)\n\t\n\t# plot the classes\n\tfor (i in 1:length(df$X1))\n\t\tif (df$Y[i] > 0 )\n\t\t\tpoints(df$X1[i],df$X2[i],col=\"red\")\n\t\telse\n\t\t\tpoints(df$X1[i],df$X2[i],col=\"blue\")\n}\n\n#### main driver routine ###\n#ds <- read.table(\"ds1.csv\", header=TRUE, sep=\",\")\nds <- as.data.frame(list(\"X1\" = c(1,3,4,5,1,2,2.5,3), \"X2\"=c(6,7,1,3,4,1,1.5,1), \"Y\"=c(-1,-1,-1,-1,1,1,1,1)))\ninteractive <- TRUE\n\nrun <- function(learningrate) {\n\tdataset(ds)\n\ttrain(ds,learningrate)\n}\n", "meta": {"hexsha": "4414841105a32708c70650620acef4c795c065f6", "size": 1788, "ext": "r", "lang": "R", "max_stars_repo_path": "assets/perceptron.r", "max_stars_repo_name": "lutzhamel/ds-assets", "max_stars_repo_head_hexsha": "2bc9540e265fcfaa91cb7d69e1368929b8c93642", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "assets/perceptron.r", "max_issues_repo_name": "lutzhamel/ds-assets", "max_issues_repo_head_hexsha": "2bc9540e265fcfaa91cb7d69e1368929b8c93642", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "assets/perceptron.r", "max_forks_repo_name": "lutzhamel/ds-assets", "max_forks_repo_head_hexsha": "2bc9540e265fcfaa91cb7d69e1368929b8c93642", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2022-02-25T17:35:46.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-25T17:35:46.000Z", "avg_line_length": 21.5421686747, "max_line_length": 109, "alphanum_fraction": 0.5648769575, "num_tokens": 733, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9362850039701653, "lm_q2_score": 0.8267117855317474, "lm_q1q2_score": 0.7740378473987746}} {"text": "#!/usr/bin/Rscript\n\nrequire(deSolve)\n\n## =======================================================================\n## Example: Numerical solution of the famous Lorenz equation, with a\n## strange attractor\n## =======================================================================\n\nparameters <- c(a = -8/3,\n b = -10,\n c = 28)\n\nstate <- c(X = 1, Y = 1, Z = 1)\n\n## the Lorenz ODE system\n\nlorenz <- function(t, state, parameters) {\n with(as.list(c(state, parameters)),{\n\n# rate of change\n\n dX <- a*X + Y*Z\n dY <- b * (Y-Z)\n dZ <- -X*Y + c*Y - Z\n\n# return the rate of change\n\n list(c(dX, dY, dZ))\n\n })\n\n}\n\ntimes <- seq(0, 100, by = 0.01)\n\nout <- ode(y = state, times = times, func = lorenz, parms = parameters)\n\nhead(out)\n\npar(oma = c(0, 0, 3, 0))\nplot(out, xlab = \"time\", ylab = \"-\")\nplot(out[, \"X\"], out[, \"Z\"], pch = \".\")\nmtext(outer = TRUE, side = 3, \"Lorenz model\", cex = 1.5)\n", "meta": {"hexsha": "0685f2bbebee54db4a620f003d2478507a6801bc", "size": 940, "ext": "r", "lang": "R", "max_stars_repo_path": "lorenz_attractor.r", "max_stars_repo_name": "siglun/etudes", "max_stars_repo_head_hexsha": "d78a76d9e6a58192041483b3ac90e9d2f5eb84fd", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lorenz_attractor.r", "max_issues_repo_name": "siglun/etudes", "max_issues_repo_head_hexsha": "d78a76d9e6a58192041483b3ac90e9d2f5eb84fd", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lorenz_attractor.r", "max_forks_repo_name": "siglun/etudes", "max_forks_repo_head_hexsha": "d78a76d9e6a58192041483b3ac90e9d2f5eb84fd", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 20.8888888889, "max_line_length": 74, "alphanum_fraction": 0.4425531915, "num_tokens": 285, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.940789742618232, "lm_q2_score": 0.8221891305219504, "lm_q1q2_score": 0.7735071004872537}} {"text": "\r\n\r\n# Goal: To do OLS by MLE.\r\n\r\n# OLS likelihood function\r\n# Note: I am going to write the LF using sigma2=sigma^2 and not sigma.\r\nols.lf1 <- function(theta, y, X) {\r\n beta <- theta[-1]\r\n sigma2 <- theta[1]\r\n if (sigma2 <= 0) return(NA)\r\n n <- nrow(X)\r\n e <- y - X%*%beta # t() = matrix transpose\r\n logl <- ((-n/2)*log(2*pi)) - ((n/2)*log(sigma2)) - ((t(e)%*%e)/(2*sigma2))\r\n return(-logl) # since optim() does minimisation by default.\r\n}\r\n\r\n# Analytical derivatives\r\nols.gradient <- function(theta, y, X) {\r\n beta <- theta[-1]\r\n sigma2 <- theta[1]\r\n e <- y - X%*%beta\r\n n <- nrow(X)\r\n\r\n g <- numeric(length(theta))\r\n g[1] <- (-n/(2*sigma2)) + (t(e)%*%e)/(2*sigma2*sigma2) # d logl / d sigma\r\n g[-1] <- (t(X) %*% e)/sigma2 # d logl / d beta\r\n\r\n return(-g)\r\n}\r\n\r\nX <- cbind(1, runif(1000))\r\ntheta.true <- c(2,4,6) # error variance = 2, intercept = 4, slope = 6.\r\ny <- X %*% theta.true[-1] + sqrt(theta.true[1]) * rnorm(1000)\r\n\r\n# Estimation by OLS --\r\nd <- summary(lm(y ~ X[,2]))\r\ntheta.ols <- c(sigma2 = d$sigma^2, d$coefficients[,1])\r\ncat(\"OLS theta = \", theta.ols, \"\\n\\n\")\r\n\r\ncat(\"\\nGradient-free (constrained optimisation) --\\n\")\r\noptim(c(1,1,1), method=\"L-BFGS-B\", fn=ols.lf1,\r\n lower=c(1e-6,-Inf,-Inf), upper=rep(Inf,3), y=y, X=X)\r\n\r\ncat(\"\\nUsing the gradient (constrained optimisation) --\\n\")\r\noptim(c(1,1,1), method=\"L-BFGS-B\", fn=ols.lf1, gr=ols.gradient,\r\n lower=c(1e-6,-Inf,-Inf), upper=rep(Inf,3), y=y, X=X)\r\n\r\ncat(\"\\n\\nYou say you want a covariance matrix?\\n\")\r\np <- optim(c(1,1,1), method=\"L-BFGS-B\", fn=ols.lf1, gr=ols.gradient,\r\n lower=c(1e-6,-Inf,-Inf), upper=rep(Inf,3), hessian=TRUE,\r\n y=y, X=X)\r\ninverted <- solve(p$hessian)\r\nresults <- cbind(p$par, sqrt(diag(inverted)), p$par/sqrt(diag(inverted)))\r\ncolnames(results) <- c(\"Coefficient\", \"Std. Err.\", \"t\")\r\nrownames(results) <- c(\"Sigma\", \"Intercept\", \"X\")\r\ncat(\"MLE results --\\n\")\r\nprint(results)\r\ncat(\"Compare with the OLS results --\\n\")\r\nd$coefficients\r\n\r\n# Picture of how the loglikelihood changes if you perturb the sigma\r\ntheta <- theta.ols\r\ndelta.values <- seq(-1.5, 1.5, .01)\r\nlogl.values <- as.numeric(lapply(delta.values,\r\n function(x) {-ols.lf1(theta+c(x,0,0),y,X)}))\r\nplot(sqrt(theta[1]+delta.values), logl.values, type=\"l\", lwd=3, col=\"blue\",\r\n xlab=\"Sigma\", ylab=\"Log likelihood\")\r\ngrid()\r\n\r\n", "meta": {"hexsha": "9f95435d505b6db7ad1fe619d83bf346e7806c86", "size": 2417, "ext": "r", "lang": "R", "max_stars_repo_path": "RFrontEndSolution/Tests Repo/Rscripts All (163 files)/p3.r", "max_stars_repo_name": "AlexandrosPlessias/CompilerFrontEndForRLanguage", "max_stars_repo_head_hexsha": "71e3e60476f6f83b05cc97c625265edbde086341", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "RFrontEndSolution/Tests Repo/Rscripts All (163 files)/p3.r", "max_issues_repo_name": "AlexandrosPlessias/CompilerFrontEndForRLanguage", "max_issues_repo_head_hexsha": "71e3e60476f6f83b05cc97c625265edbde086341", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "RFrontEndSolution/Tests Repo/Rscripts All (163 files)/p3.r", "max_forks_repo_name": "AlexandrosPlessias/CompilerFrontEndForRLanguage", "max_forks_repo_head_hexsha": "71e3e60476f6f83b05cc97c625265edbde086341", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 34.5285714286, "max_line_length": 78, "alphanum_fraction": 0.5688870501, "num_tokens": 828, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9381240194661944, "lm_q2_score": 0.8244619263765707, "lm_q1q2_score": 0.7734475362692301}} {"text": "# Polynomial regression for machine learning.\n# \n# polynomial regression is a form of regression analysis in which the\n# relationship between the independent variable x and the dependent variable y is\n# modelled as an nth degree polynomial in x. Polynomial regression fits a\n# nonlinear relationship between the value of x and the corresponding conditional\n# mean of y, denoted E(y |x)Although polynomial regression fits a nonlinear model\n# to the data, as a statistical estimation problem it is linear, in the sense\n# that the regression function E(y | x) is linear in the unknown parameters that\n# are estimated from the data. For this reason, polynomial regression is\n# considered to be a special case of multiple linear regression.\n\n\n# Importing the data set\ndataset = read.csv('Position_Salaries.csv')\ndataset = dataset[2:3]\n\n# no need to split\n# # Splitting the Dataset into a Training set and a Test set\n# # install.packages('caTools')\n# # library(caTools)\n# set.seed(123) # choose random number, only same number for debugging\n# split = sample.split(dataset$Salary, SplitRatio = 0.8)\n# training_set = subset(dataset, split==TRUE)\n# test_set = subset(dataset, split==FALSE)\n\n# Fit Polynomial regression to the dataset\ndataset$Level2 = dataset$Level^2\ndataset$Level3 = dataset$Level^3\ndataset$Level4 = dataset$Level^4\ndataset$Level5 = dataset$Level^5\npoly_reg = lm(formula = Salary ~ ., data = dataset)\nsummary(poly_reg)\n\n# Visualize graphic result of Polynomial regression\nggplot() +\n geom_point(aes(x = dataset$Level, y = dataset$Salary),\n colour='red') +\n geom_line(aes(x = dataset$Level, y = predict(poly_reg, newdata = dataset)),\n colour='blue') +\n xlab('Level') + ylab('Salary')\n\n# Predict a new result with Polynomial regression\ny_pred = predict(poly_reg, newdata = data.frame(Level = 6.5,\n Level2 = 6.5^2,\n Level3 = 6.5^3,\n Level4 = 6.5^4,\n Level5 = 6.5^5))\n", "meta": {"hexsha": "31a02214484f91a6b330ef85c3980a32f91487e3", "size": 2086, "ext": "r", "lang": "R", "max_stars_repo_path": "Regression/PolynomialRegression/regularPolynomialRegression.r", "max_stars_repo_name": "a-holm/MachinelearningAlgorithms", "max_stars_repo_head_hexsha": "a07cdddd079cd57ac77a17487a32c594e735baf8", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Regression/PolynomialRegression/regularPolynomialRegression.r", "max_issues_repo_name": "a-holm/MachinelearningAlgorithms", "max_issues_repo_head_hexsha": "a07cdddd079cd57ac77a17487a32c594e735baf8", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2021-06-01T22:07:30.000Z", "max_issues_repo_issues_event_max_datetime": "2021-06-01T22:07:30.000Z", "max_forks_repo_path": "Regression/PolynomialRegression/regularPolynomialRegression.r", "max_forks_repo_name": "a-holm/MachinelearningAlgorithms", "max_forks_repo_head_hexsha": "a07cdddd079cd57ac77a17487a32c594e735baf8", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 42.5714285714, "max_line_length": 81, "alphanum_fraction": 0.6725790988, "num_tokens": 485, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9381240073565738, "lm_q2_score": 0.8244619177503206, "lm_q1q2_score": 0.7734475181928167}} {"text": "## Author: Sergio García Prado\n## Title: Statistical Inference - Non parametric Tests - Exercise 03\n\nrm(list = ls())\n\n## H0: T(x) >= C(x)\n## H1: T(x) < C(x)\n\nn.c <- 9\nn.t <- 9\n\n(n <- n.c + n.t)\n# 18\n\n(W.t <- sum(1:8) + 18)\n# 54\n\n(W.t.mean <- n.t * (n + 1) / 2)\n# 85.5\n\n(W.t.var <- n.t * n.c * (n + 1) / 12)\n# 128.25\n\n(W.tc <- W.t - n.t * (n.t + 1) / 2)\n# 9\n\n(W.tc.mean <- n.t * n.c / 2)\n# 40.5\n\n(W.tc.var <- n.t * n.c * (n + 1) / 12)\n# 128.25\n\npnorm((W.tc + 0.5 - W.tc.mean) / sqrt(W.tc.var))\n# 0.00309665908702214\n\n\npwilcox(W.tc, n.t, n.c)\n# 0.00199506375976964\n\n## We'll reject H0 due to there aren't enough evidences in favor of T >= C,\n## so we assume that T < C\n", "meta": {"hexsha": "8fa066c54d239da71993a61f33f1a59e086a8056", "size": 667, "ext": "r", "lang": "R", "max_stars_repo_path": "statistical-inference/non-parametric/exercise-03.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "statistical-inference/non-parametric/exercise-03.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "statistical-inference/non-parametric/exercise-03.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 15.880952381, "max_line_length": 75, "alphanum_fraction": 0.5157421289, "num_tokens": 296, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9626731158685838, "lm_q2_score": 0.803173791645582, "lm_q1q2_score": 0.7731938165874371}} {"text": "dat = read.table(file=\"cookies.dat\", header=TRUE)\n\ntable(dat$location)\n\nhist(dat$chips)\n\nboxplot(chips ~ location, data=dat)\n\n\nset.seed(112)\nn_sim = 500 #number of monti carlo samples \nalpha_pri = rexp(n_sim, rate=1.0/2.0) # draw for alpha prior from exponential dist \nbeta_pri = rexp(n_sim, rate=5.0) # draw beta prior from exp \nmu_pri = alpha_pri/beta_pri # simulate mean of lambda \nsig_pri = sqrt(alpha_pri/beta_pri^2) # standard dev \n\nsummary(mu_pri) # shows lambda of gamma (gamma decides how correlated our groups are)\n\nsummary(sig_pri) # SD of gamma \n\nlam_pri = rgamma(n=n_sim, shape=alpha_pri, rate=beta_pri) # sample from gamma to get lambda distribution, to tighten values then we could modify prior to be gamma dists \nsummary(lam_pri)\n\ny_pri = rpois(n_sim, lam_pri)\nsummary(y_pri)\n\nlam_pri = rgamma(n=5, shape=alpha_pri[1:5], rate=beta_pri[1:5])\n\ny_pri = rpois(n=150, lambda=rep(lam_pri, each=30)) \n\n\nlibrary(\"rjags\")\n\n# place priors on mean and SD of gamma distribution, using informative priors \n\nmod_string = \" model {\nfor (i in 1:length(chips)) {\n chips[i] ~ dpois(lam[location[i]])\n}\n\nfor (j in 1:max(location)) {\n lam[j] ~ dgamma(alpha, beta)\n}\n\nalpha = mu^2 / sig^2\nbeta = mu / sig^2\n\nmu ~ dgamma(2.0, 1.0/5.0)\nsig ~ dexp(1.0)\n\n} \"\n\nset.seed(113)\n\ndata_jags = as.list(dat)\n\nparams = c(\"lam\", \"mu\", \"sig\")\n\nmod = jags.model(textConnection(mod_string), data=data_jags, n.chains=3)\nupdate(mod, 1e3)\n\nmod_sim = coda.samples(model=mod,\n variable.names=params,\n n.iter=5e3)\nmod_csim = as.mcmc(do.call(rbind, mod_sim))\n\n## convergence diagnostics\nplot(mod_sim)\n\ngelman.diag(mod_sim)\nautocorr.diag(mod_sim)\nautocorr.plot(mod_sim)\neffectiveSize(mod_sim)\n\n## compute DIC\ndic = dic.samples(mod, n.iter=1e3)\n\n## observation level residuals\n(pm_params = colMeans(mod_csim))\n\nyhat = rep(pm_params[1:5], each=30)\nresid = dat$chips - yhat \nplot(resid)\n\nplot(jitter(yhat), resid)\n\nvar(resid[yhat<7])\n\nvar(resid[yhat>11])\n\n## location level residuals\nlam_resid = pm_params[1:5] - pm_params[\"mu\"] # mu is the global eatimate for lambda (number of chips in cookies globally) \nplot(lam_resid)\nabline(h=0, lty=2)\n\nsummary(mod_sim)\n\n\nn_sim = nrow(mod_csim)\n\nlam_pred = rgamma(n=n_sim, shape=mod_csim[,\"mu\"]^2/mod_csim[,\"sig\"]^2, \n rate=mod_csim[,\"mu\"]/mod_csim[,\"sig\"]^2)\nhist(lam_pred)# prediction of lambda for new locations\n\nmean(lam_pred > 15) # probability the new location's lambda is > 15\n\ny_pred = rpois(n=n_sim, lambda=lam_pred)\nhist(y_pred) # posterior distribution of the number of chips per cookies of new lcations \n\nmean(y_pred > 15)\n\nhist(dat$chips)\n\ny_pred1 = rpois(n=n_sim, lambda=mod_csim[,\"lam[1]\"]) # use lambda for location 1 \nhist(y_pred1) # posterior predictive dist for number of chips for a future cookie in location 1 \n\nmean(y_pred1 < 7) # prob the next cookie will have less than 7 chips \n", "meta": {"hexsha": "a349cd99b373eb75ad99998e3273ec43ee92e1cd", "size": 2883, "ext": "r", "lang": "R", "max_stars_repo_path": "montyCarlo/hieratchicalModel.r", "max_stars_repo_name": "CharlieShelbourne/algos_practice", "max_stars_repo_head_hexsha": "bf32a739a9ab88f177461057fededb42e2d7fe10", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "montyCarlo/hieratchicalModel.r", "max_issues_repo_name": "CharlieShelbourne/algos_practice", "max_issues_repo_head_hexsha": "bf32a739a9ab88f177461057fededb42e2d7fe10", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "montyCarlo/hieratchicalModel.r", "max_forks_repo_name": "CharlieShelbourne/algos_practice", "max_forks_repo_head_hexsha": "bf32a739a9ab88f177461057fededb42e2d7fe10", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 24.4322033898, "max_line_length": 169, "alphanum_fraction": 0.7020464794, "num_tokens": 880, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9230391579526935, "lm_q2_score": 0.8376199633332891, "lm_q1q2_score": 0.7731560256395252}} {"text": "#!/usr/bin/Rscript\n\nrequire(deSolve)\n\n## =======================================================================\n## Example: Analytical and numerical solutions of logistic growth\n## =======================================================================\n\n## the derivative of the logistic\nlogist <- function(t, x, parms) {\n with(as.list(parms), {\n dx <- r * x[1] * (1 - x[1]/K)\n list(dx)\n })\n}\n\ntime <- 0:100\nN0 <- 0.1; r <- 0.5; K <- 100\nparms <- c(r = r, K = K)\nx <- c(N = N0)\n\n## analytical solution\nplot(time, K/(1 + (K/N0-1) * exp(-r*time)), ylim = c(0, 120),\n type = \"l\", col = \"red\", lwd = 2)\n\n## reasonable numerical solution with rk4\ntime <- seq(0, 100, 2)\nout <- as.data.frame(rk4(x, time, logist, parms))\npoints(out$time, out$N, pch = 16, col = \"blue\", cex = 0.5)\n\n## same time step with euler, systematic under-estimation\ntime <- seq(0, 100, 2)\nout <- as.data.frame(euler(x, time, logist, parms))\npoints(out$time, out$N, pch = 1)\n\n## unstable result\ntime <- seq(0, 100, 4)\nout <- as.data.frame(euler(x, time, logist, parms))\npoints(out$time, out$N, pch = 8, cex = 0.5)\n\n## method with automatic time step\nout <- as.data.frame(lsoda(x, time, logist, parms))\npoints(out$time, out$N, pch = 1, col = \"green\")\n\nlegend(\"bottomright\",\n c(\"analytical\",\"rk4, h=2\", \"euler, h=2\",\n \"euler, h=4\", \"lsoda\"),\n lty = c(1, NA, NA, NA, NA), lwd = c(2, 1, 1, 1, 1),\n pch = c(NA, 16, 1, 8, 1),\n col = c(\"red\", \"blue\", \"black\", \"black\", \"green\"))\n\n", "meta": {"hexsha": "1c417deb66c8398cce30ba3426b0e1832ad73d8e", "size": 1460, "ext": "r", "lang": "R", "max_stars_repo_path": "runge_kutta.r", "max_stars_repo_name": "siglun/etudes", "max_stars_repo_head_hexsha": "d78a76d9e6a58192041483b3ac90e9d2f5eb84fd", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "runge_kutta.r", "max_issues_repo_name": "siglun/etudes", "max_issues_repo_head_hexsha": "d78a76d9e6a58192041483b3ac90e9d2f5eb84fd", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "runge_kutta.r", "max_forks_repo_name": "siglun/etudes", "max_forks_repo_head_hexsha": "d78a76d9e6a58192041483b3ac90e9d2f5eb84fd", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 28.0769230769, "max_line_length": 74, "alphanum_fraction": 0.5287671233, "num_tokens": 508, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9230391579526935, "lm_q2_score": 0.837619961306541, "lm_q1q2_score": 0.7731560237687574}} {"text": "#' Coefficient of variation (CV)\n#'\n#' @description Coefficient of variation\n#'\n#' @param x numeric vector\n#' @param perc as percentage (default = T)\n#'\n#' @return Coefficient of variation\n#' @export\n#'\n#' @examples\n#'\n#' x <- rnorm(100,1)\n#'\n#' cv(x)\n#'\n\ncv <- function(x, perc = TRUE){\n\n if(!is.numeric(x)){\n stop(\"x must be numeric.\")\n }\n\n if(!is.logical(perc)){\n stop(\"perc must be logical.\")\n }\n\n mu_x <- mean(x, na.rm = TRUE)\n\n if(is.na(mu_x)){\n return(NA_real_)\n }else{\n\n if(mu_x == 0){\n warning(\"mean = 0 -> cv is NaN.\")\n }\n\n if(perc == T){\n out <- 100*sd(x, na.rm = TRUE)/mu_x\n } else{\n out <- sd(x, na.rm = TRUE)/mu_x\n }\n\n out <- abs(round(out,2))\n\n return(out)\n }\n\n}\n", "meta": {"hexsha": "eb816949e094257c94cdb1962ba1b61c776e5de7", "size": 731, "ext": "r", "lang": "R", "max_stars_repo_path": "R/cv.r", "max_stars_repo_name": "vbfelix/relper", "max_stars_repo_head_hexsha": "edb2f21087857eb4a3f44cf2af9292db632fe210", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 7, "max_stars_repo_stars_event_min_datetime": "2020-05-09T23:13:37.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-31T00:45:50.000Z", "max_issues_repo_path": "R/cv.r", "max_issues_repo_name": "vbfelix/relper", "max_issues_repo_head_hexsha": "edb2f21087857eb4a3f44cf2af9292db632fe210", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/cv.r", "max_forks_repo_name": "vbfelix/relper", "max_forks_repo_head_hexsha": "edb2f21087857eb4a3f44cf2af9292db632fe210", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2021-12-17T12:27:58.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-19T12:50:55.000Z", "avg_line_length": 14.62, "max_line_length": 42, "alphanum_fraction": 0.5335157319, "num_tokens": 235, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.907312226373181, "lm_q2_score": 0.8519528076067262, "lm_q1q2_score": 0.772987198634541}} {"text": "p_grid <- seq(from=0, to=1, length.out=1000)\nprob_p <- rep(1, 1000)\nprob_data <- dbinom(6, size=9, prob=p_grid)\nposterior <- prob_data * prob_p\nposterior <- posterior / sum(posterior)\n\nset.seed(100)\nsamples <- sample(p_grid, prob=posterior, size=1e4, replace=TRUE)\n\n# 3E1\nsum(samples < .2) / 1e4\n# [1] 4e-04\n\n# 3E2\nsum(samples > .8) / 1e4\n# [1] 0.1116\n\n# 3E3\nsum(samples > .2 & samples < .8) / 1.e4\n# [1] 0.888\n\n# 3E4\nquantile(samples, .2)\n# 20%\n# 0.5185185\n\n# 3E5\nquantile(samples, .8)\n# 80%\n# 0.7557558\n\n# 3E6\nHPDI(samples, prob=.66)\n# |0.66 0.66|\n# 0.5085085 0.7737738\n\n# 3E7\nPI(samples, prob=.66)\n# 17% 83%\n# 0.5025025 0.7697698\n\n# 3M1\np_grid <- seq(from=0, to=1, length.out=1000)\np_prior <- rep(1, 1000)\nlikelihood <- dbinom(8, size=15, prob=p_grid)\nposterior <- likelihood * p_prior\nposterior <- posterior / sum(posterior)\n\n# 3M2\nsamples <- sample(p_grid, 1e4, replace=TRUE, prob=posterior)\nHPDI(samples, .9)\n# |0.9 0.9|\n# 0.3293293 0.7167167\n\n# 3M3\n# Weighted by the posterior samples.\nw <- rbinom(1e4, size=15, prob=samples)\n\ntable(w)[9] / 1e4\n# 8\n# 0.1483\n\n# 3M4\n# So I've got this posterior distribution of `p`.\n# That's actually not related to the size of the trial.\n# Let's sample binomially, randomly, at this size, with these parameter\n# likelihoods.\n\n# Sample the parameter space (done)\nsamples <- sample(1e4, p_grid, prob=posterior, replace=TRUE)\n# Do a random binomial trial for all of those parameters\nw <- rbinom(1e4, size=9, prob=samples)\n# Events over event space:\nsum(w == 6) / 1e4\n# [1] 0.1777\n\n# 3M5\n## 3M1*\np_grid <- seq(from=0, to=1, length.out=1000)\np_prior <- rep(1, 1000)\np_prior[1:500] = 0\nlikelihood <- dbinom(8, size=15, prob=p_grid)\n\nposterior <- p_prior * likelihood\nposterior <- posterior / sum(posterior)\n\n## 3M2*\nsamples <- sample(p_grid, 1e4, prob=posterior, replace=TRUE)\nHPDI(samples, prob=.9)\n# |0.9 0.9|\n# 0.5005005 0.7107107\n\n## 3M3*\nw <- rbinom(1e4, size=15, prob=samples)\nmean(w == 8)\n# [1] 0.1588\n\n## 3M4*\nw <- rbinom(1e4, size=15, prob=samples)\nmean(w == 6)\n# [1] 0.233\n\n# 3M6\n# This seems really suspect. But all the solutions I've been finding are\n# using the .7 true probability to get the likelihood.\n#\n# I found a solution that did a complicated (to me lol) R thing with maps and\n# declarative coding using tidyverse stuff\n# (https://sr2-solutions.wjakethompson.com/bayesian-inference.html). I didn't\n# want to blindly copy-paste that, or go that deep into R yet. Another solution\n# did guess and check with a function.\n# This is my linear-search solution. It agrees with the fancy R one:\n\nassumed_water_percentage <- .7\nprior <- rep(1, 1000)\nsize <- 1\np_grid <- seq(from=0, to=1, length.out=1000)\np_99_interval <- 1\nwhile (p_99_interval > .05) {\n\tif (size > 10000) {\n\t\tbreak;\n\t}\n\n\tsize <- size + 1\n\tlikelihood <- dbinom(floor(size * assumed_water_percentage), size, p_grid)\n\tposterior <- likelihood * prior\n\tposterior <- posterior / sum(posterior)\n\tsamples <- sample(p_grid, 1e4, prob=posterior, replace=TRUE)\n\tinterval <- PI(samples, prob=.99)\n\tp_99_interval <- interval[2] - interval[1]\n}\n\nsize\n# 2169\n# I still don't understand why it's reasonable to choose .7 as the binomial\n# probability for the simulation?\n#\n# What is this problem trying to teach? Strategies for simulation?\n\n# 3H1\n# Birth probability, we will model as bionmial.\np_grid <- seq(from=0, to=1, length.out=1000)\nnum_births <- length(birth1) + length(birth2)\nnum_boys <- (sum(birth1) + sum(birth2))\n\nprior <- rep(1, length(p_grid))\n# Binomial distribution on the total number of boys observed out of the number\n# of births.\nlikelihood <- dbinom(num_boys, size=num_births, prob=p_grid)\nposterior <- likelihood * prior\nposterior <- posterior / sum(posterior)\n\n# Value for `p` probability of male birth, with maximal posterior density.\np_grid[which.max(posterior)]\n#[1] 0.5545546\n\n# 3H2\nsamples <- sample(p_grid, 1e4, prob=posterior, replace=TRUE)\n\nHPDI(prob= .5, samples)\nHPDI(prob= .89, samples)\nHPDI(prob= .97, samples)\n# |0.5 0.5|\n# 0.5305305 0.5775776\n\n# |0.89 0.89|\n# 0.4994995 0.6106106\n\n# |0.97 0.97|\n# 0.4794795 0.6296296\n\n# 3H3\nsimulated <- rbinom(1e4, 200, prob=samples)\n\nsimplhist(simulated, xlab=\"binomial trials, randomly performed, with probabilities as weighted samples from the posterior distribution\")\n# Yup, looks good\n\n# 3H4\n# Do the same binomial trial, but only one birth, since we're looking at first\n# borns.\nsimulated <- rbinom(1e4, 200, prob=samples)\ndens(simulated)\n\n# Looks like the model is skewed male. Mean birth value is .554 on the model,\n# vs .51 in birth1. Birth2 is at .6, inidicating that the second birth skews\n# male.\n# 3H5\n# Second births that followed female first borns\n# Recall, male = 1, female = 0, so we can identify sequence female -> male by\n# counting 1s in the subtraction.\nsequence <- birth2 - birth1\nfemale_after_male <- sum(sequence == 1)\n\n# We want to check the independence of the first/second births.\n\n# Ok damn. I wasn't reading literally.\n# Get the number of firstborn girls\nfemale_first_borns <- sum(birth1 == 0)\n\n# Still using our sampled posterior for the random binomial trial.\n\n# So what this says: From the count of female first borns, simulate male birth\n# binomial trials. I.e. consider each second birth an event in a binomial trial\n# of size female_first_borns.\nmale_second_birth_simulations <- rbinom(1e4, female_first_borns, prob=samples)\n#\nmedian(male_second_birth_simulations)\n# 27\nchainmode(male_second_birth_simulations)\n# [1] 27.1417\n\n# Actual\nsum((birth2 - birth1) == 1)\n# 39\n\nSo our model is underestimating male births after female births.\n", "meta": {"hexsha": "87a8498434baf373c4b4f45a83babc4479e38572", "size": 5615, "ext": "r", "lang": "R", "max_stars_repo_path": "chapter_3/code.r", "max_stars_repo_name": "MannySchneck/statistical-relearning-code", "max_stars_repo_head_hexsha": "495e4b738d88c4b6197f679b4a90ee13e9cc0bf6", "max_stars_repo_licenses": ["Unlicense"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "chapter_3/code.r", "max_issues_repo_name": "MannySchneck/statistical-relearning-code", "max_issues_repo_head_hexsha": "495e4b738d88c4b6197f679b4a90ee13e9cc0bf6", "max_issues_repo_licenses": ["Unlicense"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "chapter_3/code.r", "max_forks_repo_name": "MannySchneck/statistical-relearning-code", "max_forks_repo_head_hexsha": "495e4b738d88c4b6197f679b4a90ee13e9cc0bf6", "max_forks_repo_licenses": ["Unlicense"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 25.8755760369, "max_line_length": 136, "alphanum_fraction": 0.7008014248, "num_tokens": 1903, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9399133498259923, "lm_q2_score": 0.8221891261650247, "lm_q1q2_score": 0.7727865357642738}} {"text": "#' @export\r\nr_squared <- function(X, y){\r\n y.bar <- mean(y)\r\n e.hat <- residual(X, y)\r\n \r\n 1 - sum(e.hat^2)/sum((y-y.bar)^2)\r\n}\r\n\r\n#' @export\r\nadjusted_r_squared <- function(X, y){\r\n y.bar <- mean(y)\r\n e.hat <- residual(X, y)\r\n n <- dim(X)[1]\r\n k <- dim(X)[2]\r\n\r\n 1 - (n-1)*sum(e.hat^2)/((n-k)*sum((y-y.bar)^2))\r\n}\r\n\r\n#' @export\r\nr.tilde_squared <- function(X, y){\r\n y.bar <- mean(y)\r\n e.tilde <- prediction_error(X, y)\r\n \r\n 1 - sum(e.tilde^2)/sum((y-y.bar)^2)\r\n}", "meta": {"hexsha": "175f2300919c40688efbb019a2bbd40692145b1f", "size": 502, "ext": "r", "lang": "R", "max_stars_repo_path": "R/measures_of_fit.r", "max_stars_repo_name": "kevinkevin556/econometrics", "max_stars_repo_head_hexsha": "735a25f3eea03d9d1d1d27d90e7c1ef311604c84", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/measures_of_fit.r", "max_issues_repo_name": "kevinkevin556/econometrics", "max_issues_repo_head_hexsha": "735a25f3eea03d9d1d1d27d90e7c1ef311604c84", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/measures_of_fit.r", "max_forks_repo_name": "kevinkevin556/econometrics", "max_forks_repo_head_hexsha": "735a25f3eea03d9d1d1d27d90e7c1ef311604c84", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 20.08, "max_line_length": 52, "alphanum_fraction": 0.4780876494, "num_tokens": 178, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9343951607140233, "lm_q2_score": 0.8267117876664789, "lm_q1q2_score": 0.772475493700797}} {"text": "#задание 2\nprint (\"task 2\")\nA <- matrix (c(1,5,13,14,-12,-4,11,-13,9,3,-8,-1,-5,7,0,-11,0,-6,3,13,12,0,4,2,8,6,12,-11,4,10,13,-1,5,0,5,4),6,6)\nA\n#определитель\ndet(A) # Определитель A\n\n#задание 4\nprint (\"task 4\")\nA <- matrix (c(7,-8,2,-5,1,7,-5,-7,3,-7,8,-4,9,5,0,-12,8,8,-10,5,-6,-2,-10,-7,0,1,5,5,12,-1,3,10,5,8,-5,-5),6,6)\nA\nB <- matrix (c(3,4,-7,-2,-9,-9,-1,-3,2,0,8,5,-5,9,5,0,-4,-2,8,7,0,3,-2,0,-8,-3,0,8,1,8,-2,-3,1,0,-4,-2),6,6)\nB\nx <- solve(B,A)\nprint (\"x равен\")\nx\n\n#задание 5\nprint (\"5 task\")\na <- c(3,3,-2,1,2,3,-4,0,-1,2,3,3)\nb <- c(-2,3,3,1,1,1,0,-1,2,4,-4,2)\np <- c(4,2,2,2,5,1,3,3,0,-3,-2,-1)\n\nfir <- ((3)*a)+(4*b)\nprint (\"first answer\")\nfir\nsec <- ((2)*as.numeric(a%*%b))*p-1*(norm(p, type=\"2\"))*a\nprint (\"second answer\")\nsec\nthr <- 3*as.numeric(a%*%p)*b-2*as.numeric(b%*%p)*a-2*(norm(p, type=\"2\"))*p\nprint (\"third answer\")\nthr\n\n#6 задание\nprint (\"sixth task\")\ninstall.packages(\"lpSolveAPI\") # Загружаем библиотеку\nlibrary(lpSolveAPI) # Активируем библиотеку линейного программирования\nM <- make.lp(ncol= 2) # Объявляем количество неотрицательных переменных в M\nname.lp(M, \"Example\") # Объявляем название \"Example\"для задачи(модели) М\ncolnames(M) <- c(\"X1\", \"X2\") # Объявляем названия переменных в модели М\nlp.control(M, sense = \"max\")$sense# Объявляем задачу на минимум модели М\nset.objfn(M, c(1,1)) # Задаем целевую функцию:\nadd.constraint(M, c(2,1), \"<=\", 20) # Задаем ограничение:\nadd.constraint(M, c(0.7, 2.1), \">=\",30) #\n\nrownames(M) <- c(\"A\", \"B\") # Называем ограничения в модели М\nM # Выводим модель M на экран\nsolve.lpExtPtr(M)\nget.variables(M) # Оптимальный план\nget.objective(M) # Достигнутый min\nX1.opt<- get.variables(M)[1]; X1.opt # Оптимальное значение для X1\nX2.opt<- get.variables(M)[2]; X2.opt # Оптимальное значение для X2\nf.max<- get.objective(M); f.max# Значение целевой функции на оптимальном решении\n", "meta": {"hexsha": "3405738c2438bce132ca0d6ff70d12305e67e554", "size": 1839, "ext": "r", "lang": "R", "max_stars_repo_path": "Tasks/Task 1/solution.r", "max_stars_repo_name": "Master-sniffer/Doing-some-tasks-with-R", "max_stars_repo_head_hexsha": "629e7add02437ea22c079ecd7a4279e46028b69c", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Tasks/Task 1/solution.r", "max_issues_repo_name": "Master-sniffer/Doing-some-tasks-with-R", "max_issues_repo_head_hexsha": "629e7add02437ea22c079ecd7a4279e46028b69c", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Tasks/Task 1/solution.r", "max_forks_repo_name": "Master-sniffer/Doing-some-tasks-with-R", "max_forks_repo_head_hexsha": "629e7add02437ea22c079ecd7a4279e46028b69c", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 34.0555555556, "max_line_length": 114, "alphanum_fraction": 0.6296900489, "num_tokens": 901, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.939024825960626, "lm_q2_score": 0.8221891327004132, "lm_q1q2_score": 0.7720560072407234}} {"text": "confidence_interval <- function(vector, interval) {\r\n # Standard deviation of sample\r\n vec_sd <- sd(vector)\r\n # Sample size\r\n n <- length(vector)\r\n # Mean of sample\r\n vec_mean <- mean(vector)\r\n # Error according to t distribution\r\n error <- qt((interval + 1)/2, df = n - 1) * vec_sd / sqrt(n)\r\n # Confidence interval as a vector\r\n ans <- c(\"lower\" = vec_mean - error, \"upper\" = vec_mean + error)\r\n return(ans)\r\n}\r\nvector <- c( 29, 30, 53, 75, 89, 34, 21, 12, 58, 84, 92, 117, 115, 119, 109, 115, 134, 253, 289, 287 )\r\nconfidence_interval(vector, 0.95)\r\n", "meta": {"hexsha": "c7f076886a99b0d8cf47b0f64bd44c4415a68a7a", "size": 564, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH5/EX5.18/Ex5_18.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH5/EX5.18/Ex5_18.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH5/EX5.18/Ex5_18.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 35.25, "max_line_length": 103, "alphanum_fraction": 0.6276595745, "num_tokens": 189, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9416541659378681, "lm_q2_score": 0.8198933425148213, "lm_q1q2_score": 0.7720559816038048}} {"text": "## 2. Plotting the Residuals ##\n\nlibrary(readr)\nwilliamsburg_north <- suppressMessages(read_csv(\"williamsburg_north.csv\"))\nlibrary(dqanswerchecking)\ncondos_lm_fit <- lm(sale_price ~ gross_square_feet, data = williamsburg_north)\n\nlibrary(ggplot2)\nresiduals_df <- data.frame(condos_lm_fit$residuals)\n\nggplot(data = residuals_df, aes(x = condos_lm_fit.residuals)) +\n geom_histogram()\n\n## 4. The t-statistic ##\n\nt_statistic <- (1926.6 - 0) / 169.5\n\n## 5. The p-value ##\n\np_value <- coef(summary(condos_lm_fit))[, 4][[2]]\nreject_null_hypothesis <- TRUE\n\n## 6. Confidence Intervals ##\n\nslope_CI_lower <- condos_lm_fit$coefficients[[2]] - 2 * \n coef(summary(condos_lm_fit))[, 2][[2]]\n\nslope_CI_upper <- condos_lm_fit$coefficients[[2]] + 2 * \n coef(summary(condos_lm_fit))[, 2][[2]]\n\nslope_CI <- confint(condos_lm_fit)[2,]\n\n## 7. Residual Standard Error ##\n\nlibrary(dplyr)\n# Add residuals and squared-residuals\nwilliamsburg_north <- williamsburg_north %>%\n mutate(residuals = resid(condos_lm_fit)) %>% \n mutate(resid_squared = residuals^2)\n# Compute the residual sum of squares (RSS)\nRSS <- williamsburg_north %>% \n summarise(RSS = sum(resid_squared)) %>% \n pull()\n# Extract RSS from model output\nRSS_from_lm <- deviance(condos_lm_fit)\n# Optional: check RSS equality\nnear(RSS, deviance(condos_lm_fit))\n# Manual RSE\nRSE <- sqrt(RSS / (nrow(williamsburg_north) - 2))\n# Alternate method for RSE\nRSE <- sqrt(1 / (nrow(williamsburg_north) - 2) * RSS)\nlm_fit_sigma <- sigma(condos_lm_fit)\nare_equal <- near(RSE, lm_fit_sigma)\n\n## 8. The R-squared Statistic ##\n\n# Add residuals and squared-residuals\nwilliamsburg_north <- williamsburg_north %>%\n mutate(residuals = resid(condos_lm_fit)) %>% \n mutate(resid_squared = residuals^2)\n# Compute the residual sum of squares (RSS)\nRSS <- williamsburg_north %>% \n summarise(RSS = sum(resid_squared)) %>% \n pull()\nTSS <- sum((williamsburg_north$sale_price - \n mean(williamsburg_north$sale_price))^2)\n\nr_squared <- 1 - RSS/TSS\n\nlm_r_squared <- summary(condos_lm_fit)$r.squared\n\nare_equal <- near(r_squared, lm_r_squared)\n\nadj_r_squared <- summary(condos_lm_fit)$adj.r.squared", "meta": {"hexsha": "e55bca45d701aec4eeca7fd2c60c59f23d79db68", "size": 2123, "ext": "r", "lang": "R", "max_stars_repo_path": "Data Analyst in R/Step 6 - Predictive Modeling and Machine Learning in R/1. Linear Regression Modeling in R/4. Assessing the Accuracy of the Model.r", "max_stars_repo_name": "MyArist/Dataquest", "max_stars_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 8, "max_stars_repo_stars_event_min_datetime": "2020-07-27T12:04:54.000Z", "max_stars_repo_stars_event_max_datetime": "2021-03-01T04:39:33.000Z", "max_issues_repo_path": "Data Analyst in R/Step 6 - Predictive Modeling and Machine Learning in R/1. Linear Regression Modeling in R/4. Assessing the Accuracy of the Model.r", "max_issues_repo_name": "myarist/Dataquest", "max_issues_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Data Analyst in R/Step 6 - Predictive Modeling and Machine Learning in R/1. Linear Regression Modeling in R/4. Assessing the Accuracy of the Model.r", "max_forks_repo_name": "myarist/Dataquest", "max_forks_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 15, "max_forks_repo_forks_event_min_datetime": "2021-03-30T06:45:19.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-17T03:55:02.000Z", "avg_line_length": 28.6891891892, "max_line_length": 78, "alphanum_fraction": 0.7249175695, "num_tokens": 644, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9263037262250325, "lm_q2_score": 0.8333245932423309, "lm_q1q2_score": 0.7719116758753307}} {"text": "# Polynomial Regression\n\n# Importing the dataset\ndataset = read.csv('Position_Salaries.csv')\ndataset = dataset[2:3] # Select the second column \"Level\" and the third column \"Salary\" only\n\n# Splitting the data set into the Training set and Test set\n#library(caTools)\n#set.seed(123)\n#split = sample.split(dataset$Profit, SplitRatio = 0.8)\n#training_set = subset(dataset, split == TRUE)\n#test_set = subset(dataset, split == FALSE)\n\n# Feature Scaling\n# training_set = scale(training_set)\n# test_set = scale(test_set)\n\n# Fitting Linear Regression to the dataset\nlin_reg = lm(formula = Salary ~ .,\n data = dataset)\nsummary(lin_reg)\n\n# Fitting Polynomial Regression to the dataset\ndataset$Level2 = dataset$Level^2 # Create a new column in which values are the squared \"Level\" value\ndataset$Level3 = dataset$Level^3 \ndataset$Level4 = dataset$Level^4\npoly_reg = lm(formula = Salary ~.,\n data = dataset)\nsummary(poly_reg)\n\n# Visualizing the Linear Regression results\nggplot() +\n geom_point(aes(x = dataset$Level, y = dataset$Salary),\n color = 'red') +\n geom_line(aes(x = dataset$Level, y = predict(lin_reg, newdata = dataset)),\n color = 'blue') +\n ggtitle('Truth or Bluff (Linear Regression)') +\n xlab('Level') +\n ylab('Salary')\n\n# Visualizing the Polynomial Regression results\nggplot() +\n geom_point(aes(x = dataset$Level, y = dataset$Salary),\n color = 'red') +\n geom_line(aes(x = dataset$Level, y = predict(poly_reg, newdata = dataset)),\n color = 'blue') +\n ggtitle('Truth or Bluff (Polynomial Rgeression)') +\n xlab('Level') +\n ylab('Salary')\n\n# Predicting a new result with Linear Regression\ny_pred = predict(lin_reg, data.frame(Level = 6.5)) # make a simple prediction on value on 6.5\n\n# Predicting a new result with Polynomial Regression\ny_pred = predict(poly_reg, data.frame(Level = 6.5,\n Level2 = 6.5^2,\n Level3 = 6.5^3,\n Level4 = 6.5^4)) # make sure the 6.5 value showed in four levels \n\n\n \n", "meta": {"hexsha": "672ec9bc57c9e53512f0f4f10cfc7afaf9893a02", "size": 2080, "ext": "r", "lang": "R", "max_stars_repo_path": "Regression/Polynomial Regression/poly_reg_sample.r", "max_stars_repo_name": "les1smore/mlnotes", "max_stars_repo_head_hexsha": "c5ab6806c1725077e5de14bc293933daae2e7443", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Regression/Polynomial Regression/poly_reg_sample.r", "max_issues_repo_name": "les1smore/mlnotes", "max_issues_repo_head_hexsha": "c5ab6806c1725077e5de14bc293933daae2e7443", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Regression/Polynomial Regression/poly_reg_sample.r", "max_forks_repo_name": "les1smore/mlnotes", "max_forks_repo_head_hexsha": "c5ab6806c1725077e5de14bc293933daae2e7443", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 33.5483870968, "max_line_length": 103, "alphanum_fraction": 0.6538461538, "num_tokens": 538, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9019206870747658, "lm_q2_score": 0.8558511524823263, "lm_q1q2_score": 0.77190985948059}} {"text": "library(plotly)\nlibrary(orca)\n\n#___________________________________________LINE_CHART___________________________________________#\n\ncreatePlot <- function(fname, title, xlab, ylab, f, a) {\n # calculate points\n xs <- lapply(c(0:100), function(x) x/100)\n ys <- lapply(xs, function(y) f(y,a))\n data <- data.frame(xs, ys)\n \n # draw line plot\n fig <- plot_ly(data, x = ~xs, y = ~ys, type = 'scatter', mode = 'lines')\n fig <- fig %>% layout(\n title = title,\n xaxis = list(title = xlab, range=c(0,1)),\n yaxis = list(title = ylab, range=c(0,1))\n )\n \n # use orca to save to file\n orca(fig, file = fname)\n}\n\n#_______________________________________________NDF______________________________________________#\n\n# normal distribution function\nd <- function(nDoth, alpha) {\n (alpha^2) / (pi * (nDoth^2 * (alpha^2 - 1) + 1)^2)\n}\n\n# print plots for different alpha\ncreatePlot(paste(\"D00.png\"), \"Normal Distribution Function (alpha=0.0)\", \"n * h\", \"D(n, h, 0.0)\", d, 0.0)\ncreatePlot(paste(\"D02.png\"), \"Normal Distribution Function (alpha=0.2)\", \"n * h\", \"D(n, h, 0.2)\", d, 0.2)\ncreatePlot(paste(\"D04.png\"), \"Normal Distribution Function (alpha=0.4)\", \"n * h\", \"D(n, h, 0.4)\", d, 0.4)\ncreatePlot(paste(\"D06.png\"), \"Normal Distribution Function (alpha=0.6)\", \"n * h\", \"D(n, h, 0.6)\", d, 0.6)\ncreatePlot(paste(\"D08.png\"), \"Normal Distribution Function (alpha=0.8)\", \"n * h\", \"D(n, h, 0.8)\", d, 0.8)\ncreatePlot(paste(\"D10.png\"), \"Normal Distribution Function (alpha=1.0)\", \"n * h\", \"D(n, h, 1.0)\", d, 1.0)\n\n#_____________________________________________FRESNEL____________________________________________#\n\n# fresnel function\nf <- function(hDotv, fo) {\n return(fo + (1.0 - fo) * (1 - hDotv)^5)\n}\n\ncreatePlot(paste(\"F00.png\"), \"Fresnel Function (F0=0.0)\", \"h * v\", \"D(n, h, 0.0)\", f, 0.0)\ncreatePlot(paste(\"F02.png\"), \"Fresnel Function (F0=0.2)\", \"h * v\", \"D(n, h, 0.2)\", f, 0.2)\ncreatePlot(paste(\"F04.png\"), \"Fresnel Function (F0=0.4)\", \"h * v\", \"D(n, h, 0.4)\", f, 0.4)\ncreatePlot(paste(\"F06.png\"), \"Fresnel Function (F0=0.6)\", \"h * v\", \"D(n, h, 0.6)\", f, 0.6)\ncreatePlot(paste(\"F08.png\"), \"Fresnel Function (F0=0.8)\", \"h * v\", \"D(n, h, 0.8)\", f, 0.8)\ncreatePlot(paste(\"F10.png\"), \"Fresnel Function (F0=1.0)\", \"h * v\", \"D(n, h, 1.0)\", f, 1.0)\n\n#__________________________________________SURFACE_PLOT__________________________________________#\n\nplotSurfaceContour <- function(fname, title, xlab, ylab, zlab, f, k) {\n # setup helper functions\n normalize <- function(x) { return(x/100.0) }\n lambda <- function(x, y) { return(f(x,y,k)) }\n \n # setup arrays for x,y,z\n xs <- sapply(c(0:100), normalize)\n ys <- sapply(c(0:100), normalize)\n zs <- outer(xs, ys, lambda)\n \n # define the surface plot with contours on the x-y plane\n fig <- plot_ly(\n type = 'surface',\n showscale = FALSE,\n contours = list(z = list(show=TRUE, usecolormap=TRUE, project=list(z=TRUE))),\n x = ~xs, y = ~ys, z = ~zs\n )\n fig <- fig %>% layout(\n title = title,\n showlegend=FALSE,\n scene = list(\n camera = list(\n eye=list(x=1.6,y=-1.6,z=0.5)\n ),\n xaxis = list(title = xlab, range=c(0,1)),\n yaxis = list(title = ylab, range=c(0,1)),\n zaxis = list(title = zlab, range=c(0,1.2))\n ))\n \n # use orca to save to file\n orca(fig, file = fname)\n}\n\n#________________________________________GEOMETRY_FUNCTION_______________________________________#\n\n# geometry function\ngeomSmith <- function(a, k) { return(a / (a * (1 - k) + k)) }\ng <- function(a1, a2, k) { return(geomSmith(a1, k) * geomSmith(a2, k)) }\n\n# print the different functions\nplotSurfaceContour(\"G00.png\",\"Geometry Function (k=0.0)\", \"n * v\", \"n * l\", \"G(n,v,l)\", g, 0.0)\nplotSurfaceContour(\"G02.png\",\"Geometry Function (k=0.2)\", \"n * v\", \"n * l\", \"G(n,v,l)\", g, 0.2)\nplotSurfaceContour(\"G04.png\",\"Geometry Function (k=0.4)\", \"n * v\", \"n * l\", \"G(n,v,l)\", g, 0.4)\nplotSurfaceContour(\"G06.png\",\"Geometry Function (k=0.6)\", \"n * v\", \"n * l\", \"G(n,v,l)\", g, 0.6)\nplotSurfaceContour(\"G08.png\",\"Geometry Function (k=0.8)\", \"n * v\", \"n * l\", \"G(n,v,l)\", g, 0.8)\nplotSurfaceContour(\"G10.png\",\"Geometry Function (k=1.0)\", \"n * v\", \"n * l\", \"G(n,v,l)\", g, 1.0)", "meta": {"hexsha": "14bdc175bf160a25796461d946b5caca57920f79", "size": 4177, "ext": "r", "lang": "R", "max_stars_repo_path": "assets/images/github/plot-brdf.r", "max_stars_repo_name": "adrianderstroff/pbr", "max_stars_repo_head_hexsha": "23eb0d9ef7f577b42a0dc34391b3b12e64dc6614", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 3, "max_stars_repo_stars_event_min_datetime": "2021-08-19T06:20:08.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-17T03:09:04.000Z", "max_issues_repo_path": "assets/images/github/plot-brdf.r", "max_issues_repo_name": "adrianderstroff/pbr", "max_issues_repo_head_hexsha": "23eb0d9ef7f577b42a0dc34391b3b12e64dc6614", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "assets/images/github/plot-brdf.r", "max_forks_repo_name": "adrianderstroff/pbr", "max_forks_repo_head_hexsha": "23eb0d9ef7f577b42a0dc34391b3b12e64dc6614", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 41.77, "max_line_length": 105, "alphanum_fraction": 0.6188652143, "num_tokens": 1473, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9284087946129328, "lm_q2_score": 0.8311430457670241, "lm_q1q2_score": 0.7716405132714845}} {"text": "euclidean <- function(a, b) {\n return (sqrt(sum((a - b) ^ 2)))\n}\n\nw1 <- function(k, dist) {\n return (0.952381 ^ k)\n}\n\nkwNN <- function(dataset, points, k, dist = euclidean, weight = w1) {\n answer <- array(dim = c(length(points[,1])))\n classes = unique(iris$Species)\n \n for (i in 1:length(points[,1])) {\n cat(\"\\rPoint\", i, \"of\", length(points[,1]))\n distance <- array(dim = c(length(dataset[,1])))\n for (j in 1:length(dataset[,1])) {\n distance[j] = dist(points[i, ], dataset[j, 3:4])\n }\n sortedDataset <- dataset[order(distance),]\n distance <- sort(distance)\n \n scores <- rep(x = 0, times = length(classes))\n names(scores) = classes\n for (j in 1:k) {\n scores[sortedDataset$Species[j]] = scores[sortedDataset$Species[j]] + weight(j, distance[j])\n }\n \n answer[i] = names(which.max(scores))[1]\n }\n \n return (answer)\n}\n\npar(mfrow=c(1,1), pty=\"s\")\n\nxs <- seq(from = 0.5, to = 7.5, by = 0.2)\nys <- seq(from = -2, to = 5, by = 0.2)\n\nz <- array(dim = c(length(xs) * length(ys), 2))\n\nindex <- 1\nfor (i in xs) {\n for (j in ys) {\n z[index,] <- c(i, j)\n index <- index + 1\n }\n}\n\nresult <- kwNN(iris, z, 30)\n\ncolors <- c(\"setosa\" = \"blue\", \"virginica\" = \"red\", \"versicolor\" = \"green\")\nplot(iris[, 3:4], bg = colors[paste(iris$Species)], pch=23, asp=1)\npoints(z[,1], z[,2], col = colors[result], pch = 21)", "meta": {"hexsha": "bd7de6349f87ed6880f4793f0508f0aa2ffcf294", "size": 1356, "ext": "r", "lang": "R", "max_stars_repo_path": "1 - Nearest neighbors algorithm/kwnn-map.r", "max_stars_repo_name": "shadowusr/ml-course", "max_stars_repo_head_hexsha": "5e336dc47ed9dff71877e830a4d67afd8a23a8a1", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "1 - Nearest neighbors algorithm/kwnn-map.r", "max_issues_repo_name": "shadowusr/ml-course", "max_issues_repo_head_hexsha": "5e336dc47ed9dff71877e830a4d67afd8a23a8a1", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "1 - Nearest neighbors algorithm/kwnn-map.r", "max_forks_repo_name": "shadowusr/ml-course", "max_forks_repo_head_hexsha": "5e336dc47ed9dff71877e830a4d67afd8a23a8a1", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 25.5849056604, "max_line_length": 98, "alphanum_fraction": 0.5612094395, "num_tokens": 465, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9518632247867715, "lm_q2_score": 0.8104789109591832, "lm_q1q2_score": 0.7714650698072788}} {"text": "A <- matrix(c(-8,1,-2,-20,2,-6,-1,-38,-3,-1,7,-34), 3, 4, byrow = T)\r\nGaussJordan <- function(A) {\r\n n <- nrow(A)\r\n m <- ncol(A)\r\n for(i in 1:n) {\r\n A[i,] <- A[i, ]/A[i,i]\r\n for(j in 1:i-1){\r\n A[j,i:m] <- A[j,i:m] - (A[j,i] * A[i, i:m])\r\n }\r\n if (i==n) {\r\n break\r\n }\r\n for(j in i+1:(n-i)){\r\n A[j,i:m] <- A[j,i:m] - (A[j,i] * A[i, i:m])\r\n }\r\n }\r\n return(A)\r\n}\r\n\r\nGaussBackward <- function(A) {\r\n n <- nrow(A)\r\n m <- ncol(A)\r\n print(A)\r\n for(i in 1:n) {\r\n x <- A[i,m]\r\n print(x)\r\n }\r\n}\r\n\r\n##GaussBackward(GaussJordan(A))", "meta": {"hexsha": "bbcf60a1ecd1d162bdd414ca91199caac53fb25d", "size": 570, "ext": "r", "lang": "R", "max_stars_repo_path": "Lab-06/Extra/GaussJordan.r", "max_stars_repo_name": "hassaninamdar/legendesk", "max_stars_repo_head_hexsha": "f0487ac60167de97570bbe4d816cf434d1df6e39", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Lab-06/Extra/GaussJordan.r", "max_issues_repo_name": "hassaninamdar/legendesk", "max_issues_repo_head_hexsha": "f0487ac60167de97570bbe4d816cf434d1df6e39", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Lab-06/Extra/GaussJordan.r", "max_forks_repo_name": "hassaninamdar/legendesk", "max_forks_repo_head_hexsha": "f0487ac60167de97570bbe4d816cf434d1df6e39", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 19.0, "max_line_length": 69, "alphanum_fraction": 0.3964912281, "num_tokens": 241, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9518632316144274, "lm_q2_score": 0.8104789018037399, "lm_q1q2_score": 0.77146506662622}} {"text": "deathApprox <- function(m, sd, a) {a*pnorm(1:length(data), mean = m, sd = sd)}\nfitDn <- nlsLM(data~deathApprox(m, sd, a), start=list(m=10,sd=2,a=100))\n\nprint(summary(fitDn))\n\nl = as.list(coef(fitDn))\n\npeak = l$m\nwidth = l$sd\namplitude = l$a\namplitudeStdErr = summary(fitDn)$coefficients[3,2]\nprint('Amplitude')\nprint(amplitude)\nprint('width')\nprint(width)\nprint('peak')\nprint(peak)\nprint(peak - length(data))\nprint(as.Date(startDate) + peak)\nprint('amplitudeStdErr')\nprint(amplitudeStdErr)\n\ndataDates = 1:length(data)\ndataPerDates = cbind(dataDates, data)\ndfData = as.data.frame(dataPerDates)\n\nsimuDates = 1:60\nsimu = pnorm(1:60, mean = peak, sd = width) * amplitude\nsimuMax = simu*(1 + amplitudeStdErr/amplitude)\nsimuMin = simu*(1 - amplitudeStdErr/amplitude)\ndSimu = dnorm(1:60, mean = peak, sd = width) * amplitude * 10\ndSimuMax = dSimu*(1 + amplitudeStdErr/amplitude)\ndSimuMin = dSimu*(1 - amplitudeStdErr/amplitude)\nsimuPerDates = cbind(simuDates, simu, simuMin, simuMax, dSimu, dSimuMin, dSimuMax)\ndfSimu = as.data.frame(simuPerDates)\n\nm <- merge(dfSimu, dfData, all.x=T, by=c(1))\nm$simuDates <- as.Date(m$simuDates, origin = startDate)\n\n#g <- ggplot(m, aes(x=simuDates))+geom_line(aes(y=simu))+geom_line(aes(y=simuMin, color = 'red'))+geom_line(aes(y=simuMax, color = 'blue'))\ng <- ggplot(m, aes(x=simuDates))+geom_point(aes(y=data, color='Real Data'), col=\"steelblue\", size=2)+\n geom_line(aes(y=simu))+\n geom_line(aes(y=simuMin, color = 'Simu. Min.'))+\n geom_line(aes(y=simuMax, color = 'Simu. Max.'))+\n scale_x_date(date_minor_breaks = \"1 day\", breaks = \"7 day\",\n labels = scales::date_format(\"%m-%d\"),\n sec.axis = sec_axis(trans = ~ ., \n labels = scales::date_format(\"%m-%d\")))+\n geom_vline(xintercept = as.Date(startDate)+peak, colour = \"darkGrey\") +\n geom_text(aes(x=as.Date(startDate)+peak, label=\"\\nDecrease\", y=1000), colour=\"blue\", angle=90, text=element_text(size=10)) +\n geom_text(aes(x=as.Date(startDate)+peak, label=\"Increase\\n\", y=1000), colour=\"red\", angle=90, text=element_text(size=10))\n\n\nprint(g)\n\n", "meta": {"hexsha": "d5d0ec06be298820f90b6bf118c85641c127af8c", "size": 2085, "ext": "r", "lang": "R", "max_stars_repo_path": "rstudio/approxnlsLM.r", "max_stars_repo_name": "Taack/coronavirus", "max_stars_repo_head_hexsha": "10823cfc094def6f1102f49e9eaa18f7c040e64b", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "rstudio/approxnlsLM.r", "max_issues_repo_name": "Taack/coronavirus", "max_issues_repo_head_hexsha": "10823cfc094def6f1102f49e9eaa18f7c040e64b", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2020-03-23T05:43:14.000Z", "max_issues_repo_issues_event_max_datetime": "2020-03-23T05:43:14.000Z", "max_forks_repo_path": "rstudio/approxnlsLM.r", "max_forks_repo_name": "Taack/coronavirus", "max_forks_repo_head_hexsha": "10823cfc094def6f1102f49e9eaa18f7c040e64b", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 37.2321428571, "max_line_length": 139, "alphanum_fraction": 0.679616307, "num_tokens": 688, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9381240090865196, "lm_q2_score": 0.8221891370573388, "lm_q1q2_score": 0.7713153694836166}} {"text": "#задание 3\nprint (\"task 3\")\nA <- matrix (c(9,-1,3,5,4,-9,18,-3,8,-2,-3,8,1,-8,-12,1,-9,7,-13,7,-8,-9,-9,-4,-7,-2,5,-2,20,-2,9,2,-4,-6,-1,-6),6,6)\nA\n#определитель\ndet(A) # Определитель A\n\n\n#задание 5\nprint (\"5 task\")\na <- c(-1,2,-3,1,-2,3,0,4,-1,1,2,2)\nb <- c(1,4,5,3,2,2,-1,-3,0,1,3,3)\np <- c(2,0,3,1,-2,4,4,0,2,-5,1,2)\n\nfir <- ((3)*a)+(4*b)\nprint (\"first answer\")\nfir\nsec <- ((2)*as.numeric(a%*%b))*p+2*(norm(p, type=\"2\"))*a\nprint (\"second answer\")\nsec\nthr <- 1*as.numeric(a%*%p)*b-2*as.numeric(b%*%p)*a-2*(norm(p, type=\"2\"))*p\nprint (\"third answer\")\nthr\n\n\n#6 задание\nprint (\"sixth task\")\ninstall.packages(\"lpSolveAPI\") # Загружаем библиотеку\nlibrary(lpSolveAPI) # Активируем библиотеку линейного программирования\nM <- make.lp(ncol= 2) # Объявляем количество неотрицательных переменных в M\nname.lp(M, \"Example\") # Объявляем название \"Example\"для задачи(модели) М\ncolnames(M) <- c(\"X1\", \"X2\") # Объявляем названия переменных в модели М\nlp.control(M, sense = \"min\")$sense# Объявляем задачу на минимум модели М\nset.objfn(M, c(1,5)) # Задаем целевую функцию:\nadd.constraint(M, c(-2,4), \">=\", -4) # Задаем ограничение:\nadd.constraint(M, c(-2, -3), \"<=\",-4) #\nadd.constraint(M, c(-2, 1), \"<=\",2) #\n\n\nrownames(M) <- c(\"A\", \"B\",\"C\") # Называем ограничения в модели М\nM # Выводим модель M на экран\nsolve.lpExtPtr(M)\nget.variables(M) # Оптимальный план\nget.objective(M) # Достигнутый min\nX1.opt<- get.variables(M)[1]; X1.opt # Оптимальное значение для X1\nX2.opt<- get.variables(M)[2]; X2.opt # Оптимальное значение для X2\nf.max<- get.objective(M); f.max# Значение целевой функции на оптимальном решении\n", "meta": {"hexsha": "b6792cec3668d560425dc2b4c4b0d99c9dcb4b0b", "size": 1594, "ext": "r", "lang": "R", "max_stars_repo_path": "Tasks/Task 2/solution.r", "max_stars_repo_name": "Master-sniffer/Doing-some-tasks-with-R", "max_stars_repo_head_hexsha": "629e7add02437ea22c079ecd7a4279e46028b69c", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Tasks/Task 2/solution.r", "max_issues_repo_name": "Master-sniffer/Doing-some-tasks-with-R", "max_issues_repo_head_hexsha": "629e7add02437ea22c079ecd7a4279e46028b69c", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Tasks/Task 2/solution.r", "max_forks_repo_name": "Master-sniffer/Doing-some-tasks-with-R", "max_forks_repo_head_hexsha": "629e7add02437ea22c079ecd7a4279e46028b69c", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 33.2083333333, "max_line_length": 117, "alphanum_fraction": 0.6449184442, "num_tokens": 721, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9304582612793112, "lm_q2_score": 0.828938806208442, "lm_q1q2_score": 0.7712929603316548}} {"text": "## simple interactive edge finding using locator()\n\npupil.pars <- function(im=NULL, obstructed=FALSE) {\n\tif (!is.null(im))\n\t\timage(1:nrow(im), 1:ncol(im), im, col=grey256, asp=1, xlab=\"\", ylab=\"\", useRaster=TRUE)\n\tcat(\"click on edge of pupil; right click to exit\\n\")\n\tflush.console()\n\tedge <- locator(type=\"p\", col=\"green\")\n\tx <- edge$x\n\ty <- edge$y\n\tel <- lm(x^2+y^2 ~ x + y + I(y^2))\n\tasp2 <- 1 - coef(el)[4]\n\txc <- coef(el)[2]/2\n\tyc <- coef(el)[3]/(2*asp2)\n\trx <- sqrt(coef(el)[1] + xc^2 + yc^2*asp2)\n\try <- rx / sqrt(asp2)\n\tif ((abs(rx-ry)/rx < 0.05) || (summary(el)$coefficients[4,4]>0.01)) {\n\t\tel <- update(el, ~ . - I(y^2))\n\t\txc <- coef(el)[2]/2\n\t\tyc <- coef(el)[3]/2\n\t\trx <- sqrt(coef(el)[1] + xc^2 + yc^2)\n\t\try <- rx\n\t}\n\tobstruct <- 0\n\tif (obstructed) {\n\t\tcat(\"click on edge of obstruction; right click to exit\\n\")\n\t\tflush.console()\n\t\tedge <- locator(type=\"p\", col=\"green\")\n\t\tis (!is.null(edge))\n\t\t\tobstruct <- sqrt(mean((edge$x-xc)^2+(edge$y-yc)^2*(rx/ry)^2))/rx\n\t}\n\tx.e <- seq(-rx,rx, length=101)\n\ty.e <- ry * sqrt(1 - (x.e/rx)^2)\n\tpoints(x.e+xc, y.e + yc, type='l', lty=1,col='green')\n\ty.e <- -y.e\n\tpoints(x.e+xc, y.e + yc, type='l', lty=1, col='green')\n\tif (obstruct > 0) {\n\t\tx.e <- obstruct * x.e\n\t\ty.e <- obstruct * y.e\n\t\tpoints(x.e+xc, y.e + yc, type='l', lty=1,col='green')\n\t\ty.e <- -y.e\n\t\tpoints(x.e+xc, y.e + yc, type='l', lty=1, col='green')\n\t}\n\t\n\tlist(xc=xc, yc=yc, rx=rx, ry=ry, obstruct=obstruct)\n\n}\n\n## partial implementation of canny algorithm for edge detection\n##\n## arguments:\n## im - the image to process\n## fw - smoothing parameter for gaussian blur (pixels)\n## qt - threshold for accepting a point as a candidate edge point.\n## excl - number of pixels around edge to exclude. must be >= 1.\n## plots - plot some intermediate results?\n## details - return some extra data for testing purposes.\n\n## there are many online references. Search \"canny edge detection\" or \"canny algorithm\".\n\n\ncircle.pars <- function(im, fw=2, qt=0.995, excl=5,\n plots=TRUE, details=FALSE) {\n nr <- nrow(im)\n nc <- ncol(im)\n if (fw > 0) {\n im <- gblur(im, fw)\n }\n if (excl < 1) {\n excl <- 1\n }\n kern.sobel <- rbind(c(-1,-2,-1),c(0,0,0),c(1,2,1))\n gx <- convolve2d(im, kern.sobel)\n gy <- convolve2d(im, t(kern.sobel))\n modg <- sqrt(gx^2+gy^2)\n modg <- modg/max(modg)\n dirg <- atan2(gy, gx)\n \n # round off directions to 45 degrees\n \n dir <- dirg\n dir[abs(dirg) < 7*pi/8] <- (round(dirg[abs(dirg) < 7*pi/8]*4/pi))\n dir[abs(dirg) >= 7*pi/8] <- 0\n dir[dir < 0] <- 4+dir[dir<0]\n \n # find local maxima\n \n maxima <- NULL\n \n for (i in 0:3) {\n ptsi <- which(dir==i, arr.ind=TRUE)\n ed <- which(ptsi[,1] <= excl)\n ed <- c(ed, which(ptsi[,1] >= nr-excl+1))\n ed <- c(ed, which(ptsi[,2] <= excl))\n ed <- c(ed, which(ptsi[,2] >= nc-excl+1))\n if (length(ed) > 0) {\n ptsi <- ptsi[-ed,]\n }\n nb <- switch(i+1, c(1,0), c(1,1), c(0,1), c(1, -1))\n ptsp <- t(t(ptsi)+nb)\n ptsm <- t(t(ptsi)-nb)\n lm <- which((modg[ptsi] > modg[ptsp]) & (modg[ptsi] > modg[ptsm]))\n maxima <- rbind(maxima, ptsi[lm,])\n }\n \n # the thinned edges consist of the local maxima in the direction of gradient\n \n thin <- matrix(0, nr, nc)\n thin[maxima] <- modg[maxima]\n if (plots) {\n image(1:nr, 1:nc, thin, col=grey256, asp=1, xlab=\"X\", ylab=\"Y\", useRaster=TRUE)\n }\n \n # the rest differs from published algorithm description. I'm just picking\n # edge candidates from top qt %-ile, and feeding them to \n # nlrob from package robustbase if available or\n # lqs -- \"robust\" least squares routine. This is basically what I did\n # before.\n \n \n ec <- which(modg[maxima] >= quantile(modg[maxima], probs=qt))\n maxima <- maxima[ec,]\n x <- maxima[,1]\n y <- maxima[,2]\n if (require(robustbase)) {\n df <- data.frame(x=x, y=y)\n ecm <- nlrob(0 ~ r^2 - (x-xc)^2 - (y-yc)^2, data=df, \n start=list(r=min(nr,nc)/2, xc=nr/2, yc=nc/2))\n xc <- coef(ecm)['xc']\n yc <- coef(ecm)['yc']\n rxy <- coef(ecm)['r']\n } else {\n require(MASS)\n r2 <- x^2 + y^2\n ecm <- lqs(r2~x+y)\n xc <- coef(ecm)[2]/2\n yc <- coef(ecm)[3]/2\n rxy <- sqrt(coef(ecm)[1]+xc^2+yc^2)\n }\n# if (refine > 0) {\n# xr <- (1:nr)-xc\n# yr <- (1:nc)-yc\n# rhod <- round(outer(xr, yr, function(x,y) sqrt(x^2+y^2)))\n# edgec <- which(abs(rhod-rxy) <= refine, arr.ind=TRUE)\n# ec <- which(thin[edgec] > 0)\n# edgec <- edgec[ec,]\n# x <- edgec[,1]\n# y <- edgec[,2]\n# ecm <- nls(0 ~ r^2-(x-xc)^2-(y-yc)^2, start=list(r=rxy, xc=xc, yc=yc),\n# weights=thin[edgec]^2)\n# xc <- coef(ecm)['xc']\n# yc <- coef(ecm)['yc']\n# rxy <- coef(ecm)['r']\n# }\n \n if (plots) {\n points(xc, yc, pch=20, col=\"red\")\n points(x,y, pch=20, col=\"green\")\n symbols(xc, yc, circles=rxy, inches=FALSE, add=TRUE, fg=\"red\")\n }\n if (details) {\n finaledge <- cbind(x,y)\n list(cp=list(xc=xc, yc=yc, rx=rxy, ry=rxy, obstruct=0),\n gx=gx, gy=gy, modg=modg, dirg=dirg,\n thin=thin, maxima=maxima, finaledge=finaledge, dir_edge=dirg[finaledge],\n lsfit=ecm)\n } else {\n list(xc=xc, yc=yc, rx=rxy, ry=rxy, obstruct=0)\n }\n}\n \n \n", "meta": {"hexsha": "bd628bba01165c38aba71b3d64750f0dd1d8ee98", "size": 5186, "ext": "r", "lang": "R", "max_stars_repo_path": "R/circle.pars.r", "max_stars_repo_name": "gmke/zernike", "max_stars_repo_head_hexsha": "0880b0ae43cbb051afb54aa5decc246252467a8d", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 4, "max_stars_repo_stars_event_min_datetime": "2019-05-15T09:28:48.000Z", "max_stars_repo_stars_event_max_datetime": "2021-06-16T17:28:29.000Z", "max_issues_repo_path": "R/circle.pars.r", "max_issues_repo_name": "gmke/zernike", "max_issues_repo_head_hexsha": "0880b0ae43cbb051afb54aa5decc246252467a8d", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/circle.pars.r", "max_forks_repo_name": "gmke/zernike", "max_forks_repo_head_hexsha": "0880b0ae43cbb051afb54aa5decc246252467a8d", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2019-01-17T13:30:49.000Z", "max_forks_repo_forks_event_max_datetime": "2019-01-17T13:30:49.000Z", "avg_line_length": 29.9768786127, "max_line_length": 89, "alphanum_fraction": 0.5524489009, "num_tokens": 1947, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9184802484881361, "lm_q2_score": 0.8397339736884712, "lm_q1q2_score": 0.771279068817317}} {"text": "## Author: Sergio García Prado\n## Title: Statistical Inference - Goodness of Fit - Exercise 12\n\nrm(list = ls())\n\ny <- c(40, 24, 16, 14, 6)\nn <- sum(y)\n\n# a)\n(e1 <- c(dpois(0:3, lambda = 1), 1 - ppois(3, lambda = 1)) * n)\n(Q1 <- sum((y - e1) ^ 2 / e1))\n(pvalue1 <- 1 - pchisq(Q1, df = length(y) -1))\n\n## b)\n\n(e2 <- c(dpois(0:2, lambda = 1), 1 - ppois(2, lambda = 1)) * n)\n(y2 <- c(y[1:(length(y) - 2)], y[length(y) - 1] + y[length(y)]))\n(Q2 <- sum((y2 - e2) ^ 2 / e2))\n(pvalue1 <- 1 - pchisq(Q2, df = length(y2) -1))\n\n\n## c)\n\n(e3 <- c(dpois(0:1, lambda = 1), 1 - ppois(1, lambda = 1)) * n)\n(y3 <- c(y[1:(length(y) - 3)], sum(y[(length(y) - 2):length(y)])))\n(Q3 <- sum((y3 - e3) ^ 2 / e3))\n(pvalue3 <- 1 - pchisq(Q3, df = length(y3) - 1))\n\n\nsapply(1:15, function(i) {\n y <- c(dnbinom(0:i, size = 2, prob = 2/3), 1 - pnbinom(i, size = 2, prob = 2 / 3))\n e <- c(dpois(0:i, lambda = 1), 1 - ppois(i, lambda = 1))\n Q <- 100 * sum((y - e) ^ 2 / e)\n\n power <- 1 - pchisq(qchisq(1 - 0.05, df = i - 1), df = i - 1, ncp = Q)\n return(power)\n})\n\ni <- 4\ny <- c(dnbinom(0:i, size = 2, prob = 2/3), 1 - pnbinom(i, size = 2, prob = 2 / 3))\ne <- c(dpois(0:i, lambda = 1), 1 - ppois(i, lambda = 1))\n\nfn <- function(n) {\n Q <- n * sum((y - e) ^ 2 / e)\n 1 - pchisq(qchisq(1 - 0.05, df = i - 1), df = i - 1, ncp = Q)\n}\n\nuniroot(function(n) {0.9 - fn(n)}, c(1, 300))\n", "meta": {"hexsha": "180183e92a452e86f42bb037b08ea7908b7424ad", "size": 1352, "ext": "r", "lang": "R", "max_stars_repo_path": "statistical-inference/goodness-of-fit/exercise-12.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "statistical-inference/goodness-of-fit/exercise-12.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "statistical-inference/goodness-of-fit/exercise-12.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 27.5918367347, "max_line_length": 84, "alphanum_fraction": 0.4926035503, "num_tokens": 654, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9184802350995702, "lm_q2_score": 0.83973396967765, "lm_q1q2_score": 0.7712790538906233}} {"text": "#################################\n# Example of Rejection Sampling\n#################################\n\nlibrary(ggplot2)\n\n# Define nasty function\nf <- function(x){ x^2/exp(x)}\nx <- seq(0,10,0.01)\n\nxmin <- 0\nxmax <- 10\n\nC <- 15 # garantees that envelope is always higher than f\n# Sample from envelop distribution\nrenvelope <- function(n){runif(n,xmin,xmax)}\ndenvelope <- function(x){C*dunif(x,xmin, xmax)}\n\ndf <- data.frame(x=x, f=f(x), q=denvelope(x))\ngg <- ggplot(df, aes(x=x)) + \n geom_line(aes(y=f, color=\"real\")) + \n geom_line(aes(y=q, color=\"envelop\")) +\n theme(legend.title=element_blank()) +\n ggtitle(\"real and envelop distribution\")\nprint(gg) \n\nnsamples <- 10000\n\n# Sample from envelop distribution\nsamples <- renvelope(nsamples)\n\n# Sample from uniform distribution\nu <- runif(nsamples)\n\naccept <- u < f(samples)/denvelope(samples)\naccept <- as.numeric(accept)\n\ndf = data.frame(sample = samples, accept = factor(accept, levels= c(1,0)))\n\ngg<- ggplot(df, aes(x=df$sample)) + \n geom_histogram(aes(fill = accept), binwidth=0.1) + \n ggtitle(\"Samples\")\n \nprint(gg)\n\ncat(\"Acceptance ratio:\", sum(accept)/length(accept))", "meta": {"hexsha": "5d32cf6436f664b44c23c34905e3495bb747262b", "size": 1160, "ext": "r", "lang": "R", "max_stars_repo_path": "R_scripts/rejection_sampling.r", "max_stars_repo_name": "alumbreras/alumbreras.github.io.src", "max_stars_repo_head_hexsha": "97a8dc33ad73ba21700f4d04ee246b34ab4645ee", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R_scripts/rejection_sampling.r", "max_issues_repo_name": "alumbreras/alumbreras.github.io.src", "max_issues_repo_head_hexsha": "97a8dc33ad73ba21700f4d04ee246b34ab4645ee", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R_scripts/rejection_sampling.r", "max_forks_repo_name": "alumbreras/alumbreras.github.io.src", "max_forks_repo_head_hexsha": "97a8dc33ad73ba21700f4d04ee246b34ab4645ee", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 25.2173913043, "max_line_length": 74, "alphanum_fraction": 0.624137931, "num_tokens": 319, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9572778000158576, "lm_q2_score": 0.8056321866478979, "lm_q1q2_score": 0.7712138072562645}} {"text": "# Chapter 4 Lab: Logistic Regression, LDA, QDA, and KNN\n\n# The Stock Market Data\n\nlibrary(ISLR)\nnames(Smarket)\ndim(Smarket)\nsummary(Smarket)\npairs(Smarket)\ncor(Smarket)\ncor(Smarket[,-9])\nattach(Smarket)\nplot(Volume)\n\n# Logistic Regression\n\nglm.fits=glm(Direction~Lag1+Lag2+Lag3+Lag4+Lag5+Volume,data=Smarket,family=binomial)\nsummary(glm.fits)\ncoef(glm.fits)\nsummary(glm.fits)$coef\nsummary(glm.fits)$coef[,4]\nglm.probs=predict(glm.fits,type=\"response\")\nglm.probs[1:10]\ncontrasts(Direction)\nglm.pred=rep(\"Down\",1250)\nglm.pred[glm.probs>.5]=\"Up\"\ntable(glm.pred,Direction)\n(507+145)/1250\nmean(glm.pred==Direction)\ntrain=(Year<2005)\nSmarket.2005=Smarket[!train,]\ndim(Smarket.2005)\nDirection.2005=Direction[!train]\nglm.fits=glm(Direction~Lag1+Lag2+Lag3+Lag4+Lag5+Volume,data=Smarket,family=binomial,subset=train)\nglm.probs=predict(glm.fits,Smarket.2005,type=\"response\")\nglm.pred=rep(\"Down\",252)\nglm.pred[glm.probs>.5]=\"Up\"\ntable(glm.pred,Direction.2005)\nmean(glm.pred==Direction.2005)\nmean(glm.pred!=Direction.2005)\nglm.fits=glm(Direction~Lag1+Lag2,data=Smarket,family=binomial,subset=train)\nglm.probs=predict(glm.fits,Smarket.2005,type=\"response\")\nglm.pred=rep(\"Down\",252)\nglm.pred[glm.probs>.5]=\"Up\"\ntable(glm.pred,Direction.2005)\nmean(glm.pred==Direction.2005)\n106/(106+76)\npredict(glm.fits,newdata=data.frame(Lag1=c(1.2,1.5),Lag2=c(1.1,-0.8)),type=\"response\")\n\n# Linear Discriminant Analysis\n\nlibrary(MASS)\nlda.fit=lda(Direction~Lag1+Lag2,data=Smarket,subset=train)\nlda.fit\nplot(lda.fit)\nlda.pred=predict(lda.fit, Smarket.2005)\nnames(lda.pred)\nlda.class=lda.pred$class\ntable(lda.class,Direction.2005)\nmean(lda.class==Direction.2005)\nsum(lda.pred$posterior[,1]>=.5)\nsum(lda.pred$posterior[,1]<.5)\nlda.pred$posterior[1:20,1]\nlda.class[1:20]\nsum(lda.pred$posterior[,1]>.9)\n\n# Quadratic Discriminant Analysis\n\nqda.fit=qda(Direction~Lag1+Lag2,data=Smarket,subset=train)\nqda.fit\nqda.class=predict(qda.fit,Smarket.2005)$class\ntable(qda.class,Direction.2005)\nmean(qda.class==Direction.2005)\n\n# K-Nearest Neighbors\n\nlibrary(class)\ntrain.X=cbind(Lag1,Lag2)[train,]\ntest.X=cbind(Lag1,Lag2)[!train,]\ntrain.Direction=Direction[train]\nset.seed(1)\nknn.pred=knn(train.X,test.X,train.Direction,k=1)\ntable(knn.pred,Direction.2005)\n(83+43)/252\nknn.pred=knn(train.X,test.X,train.Direction,k=3)\ntable(knn.pred,Direction.2005)\nmean(knn.pred==Direction.2005)\n\n# An Application to Caravan Insurance Data\n\ndim(Caravan)\nattach(Caravan)\nsummary(Purchase)\n348/5822\nstandardized.X=scale(Caravan[,-86])\nvar(Caravan[,1])\nvar(Caravan[,2])\nvar(standardized.X[,1])\nvar(standardized.X[,2])\ntest=1:1000\ntrain.X=standardized.X[-test,]\ntest.X=standardized.X[test,]\ntrain.Y=Purchase[-test]\ntest.Y=Purchase[test]\nset.seed(1)\nknn.pred=knn(train.X,test.X,train.Y,k=1)\nmean(test.Y!=knn.pred)\nmean(test.Y!=\"No\")\ntable(knn.pred,test.Y)\n9/(68+9)\nknn.pred=knn(train.X,test.X,train.Y,k=3)\ntable(knn.pred,test.Y)\n5/26\nknn.pred=knn(train.X,test.X,train.Y,k=5)\ntable(knn.pred,test.Y)\n4/15\nglm.fits=glm(Purchase~.,data=Caravan,family=binomial,subset=-test)\nglm.probs=predict(glm.fits,Caravan[test,],type=\"response\")\nglm.pred=rep(\"No\",1000)\nglm.pred[glm.probs>.5]=\"Yes\"\ntable(glm.pred,test.Y)\nglm.pred=rep(\"No\",1000)\nglm.pred[glm.probs>.25]=\"Yes\"\ntable(glm.pred,test.Y)\n11/(22+11)", "meta": {"hexsha": "d7e86e028adb66e967c9ae056ee57f800aca160e", "size": 3225, "ext": "r", "lang": "R", "max_stars_repo_path": "islr/r_code/chap4.r", "max_stars_repo_name": "AtmaMani/pyChakras", "max_stars_repo_head_hexsha": "e58a4e244d65858049914cf98dcb454ef009362a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2020-07-04T06:36:25.000Z", "max_stars_repo_stars_event_max_datetime": "2020-07-04T06:36:25.000Z", "max_issues_repo_path": "theory/R_script_plus_data/part_1/chapter_4.txt", "max_issues_repo_name": "franec94/R-Script-Analyses", "max_issues_repo_head_hexsha": "a9c875759f63b63ceeeb7d44b98092dce075a7e1", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2022-03-12T01:01:42.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-12T01:01:42.000Z", "max_forks_repo_path": "theory/R_script_plus_data/part_1/chapter_4.txt", "max_forks_repo_name": "franec94/R-Script-Analyses", "max_forks_repo_head_hexsha": "a9c875759f63b63ceeeb7d44b98092dce075a7e1", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2020-03-09T02:11:45.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-24T19:34:32.000Z", "avg_line_length": 25.8, "max_line_length": 97, "alphanum_fraction": 0.751627907, "num_tokens": 1088, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9073122288794595, "lm_q2_score": 0.8499711832583695, "lm_q1q2_score": 0.7711892487654628}} {"text": "## Author: Sergio García Prado\n## Title: Statistical Inference - Non parametric Tests - Exercise 06\n\nrm(list = ls())\n\na <- c(6.0, 5.8, 6.5, 6.3)\n\nn.a <- length(a)\n# 4\n\nb <- c(7.3, 6.6, 7.1)\n\nn.b <- length(b)\n# 3\n\nA <- matrix(rep(0, n.a * n.b), n.a, n.b)\nfor(i in 1:n.a) {\n for(j in 1:n.b) {\n A[i, j] <- a[i] - b[j]\n }\n}\nmedian(A)\n# -0.8\n\nalpha <- 0.1\n\n## Resampling method (not equal results)\nfn <- function(a, b, n.a, n.b) {\n a.resampled <- sample(a, n.a, replace = TRUE)\n b.resampled <- sample(b, n.b, replace = TRUE)\n A <- matrix(rep(0, n.a * n.b), n.a, n.b)\n for(i in 1:n.a) {\n for(j in 1:n.b) {\n A[i, j] <- a.resampled[i] - b.resampled[j]\n }\n }\n return(median(A))\n}\nquantile(replicate(1000, fn(a, b, n.a, n.b)), c(alpha / 2, 1 - alpha / 2), names = FALSE)\n# -1.3, -0.45\n\n\n## Exact Method\nsort(A)[c(qwilcox(alpha / 2, n.a, n.b), qwilcox(1 - alpha / 2, n.a, n.b) + 1)]\n# -1.5 -0.1\n\n\n## Function\nwilcox.test(a, b, alternative = \"two.sided\", conf.int = TRUE, conf.level = 0.9)\n# Wilcoxon rank sum test\n#\n# data: a and b\n# W = 0, p-value = 0.05714\n# alternative hypothesis: true location shift is not equal to 0\n# 90 percent confidence interval:\n# -1.5 -0.1\n# sample estimates:\n# difference in location\n# -0.8\n", "meta": {"hexsha": "9a17ad8ec006b3ae1f2bbe4c96ad605d3d0b69f5", "size": 1252, "ext": "r", "lang": "R", "max_stars_repo_path": "statistical-inference/non-parametric/exercise-06.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "statistical-inference/non-parametric/exercise-06.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "statistical-inference/non-parametric/exercise-06.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 20.8666666667, "max_line_length": 89, "alphanum_fraction": 0.5599041534, "num_tokens": 494, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9136765234137296, "lm_q2_score": 0.8438951025545426, "lm_q1q2_score": 0.7710471434279073}} {"text": "# Parameters\nmean = 100 * 1000 # 100KB mean\nshape = 1.05 # 1.05 shape\n\n# Calculate scale\nscale = (mean * (shape - 1)) / shape\n\n# Pareto distribution function\npareto_cdf <- function(x) {\n 1 - (scale / x)^shape\n}\n\n# Calculate data points for the plot\nx = c(\n seq(1e-8, 1e-7, 1e-10), \n seq(1e-7, 1e-6, 1e-9), \n seq(1e-6, 1e-5, 1e-8), \n seq(1e-5, 1e-4, 1e-7), \n seq(1e-4, 1e-3, 1e-6), \n seq(1e-3, 1e-2, 1e-5), \n seq(1e-2, 1e-1, 1e-4), \n seq(1e-1, 1e0, 1e-3), \n seq(1e0, 1e1, 1e-2), \n seq(1e1, 1e2, 1e-1), \n seq(1e2, 1e3, 1e0), \n seq(1e3, 1e4, 1e1), \n seq(1e4, 1e5, 1e2), \n seq(1e5, 1e6, 1e3), \n seq(1e6, 1e7, 1e4), \n seq(1e7, 1e8, 1e5),\n seq(1e8, 1e9, 1e6),\n seq(1e9, 1e10, 1e7),\n seq(1e10, 1e11, 1e8)\n)\ny = pareto_cdf(x)\n\n# Plot without axis or functions\nplot(x, y,\n log=\"x\", \n xlim=c(4761.9, 10e8),\n ylim=c(0, 1),\n type=\"l\"\n)\n\n# Create data frame, filter out under zero (x > x_m)\ndf = data.frame(x, y)\ndf = df[df$y >= 0,]\n\n# Write to result file\nwrite.table(df, \"fs_pareto_s_1.05_mu_100KB_cdf.txt\", sep=\"\\t\", col.names = FALSE, row.names = FALSE)\n", "meta": {"hexsha": "7f9f9d519a62d2224b6ba92077be867c9ae83c82", "size": 1081, "ext": "r", "lang": "R", "max_stars_repo_path": "private/plots/2_workload_summarization/pareto_cdf.r", "max_stars_repo_name": "carachancla/tfg", "max_stars_repo_head_hexsha": "22af2cebca5eb598d63f83d5232334b8f46e6678", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 23, "max_stars_repo_stars_event_min_datetime": "2017-06-15T13:59:28.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-19T14:04:54.000Z", "max_issues_repo_path": "private/plots/2_workload_summarization/pareto_cdf.r", "max_issues_repo_name": "carachancla/tfg", "max_issues_repo_head_hexsha": "22af2cebca5eb598d63f83d5232334b8f46e6678", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2018-05-24T05:17:04.000Z", "max_issues_repo_issues_event_max_datetime": "2018-05-25T19:46:12.000Z", "max_forks_repo_path": "private/plots/2_workload_summarization/pareto_cdf.r", "max_forks_repo_name": "carachancla/tfg", "max_forks_repo_head_hexsha": "22af2cebca5eb598d63f83d5232334b8f46e6678", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 15, "max_forks_repo_forks_event_min_datetime": "2017-07-03T19:09:19.000Z", "max_forks_repo_forks_event_max_datetime": "2021-05-23T12:39:20.000Z", "avg_line_length": 21.1960784314, "max_line_length": 100, "alphanum_fraction": 0.5753931545, "num_tokens": 582, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9273632876167045, "lm_q2_score": 0.8311430478583168, "lm_q1q2_score": 0.7707715493416567}} {"text": "library(data.table)\nlibrary(ggplot2)\nlibrary(here)\nlibrary(boot) # alternate to verify long-hand calcs\n\ndata.dir <- paste0(here::here(), \"/datasets/\")\n\n# gamma example\n\nmy.sample <- rgamma(16, 1, 1/2)\nN <- 10e5\n\nmy.boot <- numeric(N)\n\nfor(i in 1:N)\n{\n x <- sample(x = my.sample, size = length(my.sample), replace = T) \n my.boot[i] <- mean(x)\n}\n\nggplot(data.table(value = my.sample), aes(value, fill = ..count..)) +\n geom_histogram(bins = 8)\n\nggplot(data.table(value = my.boot), aes(value, fill = ..count..)) +\n geom_histogram(bins = 30)\n\nmean(my.boot)\nsd(my.boot)\n\n### Bangladesh\n\nBangladesh <- data.table(read.csv(paste0(data.dir, \"Bangladesh.csv\"),\n header = T))\n\nArsenic <- Bangladesh$Arsenic\n\nmean(Arsenic) # sample mean\n\nggplot(data.table(value = Arsenic)) +\n geom_histogram(aes(value, fill = ..count..), bins = 30) +\n scale_x_continuous(labels = comma) +\n labs(title = \"Arsenic\")\n\nggplot(data.table(value = Arsenic), aes(sample = value)) +\n stat_qq() +\n stat_qq_line() +\n labs(title = \"Arsenic\")\n\nn <- length(Arsenic)\nN <- 10e3\n\narsenic.mean <- numeric(N)\n\nfor(i in 1:N)\n{\n x <- sample(Arsenic, n, replace = T)\n arsenic.mean[i] <- mean(x)\n}\n\nggplot(data.table(value = arsenic.mean)) +\n geom_histogram(aes(value, fill = ..count..), bins = 30) +\n geom_vline(xintercept = mean(arsenic.mean), col = \"darkorange\", alpha = .6, lwd = 2) +\n scale_y_continuous(labels = comma) +\n labs(title = \"Arsenic Bootstrap Distribution of Means\")\n\nggplot(data.table(value = arsenic.mean), aes(sample = value)) +\n stat_qq() +\n stat_qq_line() +\n labs(title = \"Arsenic\")\n\nmean(arsenic.mean) # Bootstrap mean\nmean(arsenic.mean) - mean(Arsenic) # bias\nsd(arsenic.mean) # bootstrap SE\n\n# this is not accurate: CLT cannot be used here\nlq <- mean(arsenic.mean) - 1.96 * sd(arsenic.mean)\nuq <- mean(arsenic.mean) + 1.96 * sd(arsenic.mean)\n\nsum(arsenic.mean < lq) / N\nsum(arsenic.mean > uq) / N\n\nalpha <- .05\nquantile(arsenic.mean, c(alpha/2, 1 - alpha/2)) # confidence intervals\n\nboot.fn <- function(data, index) {\n mean(data[index])\n}\n\narsenic.boot <- boot(Arsenic, boot.fn, R = N)\n\n### NC birth weights\n\nNCBirths <- data.table(read.csv(paste0(data.dir, \"NCBirths2004.csv\"),\n header = T))\n\nweights <- NCBirths$Weight\n\nboot.fn <- function(data, index) {\n mean(data[index]) \n}\n\nbw.boot <- boot(weights, boot.fn, R = 1000)\n\n# long-hand\n\nN <- 1e5\nbw.mean <- numeric(N)\n\nfor(i in 1:N)\n{\n x <- sample(weights, size = length(weights), replace = T)\n bw.mean[i] <- mean(x)\n}\n\nalpha <- 0.05\nconf <- quantile(bw.mean, c(Lower = alpha/2, Upper = 1 - alpha/2))\n\n# NC Birth weights, bootstrapped\n\nggplot(data.table(values = bw.mean), aes(values)) +\n geom_histogram(aes(fill = ..count..), bins = 30) +\n geom_vline(xintercept = mean(weights), col = \"darkorange\", alpha = .4, lwd = 1) +\n geom_vline(xintercept = conf[1], col = \"cornflowerblue\") +\n geom_vline(xintercept = conf[2], col = \"cornflowerblue\") +\n geom_rug(col = \"darkred\") +\n scale_x_continuous(labels = scales::comma) +\n scale_y_continuous(labels = scales::comma)\n\n### testosterone study\n\nSkateboard <- data.table(read.csv(paste0(data.dir, \"Skateboard.csv\"),\n header = T))\n\ntestF <- Skateboard[Experimenter == \"Female\"]$Testosterone\ntestM <- Skateboard[Experimenter == \"Male\"]$Testosterone\n\nnf <- length(testF)\nnm <- length(testM)\n\nN <- 10e4\nTestMean <- numeric(N)\n\nfor(i in 1:N)\n{\n sampleF <- sample(testF, nf, replace = T)\n sampleM <- sample(testM, nm, replace = T)\n \n TestMean[i] <- mean(sampleF) - mean(sampleM)\n}\n\nggplot(data.table(result = TestMean), aes(result)) +\n geom_histogram(aes(fill = ..count..), bins = 30) +\n geom_vline(xintercept = mean(testF) - mean(testM), col = \"darkorange\", lty = 2, lwd = 1.5, alpha = .4) +\n labs(title = \"Bootstrap distribution of difference in means\")\n\nggplot(data.table(value = TestMean), aes(sample = value)) +\n stat_qq() +\n stat_qq_line() +\n labs(title = \"Testosterone\")\n\n# bootstrap statistics\n\nmean(testF) - mean(testM)\nmean(TestMean)\n\nsd(TestMean)\n\nquantile(TestMean, c(0.025, .975)) # confidence intervals\n\nmean(TestMean) - ( mean(testF - mean(testM)) ) # bias\n\nobserved <- mean(testF) - mean(testM)\n\nresult <- numeric(N)\n\nfor(i in 1:N)\n{\n index <- sample(nf + nm, nf, replace = F)\n result[i] <- mean(Skateboard[index]$Testosterone) - mean(Skateboard[-index]$Testosterone)\n}\n\np <- (sum(result >= observed) + 1) / (N + 1)\n\nggplot(data.table(result), aes(result)) +\n geom_histogram(aes(fill = ..count..), bins = 30) +\n geom_vline(xintercept = observed, col = \"darkorange\", lty = 2, lwd = 1.5, alpha = .4) +\n labs(title = \"Permutation Test: Difference in means\")\n\nggplot(data.table(value = result), aes(sample = value)) +\n stat_qq() +\n stat_qq_line() +\n labs(title = \"Testosterone Permutation Test\")\n\n### Verizon data\n\n# Is the average repair time lower for ILEC lower than CLEC customers?\n\nVerizon <- data.table(read.csv(paste0(data.dir, \"Verizon.csv\"),\n header = T))\n\nTime.ILEC <- Verizon[Group == \"ILEC\"]$Time\nTime.CLEC <- Verizon[Group == \"CLEC\"]$Time\n\nobserved <- mean(Time.ILEC) - mean(Time.CLEC)\n\nggplot(data.table(values = Time.ILEC), aes(values)) +\n geom_histogram(aes(y = ..density.., fill = ..count..), bins = 30) +\n geom_density(aes(y = ..density..), col = \"darkorange\")\n\nggplot(data.table(values = Time.CLEC), aes(values)) +\n geom_histogram(aes(y = ..density.., fill = ..count..), bins = 30) +\n geom_density(aes(y = ..density..), col = \"darkorange\")\n\n# bootstrap difference in means\n\nset.seed(123)\n\nN <- 10e4\nresults <- numeric(N)\n\nN.ILEC <- length(Time.ILEC)\nN.CLEC <- length(Time.CLEC)\n\nfor(i in 1:N)\n{\n ilec <- sample(Time.ILEC, N.ILEC, replace = T)\n clec <- sample(Time.CLEC, N.CLEC, replace = T)\n \n results[i] <- mean(ilec) - mean(clec)\n}\n\nalpha <- 0.05\nobserved - mean(results) # Bias\n\nsd(results)\n\nquantile(results, c(Lower = alpha/2, Upper = 1 - alpha/2))\n\naov(Time ~ Group, data = Verizon)\n\n# ratio of means test\n\nobserved <- mean(Time.ILEC) / mean(Time.CLEC)\n\nN <- 10e3\ntime.ratio.mean <- numeric(N)\nfor(i in 1:N)\n{\n ILEC.sample <- sample(Time.ILEC, length(Time.ILEC), replace = T)\n CLEC.sample <- sample(Time.CLEC, length(Time.CLEC), replace = T)\n \n time.ratio.mean[i] <- mean(ILEC.sample) / mean(CLEC.sample)\n}\n\nggplot(data.table(result), aes(result)) +\n geom_histogram(aes(fill = ..count..), bins = 30) +\n geom_vline(xintercept = observed, col = \"darkorange\", lty = 2, lwd = 1.5, alpha = .4) +\n labs(title = \"Permutation Test: Difference in means\")\n\nresult <- numeric(N)\n\nfor(i in 1:N)\n{\n index <- sample(nrow(Verizon), length(Time.CLEC), replace = F)\n result[i] <- mean(Verizon[index]$Time) / mean(Verizon[-index]$Time)\n}\n\nobserved - mean(time.ratio.mean) # bias\nsd(time.ratio.mean) # standard error\n\nquantile(time.ratio.mean, c(0.025, .975))\n\ntime.ratio.bias <- mean(time.ratio.mean) - mean(Time.ILEC)/mean(Time.CLEC) # Bias\n\ntime.ratio.bias / sd(time.ratio.mean)\n\n\n# Significance\np <- (sum(result >= observed) + 1) / ( N + 1)\n\nggplot(data.table(result), aes(result)) +\n geom_histogram(aes(fill = ..count..), bins = 30) +\n geom_vline(xintercept = observed, col = \"darkorange\", lty = 2, lwd = 1.5, alpha = .4) +\n scale_y_continuous(labels = comma) +\n labs(title = \"Permutation Test: Difference in means\")\n\n", "meta": {"hexsha": "75c5dcd517f7a9b283bdd1309b63b2ec4e9b8ed5", "size": 7299, "ext": "r", "lang": "R", "max_stars_repo_path": "Mathematical Statistics/05_conf_int_bootstrap.r", "max_stars_repo_name": "bmoretz/Statistical-Computing", "max_stars_repo_head_hexsha": "606e6bb222013c38867c1aee7e79fae762e7a445", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 3, "max_stars_repo_stars_event_min_datetime": "2020-07-27T08:18:01.000Z", "max_stars_repo_stars_event_max_datetime": "2021-08-09T09:20:49.000Z", "max_issues_repo_path": "Mathematical Statistics/05_conf_int_bootstrap.r", "max_issues_repo_name": "bmoretz/Statistical-Computing", "max_issues_repo_head_hexsha": "606e6bb222013c38867c1aee7e79fae762e7a445", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Mathematical Statistics/05_conf_int_bootstrap.r", "max_forks_repo_name": "bmoretz/Statistical-Computing", "max_forks_repo_head_hexsha": "606e6bb222013c38867c1aee7e79fae762e7a445", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2020-07-27T08:18:00.000Z", "max_forks_repo_forks_event_max_datetime": "2020-08-02T11:31:27.000Z", "avg_line_length": 25.4320557491, "max_line_length": 106, "alphanum_fraction": 0.6468009316, "num_tokens": 2229, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8962513675912912, "lm_q2_score": 0.8596637559030338, "lm_q1q2_score": 0.77047481689676}} {"text": "load.packages('quantmod')\nload.packages('PerformanceAnalytics')\nload.packages('ggplot2')\nload.packages('forecast')\nload.packages('tseries')\nload.packages('FitAR')\n\ndata <- new.env()\n\ngetSymbols('JPM', src = 'yahoo', env = data, auto.assign = T)\n\nJPM = JPM[\"2018-02-01/2018-12-30\"]\nJPM = JPM[, \"JPM.Adjusted\"]\n\nplot(JPM)\n\n# Calculating the average stock price of JPM\njpm_avg <- sum(JPM)/length(JPM)\njpm_avg\n\n# Calculating the standard deviation of the JPM stock price\njpm_std <- StdDev(JPM)\njpm_std\n\n# Calculating the daily JPM stock return\njpm_log_ret <- diff(log(JPM))\njpm_log_ret\n\n# ---------------- #\n\ngetSymbols(\"^GSPC\", src = 'yahoo', env = data, auto.assign = T)\n\nGSPC <- GSPC[\"2018-02-01/2018-12-30\"]\nGSPC <- GSPC[, \"GSPC.Adjusted\"]\n\ntwo_reg_data <- cbind(JPM, GSPC)\n\nscatter.smooth(x=two_reg_data$JPM.Adjusted, y=two_reg_data$GSPC.Adjusted, main=\"JPM ~ GSPC\", xlab= \"JPM Closing Price\", ylab= \"S&P500 Closing Price\") # scatterplot\n\n# Producing a linear model with S&P500 close prices as the explanatory variable.\nlinearModel <- lm(JPM.Adjusted ~ GSPC.Adjusted, data = two_reg_data)\nsummary(linearModel)\n\n# Reading in the CSUSHPINSA monthly data \ncsushpinsa <- read.csv(\"https://fred.stlouisfed.org/graph/fredgraph.csv?bgcolor=%23e1e9f0&chart_type=line&drp=0&fo=open%20sans&graph_bgcolor=%23ffffff&height=450&mode=fred&recession_bars=on&txtcolor=%23444444&ts=12&tts=12&width=1168&nt=0&thu=0&trc=0&show_legend=yes&show_axis_titles=yes&show_tooltip=yes&id=CSUSHPINSA&scale=left&cosd=1987-01-01&coed=2019-03-01&line_color=%234572a7&link_values=false&line_style=solid&mark_type=none&mw=3&lw=2&ost=-99999&oet=99999&mma=0&fml=a&fq=Monthly&fam=avg&fgst=lin&fgsnd=2009-06-01&line_index=1&transformation=lin&vintage_date=2019-06-17&revision_date=2019-06-17&nd=1987-01-01\")\ncsushpinsa = csushpinsa$CSUSHPINSA\n\n# Confirm that we now have a simple list of doubles for values\ntypeof(csushpinsa)\n\ncsushpinsa = ts(csushpinsa, start = c(1987,1), frequency = 12)\n\ncsushpinsa\n\n# Augmented Dickey-Fuller Test\ndf <- adf.test(csushpinsa)\ndf # The p-value of 0.4609 here means that we accept the null hypothesis of non-stationarity\n\n# Using Box-Jenkins to explore the parameters for an ARIMA model\nT = length(csushpinsa)\n\ncsush0 = csushpinsa[-1]\ncsush1 = csushpinsa[-T]\n\nlag_csush = cbind(csush0, csush1)\n\nplot(lag_csush, main = \"T[x] vs T[x-1] for Case Shiller Index Values\")\n\ncor(csush0, csush1)\n\nacf(csushpinsa, lag.max = 20, plot = TRUE) # Linear decay => non-stationary\n\npacf(csushpinsa, lag.max = 20, plot = TRUE)\n\nd_csush = diff(csushpinsa)\nd_csush\n\nplot(d_csush) # More stationary than the original data\n\nacf(d_csush, lag.max = 20, plot = TRUE) # Far quicker decay than the original data\npacf_dcsush <- pacf(d_csush, lag.max = 20, plot = TRUE) # Cuts off after lag 1.\n\n# Using auto-fit to detect best model to use via AIC and MLE minimisation\nauto.arima(csushpinsa, trace = TRUE) \n\n# The above suggests ARIMA(3,1,2) with drift. No lower AIC can be found.\nmodel <- arima(csushpinsa, order = c(3, 1, 2))\nmodel\n\n# Determine the confidence intervals for the parameters of the ARIMA(3,1,2) model.\nconfint(model, level = 0.995)\n\n# Calculate the residuals from the model - checking for goodness-of-fit.\nmodel_resid = resid(model)\nmodel_resid\n\n# Residuals seem relatively stationary.\nplot(csushpinsa, model_resid, ylab=\"Residuals\", xlab=\"Observations\")\nabline(0,0)\n\n# Residual differentials look a lot like white noise, gaining intensity later on.\nresid_diff = diff(model_resid) \nplot(resid_diff) \n\n# Residual differentials appear to mostly fall along a normal distribution.\nqqnorm(resid_diff)\n\nplot(acf(model_resid), main = \"Autocorrelation of ARIMA(3,1,2) Residuals\")\nplot(pacf(model_resid), main = \"Partial autocorrelation of ARIMA(3,1,2) Residuals\")\n\nboxresult = LjungBoxTest(model_resid,k=2,lag.max =5,StartLag=1)\nplot(boxresult[,3],main= \"Ljung-Box Q Test\", ylab= \"P-values\", xlab= \"Lag\") # All well above 0.05, indicating non-significance.\n\n# Having checked that the residuals appear to be normally distributed, we go on to produce a forecast using the model.\npredict(model,n.ahead = 12)\nplot(forecast(model,h=12, level=c(99.5)))\n\n# The prediction for April 2019 (one month after the latest data) has:\n# Forecast 208.0465, Lo99.5 207.1655, Hi99.5 208.9276.\n\n# Potential exogenous variables to improve forecasting ability: mortgage rate, personal income, delinquency rate on mortgages, home ownership rate.", "meta": {"hexsha": "95fa64ad4fcf0edc69299f27196a25f9733a6303", "size": 4401, "ext": "r", "lang": "R", "max_stars_repo_path": "econometrics/M3_Lorence_code.r", "max_stars_repo_name": "thquyen11/wqu_financial_engineering", "max_stars_repo_head_hexsha": "40d0538834ea7c412399d4b0c842643089243a2f", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 4, "max_stars_repo_stars_event_min_datetime": "2021-05-20T23:15:13.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-28T20:20:42.000Z", "max_issues_repo_path": "econometrics/M3_Lorence_code.r", "max_issues_repo_name": "rajsingh7/wqu_financial_engineering", "max_issues_repo_head_hexsha": "40d0538834ea7c412399d4b0c842643089243a2f", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "econometrics/M3_Lorence_code.r", "max_forks_repo_name": "rajsingh7/wqu_financial_engineering", "max_forks_repo_head_hexsha": "40d0538834ea7c412399d4b0c842643089243a2f", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 5, "max_forks_repo_forks_event_min_datetime": "2020-04-26T18:02:15.000Z", "max_forks_repo_forks_event_max_datetime": "2021-08-31T05:08:10.000Z", "avg_line_length": 36.3719008264, "max_line_length": 616, "alphanum_fraction": 0.7491479209, "num_tokens": 1440, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9173026618464796, "lm_q2_score": 0.8397339596505965, "lm_q1q2_score": 0.7702901964303764}} {"text": "#Series temporais e analises preditivas - Fernando Amaral\r\nlibrary(forecast)\r\nlibrary(ggplot2)\r\n\r\n#tendencia linear hold\r\nautoplot(austres)\r\nmdl1 = holt(austres, h=16)\r\nautoplot(mdl1)\r\nmdl1$model\r\n\r\nmdl2 = holt(austres,alpha = 0.2, h=16)\r\nautoplot(mdl2)\r\n\r\n#compara as duas previs?es\r\nplot(mdl1)\r\nlines(mdl2$mean, col=\"red\")\r\n\r\n#tendencia amortecida\r\nmdl3 = holt(austres,damped = T, phi = 0.9, h=16)\r\nautoplot(mdl3)\r\n\r\n#mudamos phi \r\nmdl4 = holt(austres,damped = T, phi = 0.8, h=16)\r\nautoplot(mdl4)\r\n\r\n#comparar os modelos\r\nplot(mdl3)\r\nlines(mdl4$mean, col=\"red\")\r\n\r\n#compara as duas previsoes\r\nprint(mdl3$mean)\r\nprint(mdl4$mean)\r\n\r\n#holt winter - sazonal\r\n#aditivo\r\nmdl5 = hw(JohnsonJohnson,seasonal = \"additive\", h=16)\r\nautoplot(mdl5)\r\n\r\n#multiplicativo\r\nmdl6 = hw(JohnsonJohnson,seasonal = \"multiplicative\", h=16)\r\nautoplot(mdl6)\r\n\r\n#comparar os modelos\r\nplot(mdl5)\r\nlines(mdl6$mean, col=\"red\")\r\n\r\n#comparando textual\r\nprint(mdl5$mean)\r\nprint(mdl6$mean)\r\n\r\n#multiplicativo amortecido\r\nmdl7 = hw(JohnsonJohnson,seasonal = \"multiplicative\", damped = T, phi = 0.9,h=16)\r\nautoplot(mdl7)\r\n\r\n#ets \r\nmdl8 = ets(JohnsonJohnson)\r\nprint(mdl8)\r\n\r\nautoplot(mdl8$residuals)\r\nautoplot(mdl8$fitted)\r\n\r\nprev = forecast(mdl8, h=16,levels=c(85,90))\r\nprint(prev$mean)\r\nautoplot(prev)\r\n\r\nautoplot(decompose(JohnsonJohnson))\r\n\r\nmdl9 = ets(JohnsonJohnson, model = \"ZAA\", damped = T)\r\nprint(mdl9)\r\n\r\nmdl10 = ets(JohnsonJohnson, model = \"ZZZ\", damped = T)\r\nprint(mdl10)\r\n\r\n\r\n\r\n\r\n", "meta": {"hexsha": "7ba2f53890b558147f7f2b8488c7a6c69eee260d", "size": 1462, "ext": "r", "lang": "R", "max_stars_repo_path": "Udemy/Series Temporais e Analises Preditivas/Resources/Codigo/7.2.R Suavizacao Exponencial.r", "max_stars_repo_name": "tarsoqueiroz/Rlang", "max_stars_repo_head_hexsha": "b2d4fdd967ec376fbf9ddb4a7250c11d3abab52e", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Udemy/Series Temporais e Analises Preditivas/Resources/Codigo/7.2.R Suavizacao Exponencial.r", "max_issues_repo_name": "tarsoqueiroz/Rlang", "max_issues_repo_head_hexsha": "b2d4fdd967ec376fbf9ddb4a7250c11d3abab52e", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Udemy/Series Temporais e Analises Preditivas/Resources/Codigo/7.2.R Suavizacao Exponencial.r", "max_forks_repo_name": "tarsoqueiroz/Rlang", "max_forks_repo_head_hexsha": "b2d4fdd967ec376fbf9ddb4a7250c11d3abab52e", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 18.987012987, "max_line_length": 82, "alphanum_fraction": 0.6949384405, "num_tokens": 511, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9124361628580401, "lm_q2_score": 0.8438950986284991, "lm_q1q2_score": 0.770000405647295}} {"text": "# Source: https://www.kaggle.com/juejuewang/handle-missing-values-in-time-series-for-beginners\n# Author: Nishant Singh - https://www.datacamp.com/profile/NishantKumarSingh\n\nlibrary(imputeTS)\n\nView(tsAirgap)\n\nplot(tsAirgap, main=\"AirPassenger data with missing values\")\n\nstatsNA(tsAirgap)\n\n#########################################################################################\n\n# General imputation methods\n\npar(mfrow=c(2,2))\n# Mean Imputation\nplot(na_mean(tsAirgap, option = \"mean\") - AirPassengers, ylim = c(-mean(AirPassengers), mean(AirPassengers)), ylab = \"Difference\", main = \"Mean\")\nmean((na_mean(tsAirgap, option = \"mean\") - AirPassengers)^2)\n\n# Median Imputation\nplot(na_mean(tsAirgap, option = \"median\") - AirPassengers, ylim = c(-mean(AirPassengers), mean(AirPassengers)), ylab = \"Difference\", main = \"Median\")\nmean((na_mean(tsAirgap, option = \"median\") - AirPassengers)^2)\n\n# Mode Imputation\nplot(na_mean(tsAirgap, option = \"mode\") - AirPassengers, ylim = c(-mean(AirPassengers), mean(AirPassengers)), ylab = \"Difference\", main = \"Mode\")\nmean((na_mean(tsAirgap, option = \"mode\") - AirPassengers)^2) \n\n# Random Imputation\nplot(na_random(tsAirgap) - AirPassengers, ylim = c(-mean(AirPassengers), mean(AirPassengers)), ylab = \"Difference\", main = \"Random\")\nmean((na_random(tsAirgap) - AirPassengers)^2)\n\n#########################################################################################\n\n#TS specific imputation methods\n\npar(mfrow=c(2,2))\n# Last Observartion Carried Forward\nplot(na_locf(tsAirgap, option = \"locf\") - AirPassengers, ylim = c(-mean(AirPassengers), mean(AirPassengers)), ylab = \"Difference\", main = \"LOCF\")\nm1 <- mean((na_locf(tsAirgap, option = \"locf\") - AirPassengers)^2)\n\n# Next Observartion Carried Backward\nplot(na_locf(tsAirgap, option = \"nocb\") - AirPassengers, ylim = c(-mean(AirPassengers), mean(AirPassengers)), ylab = \"Difference\", main = \"NOCB\")\nm2 <- mean((na_locf(tsAirgap, option = \"nocb\") - AirPassengers)^2)\n\n# Linear Interpolation\nplot(na_interpolation(tsAirgap, option = \"linear\") - AirPassengers, ylim = c(-mean(AirPassengers), mean(AirPassengers)), ylab = \"Difference\", main = \"Linear\")\nm3 <- mean((na_interpolation(tsAirgap, option = \"linear\") - AirPassengers)^2)\n\n# Spline Interpolation\nplot(na_interpolation(tsAirgap, option = \"spline\") - AirPassengers, ylim = c(-mean(AirPassengers), mean(AirPassengers)), ylab = \"Difference\", main = \"Spline\")\n\nm4 <- mean((na_interpolation(tsAirgap, option = \"spline\") - AirPassengers)^2)\n\ndata.frame(methods=c('LOCF', 'NACB', 'Linear', 'Spline'), MSE=c(m1, m2, m3, m4))\n\n#########################################################################################\n\n#Combined imputation approach\n\npar(mfrow=c(2,2))\n# Seasonal Adjustment then Random\nplot(na_seadec(tsAirgap, algorithm = \"random\") - AirPassengers, ylim = c(-mean(AirPassengers), mean(AirPassengers)), ylab = \"Difference\", main = \"Seas-Adj -> Random\")\nma1 <- mean((na_seadec(tsAirgap, algorithm = \"random\") - AirPassengers)^2)\n\n# Seasonal Adjustment then Mean\nplot(na_seadec(tsAirgap, algorithm = \"mean\") - AirPassengers, ylim = c(-mean(AirPassengers), mean(AirPassengers)), ylab = \"Difference\", main = \"Seas-Adj -> Mean\")\nma2 <- mean((na_seadec(tsAirgap, algorithm = \"mean\") - AirPassengers)^2)\n\n# Seasonal Adjustment then LOCF\nplot(na_seadec(tsAirgap, algorithm = \"locf\") - AirPassengers, ylim = c(-mean(AirPassengers), mean(AirPassengers)), ylab = \"Difference\", main = \"Seas-Adj -> LOCF\")\nma3 <- mean((na_seadec(tsAirgap, algorithm = \"locf\") - AirPassengers)^2)\n\n# Seasonal Adjustment then Linear Interpolation\nplot(na_seadec(tsAirgap, algorithm = \"interpolation\") - AirPassengers, ylim = c(-mean(AirPassengers), mean(AirPassengers)), ylab = \"Difference\", main = \"Seas-Adj -> Linear\")\n\nma4 <- mean((na_seadec(tsAirgap, algorithm = \"interpolation\") - AirPassengers)^2)\n\ndata.frame(methods=c(\"Seas-Adj+Random\", \"Seas-Adj+Mean\", \"Seas-Adj+LOCF\",\"Seas-Adj+Linear\"),\n MSE=c(ma1, ma2, ma3, ma4))\n ", "meta": {"hexsha": "d06338fb9ce10127a49b74fc4ba58725e2c32ef4", "size": 3969, "ext": "r", "lang": "R", "max_stars_repo_path": "r/user/extras/ts_imputation.r", "max_stars_repo_name": "JBris/time_series_anomaly_detection_examples", "max_stars_repo_head_hexsha": "c0bb36be4d20128c3aca911dcce156f7e36ae6da", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 11, "max_stars_repo_stars_event_min_datetime": "2020-03-20T07:42:23.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-27T11:52:42.000Z", "max_issues_repo_path": "r/user/extras/ts_imputation.r", "max_issues_repo_name": "JBris/time_series_anomaly_detection_examples", "max_issues_repo_head_hexsha": "c0bb36be4d20128c3aca911dcce156f7e36ae6da", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 2, "max_issues_repo_issues_event_min_datetime": "2021-04-30T21:06:31.000Z", "max_issues_repo_issues_event_max_datetime": "2022-02-10T01:27:07.000Z", "max_forks_repo_path": "r/user/extras/ts_imputation.r", "max_forks_repo_name": "JBris/time_series_anomaly_detection_examples", "max_forks_repo_head_hexsha": "c0bb36be4d20128c3aca911dcce156f7e36ae6da", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2020-07-15T03:29:21.000Z", "max_forks_repo_forks_event_max_datetime": "2020-07-15T03:29:21.000Z", "avg_line_length": 49.0, "max_line_length": 173, "alphanum_fraction": 0.6686822877, "num_tokens": 1163, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8824278757303678, "lm_q2_score": 0.8723473730188543, "lm_q1q2_score": 0.7697836392719944}} {"text": "##MLE of Poission#####\r\npois.mle=function(x){\r\n n=length(x)\r\n S.x= sum(x)\r\n lambda=S.x/n\r\n lambda\r\n}\r\n#x=rpois(1000,5) # To check\r\n#pois.mle(x)\r\n#########MLE of Negative Binomial, Initial parameters is required###\r\nnb.mle=function(x,z){\r\n N=length(x)\r\n r<- z[1]\r\n p<- z[2]\r\n xsum=sum(x)\r\n neg.log.lik=function(y) {\r\n r=y[1];\r\n p=y[2];\r\n if((p<=0)||(p>1)||(r<0)) ans=-Inf else {\r\n ans= N*r*log(1-p)- N*lgamma(r) +xsum*log(p) + sum(lgamma(x+r))-sum(lgamma(x+1));\r\n }\r\n -ans;\r\n }\r\n gp<- function(g) {\r\n r=g[1];\r\n p=g[2];\r\n dr<- N*log(1-p)-N*digamma(r)+sum(digamma(x+r));\r\n dp<- (xsum/p)-(N*r/(1-p));\r\n -c(dr,dp)\r\n }\r\n \r\n estimate=optim(par=c(r,p),fn=neg.log.lik, gr=gp, method = \"L-BFGS-B\", lower = c(1, 1e-8), upper = c(1e9,1-1e-8))\r\n ans=estimate$par\r\n list(r=ans[1], p=1-ans[2])\r\n}\r\n#x=rnbinom(1000, 7, 0.3)\r\n#nb.mle(x,c(5, 0.5))\r\n\r\n######## MLE of Beta Binomial####\r\nbb.mle=function(x, b0){\r\n n=b0[1]; a=b0[2]; b=b0[3]\r\n N=length(x)\r\n neg.log.lik=function(y) {\r\n n=y[1];\r\n a=y[2];\r\n b=y[3];\r\n if((n= 0.05. This means that there is statistically significant difference in access times between controlmenu and toolpalette but no significant difference in access times between other pairs of menus. To find out which is better between controlmenu and toolpalette, we can have a look at their means:\")\n \n# Calculate means within groups\naggregate(dataset1[, \"time\"], list(dataset1$menu), mean)\nprint(\"The mean access time for controlmenu (2.388) is significantly less than the mean access time of toolpalette (2.775). Thus, controlmenu is better than toolpalette in terms of access time.\")\n\n# One tailed t-test between controlmenu and toolpalette\ncontrolmenu <- subset(dataset1, menu == \"controlmenu\")\ntoolpalette <- subset(dataset1, menu == \"toolpalette\")\nt_test_result <- t.test(controlmenu$time, toolpalette$time, alternative = \"less\")\np_value <- t_test_result$p.value\nprint(paste(\"p_value controlmenu-toolpalette: \", p_value))\nif (p_value < 0.05) {\n print(\"Since p_value < 0.05 we can reject the null hypothesis of the one tailed t-test and conclude that controlmenu has better access times than toolpalette.\")\n} else {\n print(\"Since p_value < 0.05 we can reject the null hypothesis of the one tailed t-test and conclude that controlmenu has better access times than toolpalette.\")\n}\n \n# Visualizations \nboxplot(time~menu,\n data=dataset1,\n main=\"Different boxplots for each menu\",\n xlab=\"Menu\",\n ylab=\"Time\",\n frame = FALSE,\n col = c(\"#DDEDAA\", \"#F4AC45\", \"#FFCAB1\", \"#92BFB1\"),\n border=\"black\"\n)\n\n# between-within plot\nB <- anova(lm(time ~ menu, data = dataset1))$\"Mean Sq\"\nnames(B) <- c(\"between\", \"within\")\nbarplot(B, main = \"Between vs. within\", xlab = \"Group (Menu)\", ylab = \"Sum of Squares (Time)\", col = c(\"#DDEDAA\", \"#F4AC45\"))\n\n# f distribution plots\nn <- sum(dataset1[, \"menu\"] == \"controlmenu\")[[1]]\nmeans <- aggregate(dataset1[, \"time\"], list(dataset1$menu), mean)[, 2]\ncntr <- means - mean(means)\nlambda <- n*sum(cntr^2)\nf <- function(x) df(x, df1 = 2, df2 = 4*(n - 1))\ng <- function(x) df(x, df1 = 2, df2 = 4*(n - 1), ncp = lambda)\nuplim <- qf(0.975, df1 = 2, df2 = 4*(n - 1), ncp = lambda)\ncurve(f, from = 0, to = uplim, lwd = 3, main = \"F distributions plot\",\n xlab = \"F-ratio\", ylab = \"density\")\ncurve(g, from = 0, to = uplim, lwd = 3, col = \"red\", add = TRUE)\nfstat <- summary(lm(time ~ menu, data = dataset1))$fstatistic[1]\nabline(v = fstat, lty = 2, col = \"green\", lwd = 3)\nfcrit <- 2.866\nabline(v = fcrit, lty = 2, col = \"red\", lwd = 3)\npar(mfrow = c(1,1))\n\n", "meta": {"hexsha": "a031329f7c178acde2a31c40a5ffbfbab1ae2b86", "size": 3743, "ext": "r", "lang": "R", "max_stars_repo_path": "q1.r", "max_stars_repo_name": "rmodi6/statistical-analysis-using-R", "max_stars_repo_head_hexsha": "6d8bb688eb0fadae7c806166d600dd66d5aa1825", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "q1.r", "max_issues_repo_name": "rmodi6/statistical-analysis-using-R", "max_issues_repo_head_hexsha": "6d8bb688eb0fadae7c806166d600dd66d5aa1825", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "q1.r", "max_forks_repo_name": "rmodi6/statistical-analysis-using-R", "max_forks_repo_head_hexsha": "6d8bb688eb0fadae7c806166d600dd66d5aa1825", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 49.9066666667, "max_line_length": 445, "alphanum_fraction": 0.7015762757, "num_tokens": 1059, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.933430805473952, "lm_q2_score": 0.8244619285331332, "lm_q1q2_score": 0.7695781620332903}} {"text": "#'@title Get the outliers for a given time series\n#'\n#'@description The outliers are computed using different methods based on the \\code{outlierType} parameter\n#'\n#'@usage tsData.out <- getOutliers(tsData)\n#'\n#'@param tsData A time series object.\n#'@param outlierType A string that determines the way to compute the outliers. outlierType = c(\"iqr\",\"stl\",\"firstdiff\"). Default is \"iqr\".\n#'@details \n#'\tiqr: Find outliers using the interquartile range of the given time series (boxplot method).\n#' stl: Use stl weights.\n#' firstdiff: Use the points three standard deviations from the mean of the time series of first diffs.\n#'\n#'@return A vector of indices which represents the location of the outliers within the time series\n#'\n#'@export\n\ngetOutliers <- function(tsData, outlierType = \"iqr\")\n{\n\n\ttsObj <- tsData\n\t\n\tif (outlierType == \"iqr\") {\n\t\ttsObj.outliers <- which(tsObj > quantile(tsObj,probs=.75) + 3*IQR(tsObj))\n\t} else if (outlierType == \"stl\") {\n\t\ttsObj <- tsData\n\t\ttsObj.stl <- stats::stl(tsObj,s.window=\"periodic\",robust=T)\n\t\ttsObj.outliers <- which(tsObj.stl$weights < 1e-8)\n\t} else if (outlierType == \"firstdiff\") {\n\t\ttsObj.diff <- diff(tsObj)\n\t\ttsObj.diff.mu <- mean(tsObj.diff)\n\t\ttsObj.diff.sd <- sd(tsObj.diff)\n\t\ttsObj.outliers <- which(tsObj.diff > tsObj.diff.mu + 3*tsObj.diff.sd)\n\t\ttsObj.outliers <- c(tsObj.outliers,which(tsObj.diff < tsObj.diff.mu - 3*tsObj.diff.sd))\n\t} else {\n\t\tstop(\"Invalid outlier type specified. Valid values are \\\"iqr\\\" and \\\"stl\\\"\")\n\t}\n\t\n\treturn (tsObj.outliers)\n}", "meta": {"hexsha": "21e8da9c8fb98fcce24c02b987198c47ce53623d", "size": 1533, "ext": "r", "lang": "R", "max_stars_repo_path": "R/getOutliers.r", "max_stars_repo_name": "OHDSI/Castor", "max_stars_repo_head_hexsha": "a64faf53509b50bfedf9057f042355fe2e17974b", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2021-02-11T18:51:29.000Z", "max_stars_repo_stars_event_max_datetime": "2021-03-23T16:13:55.000Z", "max_issues_repo_path": "R/getOutliers.r", "max_issues_repo_name": "OHDSI/Castor", "max_issues_repo_head_hexsha": "a64faf53509b50bfedf9057f042355fe2e17974b", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 3, "max_issues_repo_issues_event_min_datetime": "2020-10-23T18:35:15.000Z", "max_issues_repo_issues_event_max_datetime": "2021-03-17T16:41:40.000Z", "max_forks_repo_path": "R/getOutliers.r", "max_forks_repo_name": "OHDSI/Castor", "max_forks_repo_head_hexsha": "a64faf53509b50bfedf9057f042355fe2e17974b", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 38.325, "max_line_length": 141, "alphanum_fraction": 0.6921069798, "num_tokens": 453, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9207896780646392, "lm_q2_score": 0.8354835391516133, "lm_q1q2_score": 0.7693046190437194}} {"text": "# Numerical_Integration.r\r\n# Date: 28.06.2019. Created by Joshua Simon. \r\n\r\n# Create some functions you want to integrate\r\n\r\nf <- function(x) {\r\n return(sin(x))\r\n}\r\n\r\ncom_simpson <- function(f, a, b, n) {\r\n # Composite Simpson's rule\r\n # Integration of function f over interval [a,b] where n is\r\n\t# the number of subintervals. Accuracy only depends on the \r\n\t# number of subintervals.\r\n\r\n sum <- 0\r\n \r\n # Step length h\r\n h <- (b - a) / n\r\n\r\n # Calculate integral value with composite simpson's rule\r\n for (k in 1:n) {\r\n x_k <- a + k * h\r\n\t\tx_k1 <- a + (k-1) * h\r\n \r\n\t\tsimpson <- h/6 * ( f(x_k1) + 4* f((x_k1 + x_k)/2) + f(x_k) )\r\n\t\t\r\n sum <- sum + simpson\r\n }\r\n \r\n return(sum)\r\n}\r\n\r\nintegral <- com_simpson(f, 0.0, 2.0 * 3.141592654, 100000)\r\n\r\nmessage(integral)\r\n", "meta": {"hexsha": "fe7ec12816a8136318448e2b936526b70b47c5cc", "size": 821, "ext": "r", "lang": "R", "max_stars_repo_path": "R.r", "max_stars_repo_name": "SV-97/Numeric-Integration", "max_stars_repo_head_hexsha": "13099425112f2cb3b860787471218fcdbf773dac", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 3, "max_stars_repo_stars_event_min_datetime": "2019-06-28T13:54:13.000Z", "max_stars_repo_stars_event_max_datetime": "2020-03-13T03:20:28.000Z", "max_issues_repo_path": "R.r", "max_issues_repo_name": "SV-97/Numeric-Integration", "max_issues_repo_head_hexsha": "13099425112f2cb3b860787471218fcdbf773dac", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R.r", "max_forks_repo_name": "SV-97/Numeric-Integration", "max_forks_repo_head_hexsha": "13099425112f2cb3b860787471218fcdbf773dac", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.1891891892, "max_line_length": 63, "alphanum_fraction": 0.5590742996, "num_tokens": 262, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9230391685381605, "lm_q2_score": 0.8333245973817158, "lm_q1q2_score": 0.7691912434896163}} {"text": "# Example : 4.2B Chapter : 4.2 Page No: 213\r\n# Find best Possible solution\r\n\r\nsolution<-function(A,b){\r\n ATA<-t(A)%*%A\r\n ATb<-t(A)%*%b\r\n x<-solve(ATA,ATb)\r\n return(x)\r\n}\r\n\r\nA<-matrix(c(1,1,1),ncol=1)\r\nb<-matrix(c(70,80,120),ncol=1)\r\nx<-solution(A,b)\r\nprint(\"The best possible solution is \")\r\nprint(x)", "meta": {"hexsha": "3fa8dab92476e28f99afe763c3a4e5825ee49d76", "size": 310, "ext": "r", "lang": "R", "max_stars_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH4/EX4.2.b/Ex4_4.2B.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH4/EX4.2.b/Ex4_4.2B.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH4/EX4.2.b/Ex4_4.2B.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 20.6666666667, "max_line_length": 50, "alphanum_fraction": 0.5935483871, "num_tokens": 119, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9407897492587141, "lm_q2_score": 0.817574478416099, "lm_q1q2_score": 0.7691656885494057}} {"text": "#Series temporais e analises preditivas - Fernando Amaral\r\nlibrary(forecast)\r\nlibrary(ggplot2)\r\n\r\n#lambda = 0, logaritmica \r\nt1 = BoxCox(AirPassengers,lambda =0 )\r\nautoplot(t1)\r\n\r\n#lambda = 0.34 \r\nt2 = BoxCox(AirPassengers,lambda =.1 )\r\nautoplot(t2)\r\n\r\n#gera labda automático\r\nlbd = BoxCox.lambda(AirPassengers)\r\nprint(lbd)\r\nt3 = BoxCox(AirPassengers,lambda =lbd )\r\nautoplot(t3)\r\n\r\n#diferenciacao \r\nt4 = diff(AirPassengers)\r\nautoplot(t4)\r\n\r\n#logaritmica\r\nt5 = log10(AirPassengers)\r\nautoplot(t5)\r\n\r\nsplit.screen( figs = c( 2, 2 ) )\r\nscreen(1)\r\nplot(t1)\r\nscreen(2)\r\nplot(t2)\r\nscreen(3)\r\nplot(t3)\r\nscreen(4)\r\nplot(t5)\r\nclose.screen( all = TRUE )\r\n\r\n\r\n\r\n\r\n", "meta": {"hexsha": "ecd460711179eadd6c40b4834c9a6a15b83bb0de", "size": 652, "ext": "r", "lang": "R", "max_stars_repo_path": "Udemy/Series Temporais e Analises Preditivas/Resources/Codigo/5.5.Transformacoes.r", "max_stars_repo_name": "tarsoqueiroz/Rlang", "max_stars_repo_head_hexsha": "b2d4fdd967ec376fbf9ddb4a7250c11d3abab52e", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Udemy/Series Temporais e Analises Preditivas/Resources/Codigo/5.5.Transformacoes.r", "max_issues_repo_name": "tarsoqueiroz/Rlang", "max_issues_repo_head_hexsha": "b2d4fdd967ec376fbf9ddb4a7250c11d3abab52e", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Udemy/Series Temporais e Analises Preditivas/Resources/Codigo/5.5.Transformacoes.r", "max_forks_repo_name": "tarsoqueiroz/Rlang", "max_forks_repo_head_hexsha": "b2d4fdd967ec376fbf9ddb4a7250c11d3abab52e", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 15.9024390244, "max_line_length": 58, "alphanum_fraction": 0.6840490798, "num_tokens": 227, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9407897459384732, "lm_q2_score": 0.817574471748733, "lm_q1q2_score": 0.769165679562272}} {"text": "## Author: Sergio García Prado\n## Title: Exercises with Solutions 6\n\nrm(list = ls())\n\n\nP <- matrix(c( 0, 1/3, 2/3,\n 1/3, 0, 2/3,\n 1, 0, 0),\n 3, 3, byrow = TRUE)\n\nlambdas <- 1 / c(8, 3, 6)\n\n(Q <- P * lambdas + diag(-lambdas))\n# -0.1250000\t 0.04166667 0.08333333\n# 0.1111111\t-0.33333333\t 0.22222222\n# 0.1666667\t 0.00000000\t-0.16666667\n\n(A <- cbind(Q[, 1:(nrow(Q) - 1)], rep(1, nrow(Q))))\n# -0.1250000\t 0.04166667\t1\n# 0.1111111\t-0.33333333\t1\n# 0.1666667\t 0.00000000\t1\n\n(stationary <- solve(A)[nrow(A), ])\n# 0.558139534883721 0.0697674418604651 0.372093023255814\n\n(non.playing.ratio <- stationary[3])\n# 0.372093023255814\n\n(mean.pay <- sum(stationary * c(40, 30, 20)))\n# 31.8604651162791\n", "meta": {"hexsha": "f2d7f1a3caa6918b99c2cea93341d8208ab312a5", "size": 734, "ext": "r", "lang": "R", "max_stars_repo_path": "stochastic-processes/proposed-exercises/continuous-6.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "stochastic-processes/proposed-exercises/continuous-6.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "stochastic-processes/proposed-exercises/continuous-6.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.9375, "max_line_length": 56, "alphanum_fraction": 0.5885558583, "num_tokens": 341, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9381240125464115, "lm_q2_score": 0.8198933293122506, "lm_q1q2_score": 0.7691616199544449}} {"text": "\n##Loading the necessary libraries\nlibrary(deSolve)\n\n### Rosenzweig-MacArthur model###\n\n## ODE system to be integrated\nRM <- function(t, y, parms){\n with(as.list(c(y, parms)),\n {\n dR = r*R*(1-R/K) - a*R*C/(1+a*h*R)\n dC = e*a*R*C/(1 + a*h*R) - d*C\n return(list(c(R=dR,C=dC)))\n })\n}\n\n##initial parameters\nparms1 = c(r=1, K=10, a=1, h=0.1, e=0.1, d=0.1)\n\n##initial population sizes\ny0 = c(R=1,C=1)\n\n##running the numerical solution from time 1 to 1000\nout = ode(y=y0, times = seq(from=1, to=1000, by=0.5), func = RM, parms = parms1)\n\n##plotting the solution\n## In a R console the code enclosed between #'s are enough. \n## For the current version of ipython it is necessary to enclose it within\n## a with() statement, see https://github.com/takluyver/IRkernel/issues/23\nwith(.GlobalEnv, {\n #########################################################################\n matplot(x=out[,1], y=out[,2:3], type = \"l\", lwd=2, lty=1,\n col=c(\"blue\", \"darkgreen\"), xlab=\"Time\", ylab=\"Population size\")\n legend(\"topright\", legend = c(\"Resource\",\"Consumer\"), \n lty = 1, lwd=2, col=c(\"blue\", \"darkgreen\"))\n #########################################################################\n}\n )\n\n\n\n## Phase space flow and fixed points\n##first we need to calculate the coordinates for the vectors\nxs = seq(from=0.9, to=1.3, length.out=7)\nys = seq(from=0.94, to=1.04, length.out=7)\ncoords = expand.grid(R=xs, C=ys)\n## And then loop over all coordinates to calculate the derivatives at that points\ndvs = matrix(NA, ncol=2, nrow=nrow(coords))\nfor(i in 1:nrow(coords))\n dvs[i,] = unlist(RM(t=1, y = coords[i,], parms = parms1))\n\n##now we plot the trajectory\n plot(x=out[,2], y=out[,3], type=\"l\", lwd=2, col=\"blue\",\n xlab=\"Resource\",ylab=\"Consumer\", xlim=c(0.9,1.3), ylim=c(0.94,1.04))\n ##and add the vector field\n arrows(x0=coords[,1], y0=coords[,2], x1=coords[,1]+dvs[,1]*0.5,\n y1=coords[,2]+dvs[,2]*0.5, length=0.1, lwd=2)\n\n\n# now K = 15\n##Messing a little with the parameters\nparms2 = c(r=1, K=15, a=1, h=0.1, e=0.1, d=0.1)\n\nout2 = ode(y=y0, times = seq(from = 1, to = 1000, by=0.5), func = RM, parms = parms2)\n\n##plotting the solution\nwith(.GlobalEnv,{\n #####################################################################################\n matplot(x=out2[,1], y=out2[,2:3], type = \"l\", lwd=2, lty=1,col=c(\"blue\", \"darkgreen\"),\n xlab=\"Time\", ylab=\"Population size\")\n legend(\"topleft\", legend = c(\"Resource\",\"Consumer\"), lty = 1, lwd=2,\n col=c(\"blue\", \"darkgreen\"))\n #####################################################################################\n })\n\n##calculating the vectors again\nxs = seq(from=0,to=6,length.out=8)\nys = seq(from=0,to=2,length.out=8)\ncoords = expand.grid(R=xs,C=ys)\ndvs = matrix(NA, ncol=2, nrow=nrow(coords))\nfor(i in 1:nrow(coords))\n dvs[i,] = unlist(RM(t=1, y = coords[i,], parms = parms2))\n\n##The trajectory\nwith(.GlobalEnv,{\n ##################################################################################### \n plot(x=out2[,2],y=out2[,3], type=\"l\", lwd=2, col=\"blue\",\n xlab=\"Resource\", ylab=\"Consumer\", xlim=c(0,6),ylim=c(0,2))\n ##and vectors\n arrows(x0=coords[,1], y0=coords[,2], x1=coords[,1]+dvs[,1]*0.5,\n y1=coords[,2]+dvs[,2]*0.5, length=0.1, lwd=2)\n ##################################################################################### \n })\n\n##plotting minimum and maximum population sizes with different K values\n\n##object with the line numbers we will use for the following plot\nlines = (nrow(out)-500):nrow(out)\n\n##creating an empty plot\nwith(.GlobalEnv,{\n ##################################################################################### \n plot(0.1, type=\"n\", xlim=c(0,20), ylim=range(out2[lines,2:3]), log=\"y\",\n xlab=\"K\", ylab=\"Min and Max population\")\n\n##points for the K = 10\n points(x = c(10,10), y = range(out[lines,3]), pch=21,bg=\"darkgreen\", cex=3)\n points(x = c(10,10), y = range(out[lines,2]), pch=21,bg=\"blue\", cex=3)\n\n##points for the K = 15\n points(c(15,15), range(out2[lines,3]), pch=21,bg=\"darkgreen\", cex=3)\n points(c(15,15), range(out2[lines,2]), pch=21,bg=\"blue\", cex=3)\n ##################################################################################### \n })\n\n## this block calculates solutions for many K's, it should take some time\nKK = seq(from = 0.5, to=25, by=0.5)\nrminmax = matrix(NA, ncol=2, nrow=length(KK))#resource minimum and maximum\ncminmax = matrix(NA, ncol=2, nrow=length(KK))#consumer minimux ans maximum\n\n## Loop over all values of K andd get min and max population sizes\nfor(i in 1:length(KK)){\n parmsi = c(r=1, K=KK[i], a=1, h=0.1, e=0.1, d=0.1) \n y0 = c(R=1,C=1)\n out3 = ode(y=y0, times = seq(from = 1, to = 1000, by=0.5), func = RM, parms = parmsi)\n rminmax[i,] = range(out3[(nrow(out3)-500):nrow(out3),2])\n cminmax[i,] = range(out3[(nrow(out3)-500):nrow(out3),3])\n}\nwith(.GlobalEnv,{\n ##################################################################################### \n ## Plot of bifurcation digram with min and max population sizes\n plot(x=KK, y=rminmax[,1], type=\"l\", lwd=2, col=\"blue\",ylim=range(rminmax), log=\"y\",\n xlab=\"K\", ylab=\"Min and Max population\")\n points(x=KK, y=rminmax[,2], type=\"l\", lwd=2, col=\"blue\")\n points(x=KK, y=cminmax[,1], type=\"l\", lwd=2, col=\"darkgreen\",ylim=range(rminmax))\n points(x=KK, y=cminmax[,2], type=\"l\", lwd=2, col=\"darkgreen\",ylim=range(rminmax))\n ##################################################################################### \n })\n\n### Consumer-resource dynamics in a seasonal environment ###\n## time sequence \ntime <- seq(0, 2000, by = .5)\n\n## parameters: a named vector\nparameters <- c(r0=1, alpha=0.1, T=80, K=10, a=1, h=0.1, e=0.1, d=0.1)\n\n## initial conditions: a named vector\nstate <- c(R = 1, C = 1)\n\n## R function to calculate the value of the derivatives at each time value\n## Use the names of the variables as defined in the vectors above\nRM2 <- function(t, state, parameters){\n with(as.list(c(state, parameters)), {\n r = r0 * (1 + alpha*sin(2*pi*t/T))\n dR = R * ( r*(1 - R/K) - a*C / (1 + a*h*R) )\n dC = e*a*R*C / (1 + a*h*R) - d*C\n return(list(c(dR, dC)))\n })\n}\n\n## Integration with 'ode'\nout <- ode(y = state, times = time, func = RM2, parms = parameters)\n\n## Ploting with matplot\nwith(.GlobalEnv,{\n ##################################################################################### \n matplot(x = out[,1], y = out[,2:3], type=\"l\", lwd=2, lty = 1,\n col=c(\"blue\", \"darkgreen\"), xlab = \"Time\", ylab = \"Population size\")\n legend(\"topright\", c(\"Resource\", \"Consumer\"), lty=1, lwd=2, col=c(\"blue\", \"darkgreen\"))\n ##################################################################################### \n })\n\n## A resonance diagram ##\n## New time sequence \ntime <- seq(0, 6000, by = 1)\n## Sequence of values of T\nTT <- seq(1, 80, by = 2)\n## A matrix to store the results\nresults <- matrix(ncol=4, nrow=length(TT),\n dimnames=list(NULL, c(\"R.min\",\"R.max\",\"C.min\",\"C.max\")))\n## Loop over all values in TT\nfor(i in 1:length(TT)){\n parameters <- c(r0=1, alpha=0.1, T=TT[i], K=10, a=1, h=0.1, e=0.1, d=0.1)\n tmp1 <- ode(y = state, times = time, func = RM2, parms = parameters)\n results[i,1:2] <- range(tmp1[1001:nrow(tmp1), 2])\n results[i,3:4] <- range(tmp1[1001:nrow(tmp1), 3])\n}\n\n## Plot of resonance diagram\nwith(.GlobalEnv,{\n ##################################################################################### \n plot(R.min ~ TT , data=results, type=\"l\", lwd=2, lty = 1,\n col=\"blue\", xlab = \"T\", ylab = \"Min / Max population size\",\n log=\"y\", ylim = range(results))\n lines(R.max ~ TT, data=results, type=\"l\", lwd=2, lty = 1, col=c(\"blue\"))\n lines(C.min ~ TT, data=results, type=\"l\", lwd=2, lty = 1, col=c(\"darkgreen\"))\n lines(C.max ~ TT, data=results, type=\"l\", lwd=2, lty = 1, col=c(\"darkgreen\")) \n legend(\"topright\", c(\"Resource\", \"Consumer\"), lty=1, lwd=2, col=c(\"blue\", \"darkgreen\"))\n ##################################################################################### \n })\n", "meta": {"hexsha": "da8426e8e3668a0bf893e9eb173fb0ebe48cb11a", "size": 8212, "ext": "r", "lang": "R", "max_stars_repo_path": "Qualitative analysis and Bifurcation diagram Tutorial - R.r", "max_stars_repo_name": "renatocoutinho/ode_examples", "max_stars_repo_head_hexsha": "49ec6f7cb7e53c1150ac68c44c30f822c97c1162", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Qualitative analysis and Bifurcation diagram Tutorial - R.r", "max_issues_repo_name": "renatocoutinho/ode_examples", "max_issues_repo_head_hexsha": "49ec6f7cb7e53c1150ac68c44c30f822c97c1162", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Qualitative analysis and Bifurcation diagram Tutorial - R.r", "max_forks_repo_name": "renatocoutinho/ode_examples", "max_forks_repo_head_hexsha": "49ec6f7cb7e53c1150ac68c44c30f822c97c1162", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 40.855721393, "max_line_length": 93, "alphanum_fraction": 0.5088894301, "num_tokens": 2555, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9111797027760038, "lm_q2_score": 0.843895106480586, "lm_q1q2_score": 0.7689400922971044}} {"text": "## 1. Calculating Grades In R ##\n\nprint((90 + 81 + 92)/3)\n\n## 2. Performing Multiple Calculations ##\n\nprint((84 + 95 + 79)/3)\nprint((95 + 86 + 93)/3)\n\n## 3. Performing Calculations using Arithmetic Operators ##\n\nprint((77 + 85 + 90)/3)\nprint((92 + 90 + 91)/3)\nprint((85 + 88 + 95)/3)\n\n## 4. Performing Calculations with Order of Operations ##\n\nprint(88 - ((88 + 87.66667 + 86 + 91.33333 + 84 + 91 + 89.33333)/7))\n\n## 5. Creating Comments ##\n\n# Operations\n\nprint(\n 88 - ((88 + 87.66667 + 86 + 91.33333 + 84 + 91 + 89.33333)/7) \n)\n\n## 6. Assigning Values to a Variable ##\n\nmath <- 88 \n\n# Add your code below\nchemistry <- 87.66667\nwriting <- 86\nart <- 91.33333\nhistory <- 84\nmusic <- 91\nphysical_education <- 89.33333\n\n## 7. Performing Calculations Using Variables ##\n\nmath <- 88 \nchemistry <- 87.66667\nwriting <- 86\nart <- 91.33333\nhistory <- 84\nmusic <- 91\nphysical_education <- 89.33333\n\ngpa <- (math + chemistry + writing + art + history + music + physical_education)/7\n\nhistory_difference <- history - gpa\n\n## 8. Creating Vectors ##\n\nmath <- 88 \nchemistry <- 87.66667\nwriting <- 86\nart <- 91.33333\nhistory <- 84\nmusic <- 91\nphysical_education <- 89.33333\n\nfinal_scores <- c(math, chemistry, writing, art, history, music, physical_education)\n\n## 9. Calculating the Mean ##\n\nfinal_scores <- c(math, chemistry, writing, art, history, music, physical_education)\n\ngpa <- mean(final_scores)\n\n## 10. Performing Operations on Vectors ##\n\nfinal_scores <- c(math, chemistry, writing, art, history, music, physical_education)\n\nhighest_score <- max(final_scores)\nlowest_score <- min(final_scores)\nnum_classes <- length(final_scores)", "meta": {"hexsha": "e74eb05eebd279b07032abc95a30ae85f2d56380", "size": 1628, "ext": "r", "lang": "R", "max_stars_repo_path": "R Fundamentals/Introduction to R Programming-310.r", "max_stars_repo_name": "nairachyut/dataquest-projects", "max_stars_repo_head_hexsha": "0807564bb35f39df21a84c8d97ab8eb3a428fb19", "max_stars_repo_licenses": ["Unlicense"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2020-05-23T20:02:07.000Z", "max_stars_repo_stars_event_max_datetime": "2020-07-20T13:01:20.000Z", "max_issues_repo_path": "R Fundamentals/Introduction to R Programming-310.r", "max_issues_repo_name": "nairachyut/dataquest-projects", "max_issues_repo_head_hexsha": "0807564bb35f39df21a84c8d97ab8eb3a428fb19", "max_issues_repo_licenses": ["Unlicense"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R Fundamentals/Introduction to R Programming-310.r", "max_forks_repo_name": "nairachyut/dataquest-projects", "max_forks_repo_head_hexsha": "0807564bb35f39df21a84c8d97ab8eb3a428fb19", "max_forks_repo_licenses": ["Unlicense"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 20.8717948718, "max_line_length": 84, "alphanum_fraction": 0.671990172, "num_tokens": 523, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9458012732322215, "lm_q2_score": 0.8128673178375735, "lm_q1q2_score": 0.7688109441796379}} {"text": "# Case diagnostics\r\n\r\nbrain <- read.table('brain.txt',as.is=T, header=T)\r\n\r\nbrain$loggest <- log(brain$gest)\r\nbrain$logbrain <- log(brain$brain)\r\nbrain$logbody <- log(brain$body)\r\nbrain$loglitter <- log(brain$litter)\r\n\r\nbrain.lm <- lm(logbrain ~ logbody + loglitter + loggest, data=brain)\r\n\r\nrstandard(brain.lm)\r\n# internally standardized residuals\r\n\r\nrstudent(brain.lm)\r\n# externally studentized residuals (use MSE(-i))\r\n\r\ninfluence.measures(brain.lm)\r\n# computes (and prints) DFBETA's, DFFITS, Cook's D and Hii\r\n# also computes the covariance ratio, which I don't use,\r\n# but it's there if in case you want it.\r\n\r\n# result of influence.measures has class infl.\r\n# can access each bit (e.g. to plot) by burrowing into the infl \r\n# class structure, or you can access each diagnostic by specific\r\n# functions.\r\n\r\n# N.B. A plot of only one thing uses 1:N as the X axis\r\n\r\nplot(dffits(brain.lm))\r\nplot(cooks.distance(brain.lm))\r\nplot(hatvalues(brain.lm))\r\n\r\ndfb <- dfbetas(brain.lm)\r\n# there are four columns because k=3, \r\n# plot each column of dfbetas\r\noldpar <- par(mfrow=c(2,2), mar=c(3,4,2,1)+0.1)\r\nfor (i in 1:4) { plot(dfb[,i]); title(dimnames(dfb)[[2]][i])}\r\npar(oldpar)\r\n\r\n\r\n", "meta": {"hexsha": "52d40d5675827604e8314a9aa12a54ce318ee876", "size": 1186, "ext": "r", "lang": "R", "max_stars_repo_path": "RFrontEndSolution/Tests Repo/Rscripts All (163 files)/brain2.r", "max_stars_repo_name": "AlexandrosPlessias/CompilerFrontEndForRLanguage", "max_stars_repo_head_hexsha": "71e3e60476f6f83b05cc97c625265edbde086341", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "RFrontEndSolution/Tests Repo/Rscripts All (163 files)/brain2.r", "max_issues_repo_name": "AlexandrosPlessias/CompilerFrontEndForRLanguage", "max_issues_repo_head_hexsha": "71e3e60476f6f83b05cc97c625265edbde086341", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "RFrontEndSolution/Tests Repo/Rscripts All (163 files)/brain2.r", "max_forks_repo_name": "AlexandrosPlessias/CompilerFrontEndForRLanguage", "max_forks_repo_head_hexsha": "71e3e60476f6f83b05cc97c625265edbde086341", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 28.2380952381, "max_line_length": 69, "alphanum_fraction": 0.6880269815, "num_tokens": 354, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9196425355825848, "lm_q2_score": 0.8354835350552603, "lm_q1q2_score": 0.7683461966157209}} {"text": "library(deSolve)\nlibrary(rootSolve)\nlibrary(phaseR)\n\n\nsirmod = function(t, y, parms) {\n # Pull state variables from y vector\n S = y[1]\n I = y[2]\n R = y[3]\n # Pull parameter values from parms vector\n beta = parms[\"beta\"]\n mu = parms[\"mu\"]\n gamma = parms[\"gamma\"]\n N = parms[\"N\"]\n # Define equations\n dS = mu * (N - S) - beta * S * I/N\n dI = beta * S * I/N - (mu + gamma) * I\n dR = gamma * I - mu * R\n res = c(dS, dI, dR)\n # Return list of gradients\n list(res)\n}\n\ntimes = seq(0, 26, by = 1/10)\nparms = c(mu = 0, N = 1, beta = 2, gamma = 1/2)\nstart = c(S = 0.999, I = 0.001, R = 0)\n\nout = ode(y = start, times = times, func = sirmod, \n parms = parms)\nout=as.data.frame(out)\nhead(round(out, 3))\n\nplot(x = out$time, y = out$S, ylab = \"Fraction\", \n xlab = \"Time\", type = \"l\")\nlines(x = out$time, y = out$I, col = \"red\")\nlines(x = out$time, y = out$R, col = \"green\")\n\n#Calculate R0\nR0 = parms[\"beta\"]/(parms[\"gamma\"]+parms[\"mu\"])\n\n#Adjust margins to accommodate a second right axis\npar(mar = c(5,5,2,5))\n#Plot state variables\nplot(x = out$time, y = out$S, ylab = \"Fraction\",\n xlab = \"Time\", type = \"l\")\nlines(x = out$time, y = out$I, col = \"red\")\nlines(x = out$time, y = out$R, col = \"green\")\n\n#Add vertical line at turnover point\nxx = out$time[which.max(out$I)]\nlines(c(xx,xx), c(1/R0,max(out$I)), lty = 3)\n\n#prepare to superimpose 2nd plot\npar(new = TRUE)\n#plot effective reproductive ratio (w/o axes)\nplot(x = out$time, y = R0*out$S, type = \"l\", lty = 2,\n lwd = 2, col = \"black\", axes = FALSE, xlab = NA, \n ylab = NA, ylim = c(-.5, 4.5))\nlines(c(xx, 26), c(1,1), lty = 3)\n#Add right-hand axis for RE\naxis(side = 4)\nmtext(side = 4, line = 4, expression(R[E]))\n#Add legend\nlegend(\"right\", legend = c(\"S\", \"I\", \"R\", \n expression(R[E])), lty = c(1,1,1, 2), \n col = c(\"black\", \"red\", \"green\", \"black\"))\n\nequil=runsteady(y=c(S=1-1E-5, I=1E-5, R=0), \ntimes=c(0,1E5), func=sirmod, parms=parms)\nround(equil$y, 3)\n\n#Candidate values for R0 and beta\nR0 = seq(0.1, 5, length=50)\nbetas= R0 * 1/2\n#Vector of NAs to be filled with numbers\nf = rep(NA, 50)\n#Loop over i from 1, 2, ..., 50\nfor(i in seq(from=1, to=50, by=1)){\n equil=runsteady(y=c(S=1-1E-5, I=1E-5, \n R=0), times=c(0,1E5), func=sirmod, \n parms=c(mu=0, N=1, beta=betas[i], gamma=1/2))\n f[i]=equil$y[\"R\"]\n}\nplot(R0, f, type=\"l\", xlab=expression(R[0]))\ncurve(1-exp(-x), from=1, to=5, add=TRUE, col=\"red\")\n\n#Define function\nfn=function(x, R0){\n exp(-(R0*(1-x))) - x\n}\n1-uniroot(fn, lower = 0, upper = 1-1E-9, \n tol = 1e-9, R0=2)$root\n#check accuracy of approximation:\nexp(-2)-uniroot(fn, lower = 0, upper = 1-1E-9, \n tol = 1e-9, R0=2)$root\n\ntimes = seq(0, 52*50, by=.1)\nparms = c(mu = 1/(50*52), N = 1, beta = 2, \n gamma = 1/2)\nstart = c(S=0.19, I=0.01, R = 0.8)\nout = as.data.frame(ode(y=start, times=times, \n func=sirmod, parms=parms))\npar(mfrow=c(1,2)) #Make room for side-by-side plots \nplot(times, out$I, ylab=\"Fraction\", xlab=\"Time\", \n type=\"l\")\nplot(out$S, out$I, type=\"l\", xlab=\"Susceptible\", \n ylab=\"Infected\")\n\nsimod = function(t, y, parameters) {\n S = y[1]\n I = y[2]\n \n beta = parameters[\"beta\"]\n mu = parameters[\"mu\"]\n gamma = parameters[\"gamma\"]\n N = parameters[\"N\"]\n \n dS = mu * (N - S) - beta * S * I/N\n dI = beta * S * I/N - (mu + gamma) * I\n res = c(dS, dI)\n list(res)\n}\n\n#Plot vector field\nfld = flowField(simod, xlim = c(0.15,0.35), \n ylim = c(0,.01), parameters = parms, system = \"two.dim\", \n add = FALSE, ylab = \"I\", xlab = \"S\")\n#Add trajectory\nout = as.data.frame(ode(y = c(S = 0.19, I = 0.01), \n times = seq(0, 52*100, by = .1), func = simod, parms = parms))\n lines(out$S, out$I, col = \"red\")\n#Add S-isocline\ncurve(parms[\"mu\"]*(1/x-1)/parms[\"beta\"], 0.15, 0.35, \n xlab = \"S\", ylab = \"I\", add = TRUE)\n#Add I-isocline\nicline = (parms[\"gamma\"] + parms[\"mu\"])/parms[\"beta\"]\nlines(rep(icline, 2), c(0,0.01))\nlegend(\"topright\", legend = c(\"Transient\", \"Isoclines\"),\n lty = c(1, 1), col = c(\"red\", \"black\"))\n\n# Pull values from parms vector\ngamma = parms[\"gamma\"]\nbeta = parms[\"beta\"]\nmu = parms[\"mu\"]\nN = parms[\"N\"]\n# Endemic equilibrium\nSstar = (gamma + mu)/beta\nIstar = mu * (beta/(gamma + mu) - 1)/beta\neq1 = list(S = Sstar, I = Istar)\n\n# Define equations\ndS = expression(mu * (N - S) - beta * S * I/N)\ndI = expression(beta * S * I/N - (mu + gamma) * I)\n# Differentiate w.r.t. S and I\nj11 = D(dS, \"S\")\nj12 = D(dS, \"I\")\nj21 = D(dI, \"S\")\nj22 = D(dI, \"I\")\n\n#Evaluate Jacobian at equilibrium\nJ=with(data=eq1, expr=matrix(c(eval(j11),eval(j12),\n eval(j21),eval(j22)), nrow=2, byrow=TRUE))\n#Calculate eigenvalues\neigen(J)$values\n\n2 * pi/(Im(eigen(J)$values[1]))\n\neq2=list(S=1,I=0)\nJ=with(eq2, \n matrix(c(eval(j11),eval(j12),eval(j21),\n eval(j22)), nrow=2, byrow=TRUE))\neigen(J)$values\n\nchainSIR = function(t, logx, params){\nx = exp(logx)\nu = params[\"u\"]\nS = x[1]\nI = x[2:(u+1)]\nR = x[u+2]\nwith(as.list(params),{\n dS = mu * (N - S) - sum(beta * S * I) / N\n dI = rep(0, u)\n dI[1] = sum(beta * S * I) / N - (mu + u*gamma) * I[1]\n if(u>1){\n for(i in 2:u){\n dI[i] = u*gamma * I[i-1] - (mu+u*gamma)* I[i]\n }\n }\n dR = u*gamma * I[u] - mu * R\n res = c(dS/S, dI/I, dR/R)\n list(res)\n})\n}\n\ntimes = seq(0, 10, by=1/52)\nparas2 = c(mu = 1/75, N = 1, beta = 625, \n gamma = 365/14, u=1)\nxstart2 = log(c(S = .06, I = c(0.001, rep(0.0001, \n paras2[\"u\"]-1)), R = 0.0001))\nout = as.data.frame(ode(xstart2, times, chainSIR, \n paras2))\nplot(times, exp(out[,3]), ylab = \"Infected\", xlab =\n \"Time\", ylim = c(0, 0.01), type = 'l')\n\nparas2[\"u\"] = 2\nxstart2 = log(c(S = .06, I = c(0.001, rep(0.0001/\n paras2[\"u\"], paras2[\"u\"]-1)), R = 0.0001))\nout2 = as.data.frame(ode(xstart2, times, chainSIR, \n paras2))\nlines(times, apply(exp(out2[,-c(1:2,length(out2))]),\n 1 ,sum), col = 'blue')\n\nparas2[\"u\"] = 73\nxstart2 = log(c(S = .06, I = c(0.001, rep(0.0001/\n paras2[\"u\"], paras2[\"u\"]-1)), R = 0.0001))\nout3 = as.data.frame(ode(xstart2, times, chainSIR, \n paras2))\nlines(times, apply(exp(out3[,-c(1:2,length(out3))]),\n 1, sum), col='red', lwd=2, lty=2)\n\nparas2[\"u\"] = 500\nxstart2 = log(c(S = .06, I = c(0.001, rep(0.0001/\n paras2[\"u\"], paras2[\"u\"]-1)), R = 0.0001))\nout4 = as.data.frame(ode(xstart2, times, chainSIR, \n paras2))\nlines(times, apply(exp(out4[,-c(1:2,length(out4))]),\n 1,sum, na.rm = TRUE), col = 'green')\n\nlegend(\"topright\", legend = c(\"SIR\", \"u=2\", \"u=500\", \n \"u=73 (H-S)\"), lty = c(1,1,1,2), lwd = c(1,1,1, 2),\n col = c(\"black\", \"blue\", \"green\", \"red\"))\n", "meta": {"hexsha": "fb109fc3093b300df4029295d9a58f21c59f798a", "size": 6571, "ext": "r", "lang": "R", "max_stars_repo_path": "models/bjornstad_2018/chapter2_sir.r", "max_stars_repo_name": "epimodels/epicookbook", "max_stars_repo_head_hexsha": "496088ddc8fc913505d92877e0a687c81976c8f2", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "models/bjornstad_2018/chapter2_sir.r", "max_issues_repo_name": "epimodels/epicookbook", "max_issues_repo_head_hexsha": "496088ddc8fc913505d92877e0a687c81976c8f2", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "models/bjornstad_2018/chapter2_sir.r", "max_forks_repo_name": "epimodels/epicookbook", "max_forks_repo_head_hexsha": "496088ddc8fc913505d92877e0a687c81976c8f2", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2020-10-10T12:46:31.000Z", "max_forks_repo_forks_event_max_datetime": "2020-10-10T12:46:31.000Z", "avg_line_length": 28.2017167382, "max_line_length": 68, "alphanum_fraction": 0.5586668696, "num_tokens": 2656, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8976952975813454, "lm_q2_score": 0.855851143290548, "lm_q1q2_score": 0.7682935467615432}} {"text": "\r\n\r\n# Goals: Scare the hell out of children with the Cauchy distribution.\r\n\r\n# A function which simulates N draws from one of two distributions,\r\n# and returns the mean obtained thusly.\r\none.simulation <- function(N=100, distribution=\"normal\") {\r\n if (distribution == \"normal\") {\r\n x <- rnorm(N)\r\n } else {\r\n x <- rcauchy(N)\r\n }\r\n mean(x)\r\n}\r\n\r\nk1 <- density(replicate(1000, one.simulation(20)))\r\nk2 <- density(replicate(1000, one.simulation(20, distribution=\"cauchy\")))\r\n\r\nxrange <- range(k1$x, k2$x)\r\nplot(k1$x, k1$y, xlim=xrange, type=\"l\", xlab=\"Estimated value\", ylab=\"\")\r\ngrid()\r\nlines(k2$x, k2$y, col=\"red\")\r\nabline(v=.5)\r\nlegend(x=\"topleft\", bty=\"n\",\r\n lty=c(1,1),\r\n col=c(\"black\", \"red\"),\r\n legend=c(\"Mean of Normal\", \"Mean of Cauchy\"))\r\n# The distribution of the mean of normals collapses into a point;\r\n# that of the cauchy does not.\r\n\r\n# Here's more scary stuff --\r\nfor (i in 1:10) {\r\n cat(\"Sigma of distribution of 1000 draws from mean of normal - \",\r\n sd(replicate(1000, one.simulation(20))), \"\\n\")\r\n}\r\nfor (i in 1:10) {\r\n cat(\"Sigma of distribution of 1000 draws from mean of cauchy - \",\r\n sd(replicate(1000, one.simulation(20, distribution=\"cauchy\"))), \"\\n\")\r\n}\r\n\r\n# Exercise for the reader: Compare the distribution of the median of\r\n# the Normal against the distribution of the median of the Cauchy.\r\n\r\n", "meta": {"hexsha": "6fa8c67cc777ae8f570b0594225c8dbfdb035ec6", "size": 1360, "ext": "r", "lang": "R", "max_stars_repo_path": "RFrontEndSolution/Tests Repo/Rscripts All (163 files)/p7.r", "max_stars_repo_name": "AlexandrosPlessias/CompilerFrontEndForRLanguage", "max_stars_repo_head_hexsha": "71e3e60476f6f83b05cc97c625265edbde086341", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "RFrontEndSolution/Tests Repo/Rscripts All (163 files)/p7.r", "max_issues_repo_name": "AlexandrosPlessias/CompilerFrontEndForRLanguage", "max_issues_repo_head_hexsha": "71e3e60476f6f83b05cc97c625265edbde086341", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "RFrontEndSolution/Tests Repo/Rscripts All (163 files)/p7.r", "max_forks_repo_name": "AlexandrosPlessias/CompilerFrontEndForRLanguage", "max_forks_repo_head_hexsha": "71e3e60476f6f83b05cc97c625265edbde086341", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 30.9090909091, "max_line_length": 76, "alphanum_fraction": 0.6448529412, "num_tokens": 395, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9149009596336303, "lm_q2_score": 0.8397339716830605, "lm_q1q2_score": 0.7682734165297918}} {"text": "n <- 1000 # assigns the value of one thousand to n\n+ x <- seq(1,n) # the above is how a sequence is created\n+ sum(x) # this is a list of numbers and sum adds them together\n\n# what I've in math and more in programming is that we say we evaluate a function when arguments are replaced specific values\n# for example if we type log2(16) we evaluate the log2 function to get the log base 2 of 16 which will return 4\nlog2(16)\n\n# from experience in R it is useful to evaluate a function inside another function\n# for example sqrt(log2(16)) which will calculate the log to the base 2 of 16 and then compute the square root of that returned value\nsqrt(log2(16))\n\n# so the first evaluation returns 4 and this is then evaluated by sqrt to give the final answer of 2\n\nx <-5 # 5 is a random number that I chose for testing\nlog(exp(x)) # this will always return the numeric value stored in x\n", "meta": {"hexsha": "a49d0d2bd91441a3d772c13d18b9fd4d52d9c150", "size": 878, "ext": "r", "lang": "R", "max_stars_repo_path": "Variables/Sequential Sum.r", "max_stars_repo_name": "Proff-Matth/R-Basics", "max_stars_repo_head_hexsha": "5055d8b2e4a52f8809f729f48f77f9481e606048", "max_stars_repo_licenses": ["Unlicense"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2020-05-24T00:52:37.000Z", "max_stars_repo_stars_event_max_datetime": "2020-05-24T00:52:37.000Z", "max_issues_repo_path": "Variables/Sequential Sum.r", "max_issues_repo_name": "Proff-Matth/R-Basics", "max_issues_repo_head_hexsha": "5055d8b2e4a52f8809f729f48f77f9481e606048", "max_issues_repo_licenses": ["Unlicense"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Variables/Sequential Sum.r", "max_forks_repo_name": "Proff-Matth/R-Basics", "max_forks_repo_head_hexsha": "5055d8b2e4a52f8809f729f48f77f9481e606048", "max_forks_repo_licenses": ["Unlicense"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2021-03-24T15:19:14.000Z", "max_forks_repo_forks_event_max_datetime": "2021-11-17T22:27:40.000Z", "avg_line_length": 51.6470588235, "max_line_length": 133, "alphanum_fraction": 0.7517084282, "num_tokens": 224, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9219218370002787, "lm_q2_score": 0.8333245994514084, "lm_q1q2_score": 0.7682601455437639}} {"text": "## coef effect sizes from association tests of features\n## se standard errors of the coefficients\n## mat input data matrix (features x samples)\nivwfe.stats <- function(coef, se, mat=NULL, rho=NULL) {\n ## From James Staley:\n ## Here is the link to Stephen Burgess’ paper we discussed on\n ## Thursday last week:\n ## http://onlinelibrary.wiley.com/doi/10.1002/sim.6835/full \n ## I have taken a look at the maths and Stouffer’s test statistic\n ## weighted by 1/SE is the same as IVW FE meta-analysis beta/SE. So, the\n ## generalised linear model approach in Stephen’s paper which is based on\n ## IVW FE meta-analysis would probably be very similar to your Stouffer’s\n ## method corrected for correlated Z-statistics. \n ## The test statistic would be: T = B/S ~ N(0,1) \n ## where B = (1^TΩ^-11)^-11^TΩ^-1β and S = sqrt((1^TΩ^-11)^-1) where β are\n ## the effect estimates, Ω is the variance-covariance matrix of the CpGs\n ## and 1 is a vector of 1’s the same length as the number of CpGs.\n\n if (is.null(rho)) {\n stopifnot(!is.null(mat))\n rho <- ivwfe.rho(mat) \n }\n ## The second diagonal matrix is the 'nudge' matrix to ensure matrix inversion\n\n ## remove missing values\n na <- is.na(coef) | is.na(se)\n if (sum(na) > 0) {\n if (sum(na) == length(coef))\n return(c(B=NA, S=NA))\n\n coef <- coef[!na]\n se <- se[!na]\n rho <- rho[!na,!na,drop=F]\n }\n \n omega <- (se%*%t(se))*rho\n omega.inv <- solve(omega)\n one <- matrix(1,nrow=nrow(omega.inv), ncol=1)\n S2 <- 1/(t(one) %*% omega.inv %*% one)\n c(B=S2 * (t(one) %*% omega.inv) %*% coef,\n S=sqrt(S2)) \n}\n\nivwfe.getz <- function(coef, se, mat=NULL, rho=NULL) {\n stats <- ivwfe.stats(coef, se, mat, rho)\n as.vector(stats[\"B\"]/stats[\"S\"])\n}\n\n\n\nivwfe.rho <- function(mat) {\n mat <- t(mat)\n rho <- cor(mat, use=\"p\") + diag(x=0.05,ncol(mat),ncol(mat))\n}\n\nivwfe.ma <- function(estimates, se) {\n weights <- 1/se^2\n se <- sqrt(1/rowSums(weights, na.rm=T))\n estimates <- rowSums(estimates * weights, na.rm=T)/rowSums(weights, na.rm=T)\n z <- estimates/se\n p <- 2*pnorm(-abs(z), lower.tail=T)\n data.frame(estimate=estimates,\n se=se,\n z=z,\n p.value=p)\n}\n\n", "meta": {"hexsha": "cb822cd8dd2a6c45d345f027189197a7893ec39d", "size": 2314, "ext": "r", "lang": "R", "max_stars_repo_path": "R/ivwfe.r", "max_stars_repo_name": "pjhop/dmrff", "max_stars_repo_head_hexsha": "1f4b6785e18701eac4f76adde0e37f51bd0d1bcf", "max_stars_repo_licenses": ["Artistic-2.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/ivwfe.r", "max_issues_repo_name": "pjhop/dmrff", "max_issues_repo_head_hexsha": "1f4b6785e18701eac4f76adde0e37f51bd0d1bcf", "max_issues_repo_licenses": ["Artistic-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/ivwfe.r", "max_forks_repo_name": "pjhop/dmrff", "max_forks_repo_head_hexsha": "1f4b6785e18701eac4f76adde0e37f51bd0d1bcf", "max_forks_repo_licenses": ["Artistic-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 34.0294117647, "max_line_length": 82, "alphanum_fraction": 0.5859982714, "num_tokens": 720, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9449947070591977, "lm_q2_score": 0.8128673246376008, "lm_q1q2_score": 0.7681553193239034}} {"text": "source('./libraries.R')\n\n#### Functions ----\nT_hotelling_radial <- function(r, phi, critical, norm_data, n, p){\n n * r^2 * (t(c(cos(phi), sin(phi))) %*% solve(cov(norm_data)) %*% (c(cos(phi), sin(phi)))) * ((n - p)/(p * (n - 1))) - critical\n}\n\nT_likelihood_phi <- function(r, phi, rho, sigma_x, sigma_y, n, critical){\n ((n) / (1 - rho**2)) * \n (((r * cos(phi)) / (sigma_x))**2 +\n ((r * sin(phi)) / (sigma_y))**2 - \n (2 * rho * ((r * cos(phi)) / (sigma_x)) * ((r * sin(phi)) / (sigma_y)))\n ) - critical\n}\n\nmvnormSample_2d <- function(mu_x = 0, mu_y = 0, n = 20, rho = 0.5, sigma_x = 1, sigma_y = 1){\n mu <- c(mu_x , mu_y)\n names(mu) <- c('mu_x', 'mu_y')\n Sigma <- matrix(c(sigma_x^2, \n sigma_x * sigma_y * rho, \n sigma_x * sigma_y * rho, \n sigma_y^2), \n 2, 2, byrow = TRUE)\n sample <- mvrnorm(n = n, mu = mu, Sigma = Sigma) %>% as.data.frame()\n names(sample) <- c('x', 'y')\n return(sample)\n}\n\nHotelling_radial_cr <- function(data, len_out=180, signf_lvl = 0.05){\n n <- nrow(data)\n p <- ncol(data)\n critical <- qf(1 - signf_lvl, df1 = p, df2 = n - p)\n col_means <- colMeans(data)\n \n vred <- data.frame(phi = seq(0, 2 * pi, length.out = len_out)) %>%\n rowwise() %>%\n mutate(r = uniroot(\n f = T_hotelling_radial,\n phi = phi,\n critical = critical,\n norm_data = data,\n n = n,\n p = p,\n interval = c(0, 400)\n )$root) %>%\n ungroup() %>%\n transmute(x = col_means[1] + r * cos(phi), y = col_means[2] + r * sin(phi))\n return(vred)\n}\n\nLikelihood_radial_cr <- function(data, len_out = 180, signf_lvl = 0.05){\n n = nrow(data)\n col_sd <- apply(data, 2, sd)\n col_means <- colMeans(data)\n hat_rho <- cor(data)[1,2]\n critical <- qchisq(1 - signf_lvl, df = 2)\n vred <- data.frame(phi = seq(0, 2 * pi, length.out = len_out)) %>%\n rowwise() %>%\n mutate(r = uniroot(\n f = T_likelihood_phi,\n phi = phi,\n rho = hat_rho,\n sigma_x = col_sd[1],\n sigma_y = col_sd[2],\n n = n,\n critical = critical,\n interval = c(0,400)\n )$root) %>% \n ungroup() %>% \n transmute(x = col_means[1] + r * cos(phi), y = col_means[2] + r * sin(phi))\n # return points to plot\n return(vred)\n}\n\n# 3D sample\nmvnormSample_3d <- function(n = 20){\n mu <- c(0,0,0)\n names(mu) <- c('mu_x', 'mu_y', 'mu_z')\n Sigma <- matrix(c(1, 0.5, 0.5,\n 0.5, 1, 0.5,\n 0.5, 0.5, 1), \n 3, 3, byrow = TRUE)\n sample <- mvrnorm(n = n, mu = mu, Sigma = Sigma) %>% as.data.frame()\n names(sample) <- c('x', 'y', 'z')\n return(sample)\n}\n\n# Hotelling 3D \nHot_pivot <- function(r, phi_1, phi_2, n, p, data, critical){\n n * r^2 * \n t(c(\n cos(phi_1),\n sin(phi_1) * cos(phi_2),\n sin(phi_1) * sin(phi_2)\n )) %*%\n solve(cov(data)) %*% \n c(\n cos(phi_1),\n sin(phi_1) * cos(phi_2),\n sin(phi_1) * sin(phi_2)\n ) *\n ((n - p)/(p * (n - 1))) - critical\n}\n\nHot_cr_3d <- function(data, len_out=180, signf_lvl = 0.05){\n len_2 <- floor(sqrt(len_out/2))\n len_1 <- 2 * len_2\n n <- nrow(data)\n p <- ncol(data)\n critical <- qf(1-signf_lvl, df1 = p, df2 = n-p)\n col_means <- colMeans(data)\n phi_1 = seq(0, pi, length.out = len_1)\n phi_2 = seq(0, 2 * pi, length.out = len_2)\n vred <- expand_grid(phi_1, phi_2) %>%\n rowwise() %>%\n mutate(r = uniroot(\n f = Hot_pivot,\n phi_1 = phi_1,\n phi_2 = phi_2,\n critical = critical,\n data = data,\n n = n,\n p = p,\n interval = c(0, 400)\n )$root) %>%\n ungroup() %>%\n transmute(x = col_means[1] + r * cos(phi_1), y = col_means[2] + r * sin(phi_1) * cos(phi_2), z = col_means[3] + r * sin(phi_1) * sin(phi_2))\n return(vred)\n}\n\n# Likelihood 3D\nell_0 <- function(x, mu_hat, k, Sigma_inv, Sigma_det){\n -(1/2) * (\n t(x - mu_hat) %*%\n Sigma_inv %*%\n (x - mu_hat)\n ) -\n (k/2) * log(2* pi) - (1/2) * log(Sigma_det)\n}\n\nell <- function(r, x, phi_1, phi_2, mu_hat, k, Sigma_inv, Sigma_det){\n -(1/2) * (\n t(x - mu_hat - r * \n c(\n cos(phi_1),\n sin(phi_1) * cos(phi_2),\n sin(phi_1) * sin(phi_2)\n )\n ) %*%\n Sigma_inv %*%\n (x - mu_hat - r * \n c(\n cos(phi_1),\n sin(phi_1) * cos(phi_2),\n sin(phi_1) * sin(phi_2)\n )\n )\n ) -\n (k/2) * log(2* pi) - (1/2) * log(Sigma_det)\n}\n\nLik_pivot <- function(r, phi_1, phi_2, mu_hat, k, critical, Sigma_inv, Sigma_det, data){\n \n ells <- data %>%\n rowwise() %>% \n transmute(\n var_ell = ell(\n r = r,\n x = c(x, y, z),\n phi_1 = phi_1,\n phi_2 = phi_2,\n mu_hat = mu_hat,\n k = k,\n Sigma_inv = Sigma_inv,\n Sigma_det = Sigma_det\n ),\n var_ell_0 = ell_0(\n x = c(x, y, z),\n mu_hat = mu_hat,\n k = k,\n Sigma_inv = Sigma_inv,\n Sigma_det = Sigma_det\n )\n ) %>% \n ungroup() %>%\n summarise(sum_ell = sum(var_ell),\n sum_ell_0 = sum(var_ell_0))\n value <- -2 * (ells$sum_ell - ells$sum_ell_0) - critical\n return(value)\n}\n\nLik_cr_3d <- function(data, len_out=180, signf_lvl=0.05){\n k <- ncol(data)\n n <- nrow(data)\n cov_mtrx <- cov(data)\n Sigma_inv <- solve(cov_mtrx)\n Sigma_det <- det(cov_mtrx)\n critical <- qchisq(1-signf_lvl, df = k)\n mu_hat <- colMeans(data)\n len_2 <- floor(sqrt(len_out/2))\n len_1 <- 2 * len_2\n \n phi_1 = seq(0, pi, length.out = len_1)\n phi_2 = seq(0, 2 * pi, length.out = len_2)\n vred <- expand_grid(phi_1, phi_2) %>%\n rowwise() %>%\n mutate(r = uniroot(\n f = Lik_pivot,\n phi_1 = phi_1,\n phi_2 = phi_2,\n mu_hat = mu_hat,\n k = k,\n critical = critical,\n Sigma_inv = Sigma_inv,\n Sigma_det = Sigma_det,\n data = data,\n interval = c(0, 400)\n )$root) %>%\n ungroup() %>%\n transmute(x = mu_hat[1] + r * cos(phi_1), y = mu_hat[2] + r * sin(phi_1) * cos(phi_2), z = mu_hat[3] + r * sin(phi_1) * sin(phi_2))\n return(vred)\n \n}\n\n#### 2D example ----\n# Generate 2D data\n\n\ndata_2d <- mvnormSample_2d(n = 20)\nmu_hat <- colMeans(data_2d)\ncr_2d_hot <- Hotelling_radial_cr(data = data_2d, len_out = 180) %>% slice(chull(x, y))\ncr_2d_lik <- Likelihood_radial_cr(data = data_2d, len_out = 180) %>% slice(chull(x, y))\n\ndata_2d %>% ggplot(aes(x = x, y = y)) +\n geom_point() + \n geom_point(aes(x = mu_hat[1], y = mu_hat[2]), size = 3, alpha = .5, color = 'red') +\n geom_polygon(data = cr_2d_hot, alpha = 0.3, fill='darkgreen') +\n geom_polygon(data = cr_2d_lik, alpha = 0.3, fill='yellow')\n\n\n#### 3D example ----\ncr_plot <- function(data, colour){\n chul_3d <- convhulln(data, options = 'FA')\n mesh_3d <- mesh3d(chul_3d$p)\n mesh_3d$it <- chul_3d$hull %>% t()\n mesh_3d$ib <- NULL\n wire3d(mesh_3d, col = colour, alpha = 0.4)\n shade3d(mesh_3d, col = colour, alpha = 0.1, override = T)\n}\n\nrun_3d <- function(n_pts, n_bnry_pts){\n \n data_3d <- mvnormSample_3d(n = n_pts)\n mean_3d <- colMeans(data_3d) %>% t()\n \n # confidence regions\n data_3d_cr_hot <-\n Hot_cr_3d(data = data_3d,\n len_out = n_bnry_pts,\n signf_lvl = 0.05)\n data_3d_cr_lik <-\n Lik_cr_3d(data = data_3d,\n len_out = n_bnry_pts,\n signf_lvl = 0.05)\n \n # plot points, mu and estimates\n points3d(data_3d, alpha = 0.5)\n axes3d(c('x', 'y', 'z'))\n points3d(data_3d,\n size = 20,\n alpha = 0.2,\n col = 'grey')\n points3d(mean_3d, size = 3, col = 'red')\n points3d(mean_3d,\n size = 20,\n alpha = 0.3,\n col = 'red')\n \n # original\n points3d(data.frame(x = 0, y = 0, z = 0), size = 3, col = 'orange')\n points3d(\n data.frame(x = 0, y = 0, z = 0),\n size = 20,\n alpha = 0.3,\n col = 'orange'\n )\n \n # CR\n cr_plot(data = data_3d_cr_hot, colour = 'green')\n cr_plot(data = data_3d_cr_lik, colour = 'blue')\n}\nrun_3d(n_pts = 20, n_bnry_pts = 180)\n\n\n\n\n", "meta": {"hexsha": "d0e8fa6904c1361e6d566cc24c98ca6ad90f353d", "size": 7919, "ext": "r", "lang": "R", "max_stars_repo_path": "demo.r", "max_stars_repo_name": "VidicL13/Confidence-regions", "max_stars_repo_head_hexsha": "6ac06a0e05d16f2bf4d0cb4c38f499a32801d3e6", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "demo.r", "max_issues_repo_name": "VidicL13/Confidence-regions", "max_issues_repo_head_hexsha": "6ac06a0e05d16f2bf4d0cb4c38f499a32801d3e6", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "demo.r", "max_forks_repo_name": "VidicL13/Confidence-regions", "max_forks_repo_head_hexsha": "6ac06a0e05d16f2bf4d0cb4c38f499a32801d3e6", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.6632996633, "max_line_length": 144, "alphanum_fraction": 0.5269604748, "num_tokens": 2910, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9449947086083138, "lm_q2_score": 0.8128673178375735, "lm_q1q2_score": 0.7681553141571393}} {"text": "#Example : 2.2A Chapter : 2.2 page no : 50\r\n#Pivots and Multipliers in converting matrix to upper traingular system\r\nmatrix(c(1,-1,0,-1,2,-1,0,-1,2),ncol=3)->A\r\nA\r\nprint(paste(\"First pivot is\",A[1,1]))\r\nl21<-A[2,1]/A[1,1]\r\nprint(paste(\"Multiplier L21 to convert the second row first element to 0 is\",l21))\r\nA[2,]<-A[2,]-l21*A[1,]\r\nA\r\nprint(paste(\"The second pivot is \",A[2,2]))\r\nl32<-A[3,2]/A[2,2]\r\nA[3,]<-A[3,]-l32*A[2,]\r\nprint(\"The equivalent Upper traingular system for the matrix A is \")\r\nA", "meta": {"hexsha": "f543583ee8925c9140e2d3ac7783631304ac0218", "size": 505, "ext": "r", "lang": "R", "max_stars_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH2/EX2.2.a/Ex2_2.2a.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH2/EX2.2.a/Ex2_2.2a.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH2/EX2.2.a/Ex2_2.2a.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 36.0714285714, "max_line_length": 83, "alphanum_fraction": 0.6356435644, "num_tokens": 206, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9314625069680097, "lm_q2_score": 0.8244619350028204, "lm_q1q2_score": 0.7679553808774233}} {"text": "'''\n1.17 (Brockwell et al., 2016, p. 36)\n\nLoad the dataset deaths in R using the read.table function. Plot the data. Also create a histogram of\nthe data using the R function hist. Plot the sample autocorrelation function using the acf function. The\npresence of a strong seasonal component with period 12 is evident in the graph of the data and in the sample\nautocorrelation function.\n'''\n\ndata = read.table(\"C:/prosjekt/Time_Series_stat211/data/deaths.txt\", skip = 9, header=FALSE)\nnames(data) = c(\"month\",\"year\",\"deaths\")\ndata$time = as.Date(paste(data$year,data$month,\"15\",sep=\"-\"))\nattach(data)\nplot(time,deaths/1000, type=\"l\", xlab=\"\", ylab = \"deaths (thousands)\")\n\nacf(deaths ,lag.max = 24) #computes (and by default plots) estimates of the autocovariance or autocorrelation function\n\nhist(deaths, breaks = 15)\n\n'''\nProblem 1.6\n[BD, Exercise 1.18, page 37]\nWe are still studying the dataset deaths. In this exercise, you are supposed to reproduce the figures 1-24 and 1-25 in [BD, pp. 27-28] . \nIn 1.17, we found a period of length 12. \nFit a seasonal component using the procedure described in section 1.5.2.1 on page 26.\nYou may use the following functions or write your own:\n'''\n# Function for calculating a moving average when d is even\nma <- function(x, n=12){filter(x,c(.5,rep(1,n-1),.5)/n, sides=2)}\n# Function for finding the seasonal component\nseasonal.component <- function(x){ # x- deaths\n\t# First step: detrending\n\tdetrended <- x - ma(x)\n\t# Second step: Calculating sesonal component from detrended data\n\twt <- rowMeans(matrix(detrended[!is.na(detrended)], nrow=12,byrow=FALSE))\n\tst<-(wt - mean(wt))[c(7:12,1:6)] #seasonal component\n\treturn(st)\n}\n\n\n#sol\nlibrary(itsmr)\ndetrended <- deaths - seasonal.component(deaths) #season(deaths, 12) #removing season\n\n'''\nPlot the deseasonalized data (as in figure 1-24). Fit a quadratic trend (polynomial of\norder two) to the deseasonalized data and add the curve to the plot you just created. The\ntrend should be mb = 9952 − 71.82t + 0.8260t2 for 1 ≤ t ≤ 72. This can be done using the\nfollowing code:\n'''\n\nM <- poly(1:72, degree=2, raw=TRUE)\ntrend <- lm(detrended ~ M) # Re-estimating trend of the detrended data\n'''\nPlot the sample autocorrelation function of Yt. Forecast the data for the next 24 months\nwithout allowing for this dependence, based on the assumption that the estimated seasonal\nand trend components are true values and that Yt is a white noise sequence with zero\nmean. Calculate sb72+k for k = 1, . . . , 24 and do the forecasting by\nXbt = mb 72+k + sb72+k, k = 1, . . . , 24.\n'''\n\n#solution\nplot(data$time, detrended/1000, type=\"b\", xlab=\"\",ylab=\"(thousands)\") #plotting deseasonalized data\n\nlines(data$time, trend(detrended, 2)/1000, col=2)\n\nplot(data$time,season(deaths,12)/1000, type=\"b\",xlab=\"\",ylab=\"(thousands)\") # Plotting seasonal component\nabline(h=0) # adding horizontal line at zero\n\n##########\n'''\nPlot the original data with the forecasts appended. Later we shall see how to improve on\nthese forecasts by taking into account the dependence in the series Yt. Hint: To calculate\nmb 72+k the following code may be useful:\n'''\nM <- poly(72 + 1:24, 2, raw=TRUE)\nyhat <- predict(trend, newdata= M)\n\n#######\np.time <- seq(as.Date(\"1979-01-15\"),by=\"month\",length.out=24)\n\n#plot(time,deaths/1000,xlim=range(time,p.time),type=\"b\",\nplot(time,detrended/1000,xlim=range(time,p.time),type=\"b\",\n\t#ylim = range(deaths, yhat)/1000,\n\tylim = range(trend(detrended, 2), yhat)/1000,\n\tylab = \"(thousands)\", xlab =\"\")\n\nlines(data$time, trend(detrended, 2)/1000, col=2)\t\nlines(p.time,yhat/1000, type=\"b\", col = \"blue\")\n\n\n\n'''\nReferences\nPeter J Brockwell and Richard A Davis. Introduction to time series and forecasting;\n3rd ed. Springer texts in statistics. Springer, Cham, 2016. doi: 10.1007/\n'''\n", "meta": {"hexsha": "1ed8b97d8ab325e5caad366416e91e52f2ff6089", "size": 3766, "ext": "r", "lang": "R", "max_stars_repo_path": "hw1/hw1.r", "max_stars_repo_name": "emoen/Time_Series_stat211", "max_stars_repo_head_hexsha": "f30eb0c6a34c1eab8d347670c3b7a54f2c4c89c0", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2022-01-06T19:14:00.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-06T19:14:00.000Z", "max_issues_repo_path": "hw1/hw1.r", "max_issues_repo_name": "emoen/Time_Series_stat211", "max_issues_repo_head_hexsha": "f30eb0c6a34c1eab8d347670c3b7a54f2c4c89c0", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "hw1/hw1.r", "max_forks_repo_name": "emoen/Time_Series_stat211", "max_forks_repo_head_hexsha": "f30eb0c6a34c1eab8d347670c3b7a54f2c4c89c0", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-11-22T07:40:48.000Z", "max_forks_repo_forks_event_max_datetime": "2021-11-22T07:40:48.000Z", "avg_line_length": 38.4285714286, "max_line_length": 137, "alphanum_fraction": 0.7182687201, "num_tokens": 1137, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8596637577007393, "lm_q2_score": 0.8933093982432729, "lm_q1q2_score": 0.7679457140831982}} {"text": "\r\n# #This will be a different path if in the lab or at home\r\n# dird=\"E:\\\\OneDrive\\\\MATH4753\\\\DATAxls\\\\\" # 2017\r\n# \r\n# #my function to read data \r\n# myread=function(csv){\r\n# fl=paste(dird,csv,sep=\"\")\r\n# read.table(fl,header=TRUE,sep=\",\")\r\n# }\r\n# #EASY WAY TO READ IN FILES\r\n\r\n#spruce.df=myread(\"SPRUCE.csv\")#MS pg478\r\n\r\nspruce.df = read.csv(\"SPRUCE.csv\")\r\n\r\n#with(spruce.df, dput(list(D=BHDiameter,H=Height), \r\n #file=\"spruce.dat\"))\r\n# Or use \r\n#spruce.df=read.table(file.choose(),header=TRUE,sep=\",\")\r\n\r\n#get wd\r\ngetwd()\r\n\r\n#Top six lines\r\ntail(spruce.df)\r\n\r\n#Plot the points\r\nwindows()\r\n\r\nplot(Height~BHDiameter,bg=\"Blue\",pch=21,cex=1.2,\r\nylim=c(0,max(Height)),xlim=c(0,max(BHDiameter)), \r\nmain=\"Spruce height prediction\",data=spruce.df)\r\n\r\n\r\nlibrary(ggplot2)\r\nwindows()\r\ng = ggplot(spruce.df,mapping = aes(x = BHDiameter, y = Height)) + \r\n geom_point()\r\nprint(g)\r\n\r\ng = g+ geom_smooth(formula = y~ log(x), method = \"lm\", col = \"steelblue\")\r\ng = g + geom_smooth(formula = y ~ x, method = \"lm\", col = \"Black\")\r\ng = g + geom_smooth(formula = y~ x+ I(x^2), method =\"lm\", col = \"Red\")\r\nprint(g)\r\n\r\ng = g + geom_smooth(formula = y~ poly(x,3), method =\"lm\", col = \"green3\")\r\ng\r\n\r\n\r\n\r\n#load s20x library and make lowess smoother\r\nlibrary(s20x)\r\n\r\ntrendscatter(Height~BHDiameter,f=0.5,data=spruce.df)\r\n# Now make the linear model\r\nspruce.lm=lm(Height~BHDiameter,data=spruce.df)\r\nsummary(spruce.lm)\r\n#residuals created from the linear model object\r\nheight.res=residuals(spruce.lm)\r\n\r\n#fitted values made from the linear model object\r\nheight.fit=fitted(spruce.lm)\r\n\r\nwindows()\r\n#Make the plot using the plot function \r\nplot(height.fit,height.res)\r\n\r\n# Put a lowess smoother through res vs fitted\r\ntrendscatter( height.fit,height.res)\r\n\r\n# Quick way to make a residual plot\r\nplot(spruce.lm, which =1)\r\n\r\n# Two plots testing normality\r\nwindows()\r\nnormcheck(spruce.lm,shapiro.wilk = TRUE)\r\n\r\n\r\n## Quadratic object using the linear model\r\nquad.lm=lm(Height~BHDiameter + I(BHDiameter^2),data=spruce.df)\r\nsummary(quad.lm)\r\nadd1(spruce.lm,.~.+I(BHDiameter^2))\r\nanova(spruce.lm)\r\nanova(quad.lm)\r\nanova(spruce.lm,quad.lm)\r\ncubic.lm=lm(Height~BHDiameter + I(BHDiameter^2)+I(BHDiameter^3),data=spruce.df)\r\nanova(cubic.lm)\r\nadd1(quad.lm,.~.+I(BHDiameter^3))\r\n#add to the scatter plot\r\nwindows()\r\nplot(Height~BHDiameter,bg=\"Blue\",pch=21,cex=1.2,\r\nylim=c(0,max(Height)),xlim=c(0,max(BHDiameter)), \r\nmain=\"Spruce height prediction\",data=spruce.df)\r\n\r\ncoef(quad.lm)\r\nnames(quad.lm)\r\nquad.lm$coef[2]\r\n\r\nmyplot=function(x){\r\n 0.86089580 +1.46959217*x -0.02745726*x^2\r\n }\r\n \r\n #Or more general method\r\nmyplot=function(x){\r\n quad.lm$coef[1] +quad.lm$coef[2]*x + quad.lm$coef[3]*x^2\r\n } \r\n \r\ncurve(myplot, lwd=2, col=\"steelblue\",add=TRUE)\r\n \r\n \r\nplot(quad.lm, which=1)\r\n\r\nplot(spruce.lm,which=1)\r\nnormcheck(quad.lm,shapiro.wilk = TRUE)\r\n\r\n\r\nsummary(quad.lm)\r\n\r\npredict(quad.lm, data.frame(BHDiameter=c(3,6,8)))\r\n\r\n\r\nciReg(quad.lm)\r\n\r\n\r\n\r\npredict(quad.lm, data.frame(BHDiameter=c(15,18,20)))\r\n\r\nanova(spruce.lm,quad.lm)\r\n\r\ndata = 15:24\r\npredict20x(quad.lm,data.frame(BHDiameter = data, `I(BhDiameter)^2`=data^2))\r\n\r\nanova(quad.lm)\r\nanova(spruce.lm)\r\n\r\nheight.qfit=fitted(quad.lm)\r\n\r\nRSS=with(spruce.df, sum((Height-height.qfit)^2))\r\nRSS\r\nMSS = with(spruce.df, sum((height.qfit-mean(Height))^2))\r\nMSS\r\n\r\nTSS = with(spruce.df, sum((Height-mean(Height))^2))\r\nTSS\r\n\r\n\r\nMSS/TSS\r\n\r\n\r\ncooks20x(quad.lm)\r\n\r\n\r\n#Now remove the 24th datum and reanalyze data\r\n\r\nquad2.lm=lm(Height~BHDiameter + I(BHDiameter^2) , data=spruce.df[-24,])\r\nsummary(quad2.lm)\r\nsummary(quad.lm)\r\n\r\n\r\n###############################################################################\r\n\r\n#some other code you might need\r\n#The following code plots residuals\r\nwindows()\r\n#Plot the data\r\nplot(Height~BHDiameter,bg=\"Blue\",pch=21,cex=1.2,\r\nylim=c(0,max(Height)),xlim=c(0,max(BHDiameter)), \r\nmain=\"Spruce height prediction\",data=spruce.df)\r\n\r\n#Make a quadratic model\r\nquad.lm=lm(Height~BHDiameter + I(BHDiameter^2),data=spruce.df)\r\n\r\n# Find the coefficients\r\ncoef(quad.lm)\r\n\r\n#Make a function that produces heights for inputs \"x\"\r\nmyplot=function(x){\r\n 0.86089580 +1.46959217*x -0.02745726*x^2\r\n }\r\n\r\n# add the quadratic to the points \r\ncurve(myplot, lwd=2, col=\"steelblue\",add=TRUE)\r\n\r\n#Place segments (residuals) on the plot (except for the 3 largest cooks distances. 18, 21, 24)\r\nwith(spruce.df[-c(18,21,24),],segments(BHDiameter, Height, BHDiameter, height.qfit[-c(18,21,24)]) )\r\nwith(spruce.df[c(18,21,24),],segments(BHDiameter, Height, BHDiameter, height.qfit[c(18,21,24)], col=\"Red\", lwd=3) )\r\nwith( spruce.df, arrows(5,Height[24], BHDiameter[24], Height[24],lwd=2,col=\"Blue\"))\r\nwith(spruce.df,text(2,Height[24], paste(\"Highest Cook's\",\"\\n\", \"distance\",sep=\" \")))\r\nwith(spruce.df, text(BHDiameter,Height, 1:36,cex=0.5,pos=4))\r\n #########################################################################\r\n\r\n\r\nlayout(matrix(1:4,nr=2,nc=2,byrow=TRUE))\r\n\r\n#Lets look at where the plots will go\r\nlayout.show(4)\r\n\r\n#Plot the data\r\nplot(Height~BHDiameter,bg=\"Blue\",pch=21,cex=1.2,\r\nylim=c(0,1.1*max(Height)),xlim=c(0,1.1*max(BHDiameter)), \r\nmain=\"Spruce height prediction\",data=spruce.df)\r\n# add the line\r\nabline(spruce.lm)\r\n\r\n\r\n#make a new plot\r\nplot(Height~BHDiameter,bg=\"Blue\",pch=21,cex=1.2,\r\nylim=c(0,1.1*max(Height)),xlim=c(0,1.1*max(BHDiameter)), \r\nmain=\"Spruce height prediction\",data=spruce.df)\r\n\r\nabline(spruce.lm)\r\n\r\n#make yhat the estimates of E[Height | BHDiameter]\r\nyhat=with(spruce.df,predict(spruce.lm,data.frame(BHDiameter)))\r\nyhat=fitted(spruce.lm)\r\n# Draw in segments making the residuals (regression errors)\r\nwith(spruce.df,{\r\nsegments(BHDiameter,Height,BHDiameter,yhat)\r\n})\r\n\r\nRSS=with(spruce.df,sum((Height-yhat)^2))\r\n\r\nRSS\r\n\r\n#make a new plot\r\nplot(Height~BHDiameter,bg=\"Blue\",pch=21,cex=1.2,\r\nylim=c(0,1.1*max(Height)),xlim=c(0,1.1*max(BHDiameter)), \r\nmain=\"Spruce height prediction\",data=spruce.df)\r\n\r\n#make nieve model\r\nwith(spruce.df, abline(h=mean(Height)))\r\nabline(spruce.lm)\r\n\r\n#make the explained errors (explained by the model)\r\nwith(spruce.df, segments(BHDiameter,mean(Height),BHDiameter,yhat,col=\"Red\"))\r\nMSS=with(spruce.df,sum((yhat-mean(Height))^2))\r\nMSS\r\n\r\n# Total error\r\n#make a new plot\r\nplot(Height~BHDiameter,bg=\"Blue\",pch=21,cex=1.2,\r\nylim=c(0,1.1*max(Height)),xlim=c(0,1.1*max(BHDiameter)), \r\nmain=\"Spruce height prediction\",data=spruce.df)\r\n\r\nwith(spruce.df,abline(h=mean(Height)))\r\nwith(spruce.df, segments(BHDiameter,Height,BHDiameter,mean(Height),col=\"Green\"))\r\nTSS=with(spruce.df,sum((Height-mean(Height))^2))\r\nTSS\r\nRSS + MSS\r\nMSS/TSS\r\n\r\nsummary(spruce.lm)\r\n\r\n#obtain coefft values\r\ncoef(spruce.lm)\r\n\r\n#Calculate new y values given x\r\npredict(spruce.lm, data.frame(BHDiameter=c(15,18,20)))\r\n\r\nanova(spruce.lm)\r\n\r\nspruce2.lm=lm(Height~BHDiameter + I(BHDiameter^2),data=spruce.df)\r\nsummary(spruce2.lm)\r\n\r\n\r\n### More on the problem\r\nwindows()\r\nplot(Height~BHDiameter,bg=\"Blue\",pch=21,cex=1.2,\r\n ylim=c(0,1.1*max(Height)),xlim=c(0,1.1*max(BHDiameter)), \r\n main=\"Spruce height prediction\",data=spruce.df)\r\n\r\nyhatt=with(spruce.df,fitted(spruce2.lm))\r\nwith(spruce.df,plot(BHDiameter,yhatt,col=\"Red\")\r\n)\r\n\r\nsum(residuals(spruce2.lm)^2)\r\nplot(yhatt~BHDiameter,data=spruce.df,type=\"p\")\r\nsummary(spruce2.lm)\r\nanova(spruce2.lm)\r\nanova(spruce.lm,spruce2.lm)\r\nMSS\r\nRSS\r\n\r\n## piecewise linear model in R\r\n## Model y = b0 + b1x + b2(x-xk)*(x>xk)\r\n## You will need to change the code appropriately\r\nsp2.df=within(spruce.df, X<-(BHDiameter-20)*(BHDiameter>20)) # this makes a new variable and places it within the same df\r\nsp2.df\r\n\r\nlmp=lm(Height~BHDiameter + X,data=sp2.df)\r\ntmp=summary(lmp)\r\nnames(tmp)\r\nmyf = function(x,coef){\r\n coef[1]+coef[2]*(x) + coef[3]*(x-18)*(x-18>0)\r\n}\r\nplot(spruce.df,main=\"Piecewise regression\")\r\nmyf(0, coef=tmp$coefficients[,\"Estimate\"])\r\ncurve(myf(x,coef=tmp$coefficients[,\"Estimate\"] ),add=TRUE, lwd=2,col=\"Blue\")\r\nabline(v=18)\r\ntext(18,16,paste(\"R sq.=\",round(tmp$r.squared,4) ))\r\n", "meta": {"hexsha": "dd79d29cc5e36066356cf9a385bdcfbcf1c03569", "size": 7906, "ext": "r", "lang": "R", "max_stars_repo_path": "labs/lab4/lab4.r", "max_stars_repo_name": "1marcos6/MATH4753BERN0021", "max_stars_repo_head_hexsha": "6c3d14c90e4f67e8b01a11028c877c9c226dd0e2", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "labs/lab4/lab4.r", "max_issues_repo_name": "1marcos6/MATH4753BERN0021", "max_issues_repo_head_hexsha": "6c3d14c90e4f67e8b01a11028c877c9c226dd0e2", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "labs/lab4/lab4.r", "max_forks_repo_name": "1marcos6/MATH4753BERN0021", "max_forks_repo_head_hexsha": "6c3d14c90e4f67e8b01a11028c877c9c226dd0e2", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.2657807309, "max_line_length": 122, "alphanum_fraction": 0.6713888186, "num_tokens": 2653, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8499711794579723, "lm_q2_score": 0.9032941975921686, "lm_q1q2_score": 0.7677740345249582}} {"text": "area <- function(a, b, c) {\n s = (a + b + c) / 2\n a2 = s*(s-a)*(s-b)*(s-c)\n if (a2>0) sqrt(a2) else 0\n}\n\nis.heronian <- function(a, b, c) {\n h = area(a, b, c)\n h > 0 && 0==h%%1\n}\n\n# borrowed from stackoverflow http://stackoverflow.com/questions/21502181/finding-the-gcd-without-looping-r\ngcd <- function(x,y) {\n r <- x%%y;\n ifelse(r, gcd(y, r), y)\n}\n\ngcd3 <- function(x, y, z) {\n gcd(gcd(x, y), z)\n}\n\nmaxside = 200\nr <- NULL\nfor(c in 1:maxside){\n for(b in 1:c){\n for(a in 1:b){\n if(1==gcd3(a, b, c) && is.heronian(a, b, c)) {\n r <- rbind(r,c(a=a, b=b, c=c, perimeter=a+b+c, area=area(a,b,c)))\n }\n }\n }\n}\n\ncat(\"There are \",nrow(r),\" Heronian triangles up to a maximal side length of \",maxside,\".\\n\", sep=\"\")\ncat(\"Showing the first ten ordered first by perimeter, then by area:\\n\")\nprint(head(r[order(x=r[,\"perimeter\"],y=r[,\"area\"]),],n=10))\n", "meta": {"hexsha": "f1ee32ebf1e8a37857b8e5cae78f8793548f73ad", "size": 917, "ext": "r", "lang": "R", "max_stars_repo_path": "Task/Heronian-triangles/R/heronian-triangles-1.r", "max_stars_repo_name": "mullikine/RosettaCodeData", "max_stars_repo_head_hexsha": "4f0027c6ce83daa36118ee8b67915a13cd23ab67", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Heronian-triangles/R/heronian-triangles-1.r", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Heronian-triangles/R/heronian-triangles-1.r", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 24.7837837838, "max_line_length": 107, "alphanum_fraction": 0.5288985823, "num_tokens": 329, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9416541577509315, "lm_q2_score": 0.8152324915965392, "lm_q1q2_score": 0.7676670652455325}} {"text": "mul_inv <- function(a, b)\n{\n b0 <- b\n x0 <- 0L\n x1 <- 1L\n\n if (b == 1) return(1L)\n while(a > 1){\n q <- as.integer(a/b)\n\n t <- b\n b <- a %% b\n a <- t\n\n t <- x0\n x0 <- x1 - q*x0\n x1 <- t\n }\n\n if (x1 < 0) x1 <- x1 + b0\n return(x1)\n}\n\nchinese_remainder <- function(n, a)\n{\n len <- length(n)\n\n prod <- 1L\n sum <- 0L\n\n for (i in 1:len) prod <- prod * n[i]\n\n for (i in 1:len){\n p <- as.integer(prod / n[i])\n sum <- sum + a[i] * mul_inv(p, n[i]) * p\n }\n\n return(sum %% prod)\n}\n\nn <- c(3L, 5L, 7L)\na <- c(2L, 3L, 2L)\n\nchinese_remainder(n, a)\n", "meta": {"hexsha": "27beec5369fc367324a39529cf2dbf2a573dac0f", "size": 575, "ext": "r", "lang": "R", "max_stars_repo_path": "Task/Chinese-remainder-theorem/R/chinese-remainder-theorem.r", "max_stars_repo_name": "LaudateCorpus1/RosettaCodeData", "max_stars_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Chinese-remainder-theorem/R/chinese-remainder-theorem.r", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Chinese-remainder-theorem/R/chinese-remainder-theorem.r", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 12.7777777778, "max_line_length": 44, "alphanum_fraction": 0.4504347826, "num_tokens": 257, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9362850128595114, "lm_q2_score": 0.8198933381139645, "lm_q1q2_score": 0.767653844619461}} {"text": "# confidence interval for indpendent sample\r\n \r\nn1= 10\r\nn2= 9\r\ny1bar = 8.27\r\ny2bar=6.78\r\ns1=2.956\r\ns2=2.565\r\n# common standard deviation \r\nsp=sqrt(((n1-1)*s1*s1+(n2-1)*s2*s2)/(n1+n2-2))\r\n\r\n# the t-percentile based on df for 95% confidence interval\r\ntstar=qt( .975, df=18)\r\nmargin=tstar*sp*sqrt((1/n1)+(1/n2))\r\nleft_i=(y1bar-y2bar)-margin\r\nright_i=(y1bar-y2bar)+margin\r\nprint(\"confidence interval is\")\r\nprint(left_i)\r\nprint(right_i)\r\n", "meta": {"hexsha": "60bb1c29c157852bb2b21a5b4ae0bce93a2613de", "size": 433, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH6/EX6.2/Ex6_2.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH6/EX6.2/Ex6_2.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH6/EX6.2/Ex6_2.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 21.65, "max_line_length": 59, "alphanum_fraction": 0.6836027714, "num_tokens": 169, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9441768620069627, "lm_q2_score": 0.8128673223709251, "lm_q1q2_score": 0.7674905176641822}} {"text": "mix.dist <- function(n,mix.par,mu1,sigma1,mu2,df) {\r\n#Purpose:\r\n# Create n samples from the mixture distribution\r\n#Inputs:\r\n# n - number of samples to return\r\n# mix.par - pi in the practical notes -- proportion of samples from norm dist\r\n# mu1 - mean of norm dist\r\n# sigma1 - sd of norm dist\r\n# mu2 - mean of t dist\r\n# df - df for t dist\r\n#Outputs:\r\n# vector of n values from the mixture distribution\r\n#Implementation note:\r\n# Uses vectorization - generates 'n' samples from both distributions (hmmm...)\r\n\r\n#sample n values from a Bernoulli dist, to determine parent distribution for each data point\r\n nu <- rbinom(n,1,mix.par)\r\n#sample values from the normal\r\n X <- rnorm(n,mu1,sigma1)\r\n#sample values from the t\r\n Y <- mu2 + rt(n,df)\r\n# combine\r\n Z <- nu*X + (1-nu)*Y\r\n return(Z)\r\n}", "meta": {"hexsha": "a60e800a4fdef0bcee1afca8688fb89fec51a013", "size": 790, "ext": "r", "lang": "R", "max_stars_repo_path": "Practicals/Practical 3/functions/mix.dist.r", "max_stars_repo_name": "yc59/2018", "max_stars_repo_head_hexsha": "4c74a67a4d0dadecc4213dd57289120b31806aa6", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Practicals/Practical 3/functions/mix.dist.r", "max_issues_repo_name": "yc59/2018", "max_issues_repo_head_hexsha": "4c74a67a4d0dadecc4213dd57289120b31806aa6", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Practicals/Practical 3/functions/mix.dist.r", "max_forks_repo_name": "yc59/2018", "max_forks_repo_head_hexsha": "4c74a67a4d0dadecc4213dd57289120b31806aa6", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 31.6, "max_line_length": 93, "alphanum_fraction": 0.6848101266, "num_tokens": 225, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9496693674025232, "lm_q2_score": 0.8080672204860316, "lm_q1q2_score": 0.7673966860976849}} {"text": "#' Bias correction function from Pang et al. (2009).\n#'\n#' This function computes the function \\eqn{h_{\\nu, p}(t)} on page 1023 of Pang\n#' et al. (2009).\n#'\n#' @param nu a specified constant (nu = N - K)\n#' @param p the feature space dimension.\n#' @param t a constant specified by the user that indicates the exponent to use\n#' with the variance estimator. By default, t = -1 as in Pang et al. See the\n#' paper for more details.\n#'\n#' @references Pang, H., Tong, T., & Zhao, H. (2009). \"Shrinkage-based Diagonal\n#' Discriminant Analysis and Its Applications in High-Dimensional Data,\"\n#' Biometrics, 65, 4, 1021-1029.\n#' \\url{http://onlinelibrary.wiley.com/doi/10.1111/j.1541-0420.2009.01200.x/abstract}\n#' @return the bias correction value\nh <- function(nu, p, t = -1) {\n if (nu <= 0) {\n rlang::abort(\"The value for 'nu' must be positive.\")\n }\n\n if(nu / 2 + t / p > 0) {\n (nu / 2)^t * (gamma(nu / 2) / gamma(nu / 2 + t / p))^p\n } else {\n rlang::warn(\"The bias-correction has resulted in a NaN. Incrementing nu by 1...\")\n (nu / 2)^t * (gamma(nu / 2) / gamma((nu + 1) / 2 + t / p))^p\n }\n}\n\n#' Stein Risk function from Pang et al. (2009).\n#'\n#' This function finds the value for \\eqn{\\alpha \\in [0,1]} that empirically\n#' minimizes the average risk under a Stein loss function, which is given on\n#' page 1023 of Pang et al. (2009).\n#'\n#' @param N the sample size.\n#' @param K the number of classes.\n#' @param var_feature a vector of the sample variances for each dimension.\n#' @param num_alphas The number of values used to find the optimal amount of\n#' shrinkage.\n#' @param t a constant specified by the user that indicates the exponent to use\n#' with the variance estimator. By default, t = -1 as in Pang et al. See the\n#' paper for more details.\n#' @references Pang, H., Tong, T., & Zhao, H. (2009). \"Shrinkage-based Diagonal\n#' Discriminant Analysis and Its Applications in High-Dimensional Data,\"\n#' Biometrics, 65, 4, 1021-1029.\n#' \\url{http://onlinelibrary.wiley.com/doi/10.1111/j.1541-0420.2009.01200.x/abstract}\n#' @return list with\n#' \\itemize{\n#' \\item `alpha`: the alpha that minimizes the average risk under a Stein\n#' loss function. If the minimum is not unique, we randomly select an\n#' `alpha` from the minimizers.\n#' \\item `risk`: the minimum average risk attained.\n#' }\nrisk_stein <- function(N, K, var_feature, num_alphas = 101, t = -1) {\n nu <- N - K\n p <- length(var_feature)\n alphas <- seq(0, 1, length = num_alphas)\n\n # The pooled variance is defined in Pang et al. (2009) as the geometric mean\n # of the sample variances of each feature.\n var_pool <- prod(var_feature)^(t / p)\n\n # Here we compute the average risk for the Stein loss function on page 1023\n # for all values of alpha.\n risk_alphas <- sapply(alphas, function(alpha) {\n risk <- h(nu = nu, p = p)^alpha * h(nu = nu, p = 1)^(1 - alpha)\n risk <- risk / (h(nu = nu, p = 1, t = alpha * t / p))^(p - 1)\n risk <- risk / h(nu = nu, p = 1, t = (1 - alpha + alpha / p) * t)\n risk <- risk * (var_pool)^(alpha * t)\n risk <- risk * mean(var_feature^(-alpha * t))\n risk <- risk - log(h(nu = nu, p = p)^alpha * h(nu = nu, p = 1)^(1 - alpha))\n risk <- risk - t * digamma(nu / 2)\n risk <- risk + t * log(nu / 2) - 1\n risk\n })\n\n # Which of the alphas empirically minimize this risk?\n # If there are ties in the minimum risk, we randomly select\n # the value of alpha from the minimizers.\n alpha_min_risk <- alphas[which(min(risk_alphas) == risk_alphas)]\n alpha_star <- sample(alpha_min_risk, 1)\n\n list(alpha = alpha_star, var_pool = var_pool)\n}\n\n#' Shrinkage-based estimator of variances for each feature from Pang et al.\n#' (2009).\n#'\n#' This function computes the shrinkage-based estimator of variance of each\n#' feature (variable) from Pang et al. (2009) for the SDLDA classifier.\n#'\n#' @param N the sample size.\n#' @param K the number of classes.\n#' @param var_feature a vector of the sample variances for each feature.\n#' @param num_alphas The number of values used to find the optimal amount of\n#' shrinkage.\n#' @param t a constant specified by the user that indicates the exponent to use\n#' with the variance estimator. By default, t = -1 as in Pang et al. See the\n#' paper for more details.\n#'\n#' @references Pang, H., Tong, T., & Zhao, H. (2009). \"Shrinkage-based Diagonal\n#' Discriminant Analysis and Its Applications in High-Dimensional Data,\"\n#' Biometrics, 65, 4, 1021-1029.\n#' \\url{http://onlinelibrary.wiley.com/doi/10.1111/j.1541-0420.2009.01200.x/abstract}\n#' @return a vector of the shrunken variances for each feature.\nvar_shrinkage <- function(N, K, var_feature, num_alphas = 101, t = -1) {\n nu <- N - K\n p <- length(var_feature)\n\n risk_stein_out <- risk_stein(N = N, K = K, var_feature = var_feature,\n num_alphas = num_alphas, t = t)\n\n var_pool <- risk_stein_out$var_pool\n alpha <- risk_stein_out$alpha\n\n var_feature_shrink <- (h(nu = nu, p = p, t = t) * var_pool)^alpha *\n (h(nu = nu, p = 1, t = t) * var_feature)^(1 - alpha)\n var_feature_shrink\n}\n", "meta": {"hexsha": "9ca83f47305d43c59c8af645824611cb019c7a1c", "size": 5046, "ext": "r", "lang": "R", "max_stars_repo_path": "R/stein-shrinkage.r", "max_stars_repo_name": "topepo/sparsediscrim", "max_stars_repo_head_hexsha": "60198a54e0ced0afa3909121eea55321dd04c56f", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 3, "max_stars_repo_stars_event_min_datetime": "2020-11-16T08:13:49.000Z", "max_stars_repo_stars_event_max_datetime": "2021-11-28T21:44:00.000Z", "max_issues_repo_path": "R/stein-shrinkage.r", "max_issues_repo_name": "topepo/sparsediscrim", "max_issues_repo_head_hexsha": "60198a54e0ced0afa3909121eea55321dd04c56f", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 3, "max_issues_repo_issues_event_min_datetime": "2021-05-26T12:02:17.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-10T03:00:06.000Z", "max_forks_repo_path": "R/stein-shrinkage.r", "max_forks_repo_name": "topepo/sparsediscrim", "max_forks_repo_head_hexsha": "60198a54e0ced0afa3909121eea55321dd04c56f", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 41.7024793388, "max_line_length": 85, "alphanum_fraction": 0.6597304796, "num_tokens": 1568, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9161096135894201, "lm_q2_score": 0.8376199633332891, "lm_q1q2_score": 0.7673517009440438}} {"text": "# \n# Don't complain; just work harder! Dan Stanford\n# \n# Our responsibility is to do what we can, learn what we can, improve the solutions, and pass them on. RF\n# \n# @author: me@andreagirardi.it\n# @since: Wed Jan 15 18:34:22 CET 2020\n# @project: RExercises\n# @module: Programming basic lesson\n# @desc: \n#\n#\n# Exercises\n\n## \n#### Standard deviation and Geometric mean\n## \n\nprint ('#### Standard deviation and Geometric mean ####')\ntemps <- c(32, 32, 31, 28, 29, 31, 39, 32, 32, 35, 26, 29)\n\nmean <- mean(temps)\nnum_items <- length(temps)\nsquared_differences <- rep(0, num_items)\nproducts <- 1\nindex <- 1\ngeometric_mean <- 0\n\nfor ( temp in temps ) {\n products <- products * temp\n geometric_mean <- products ^ (1. / num_items)\n squared_differences[index] <- (temp - mean) ^ 2\n index <- index + 1\n}\n\n# Calculate VARIANCE\naverage_squared_difference <- mean(squared_differences)\n\n# Calculate standard deviation\nstandard_deviation <- sqrt(average_squared_difference)\n\npaste0 ('mean: ', mean)\npaste0 ('variance: ', average_squared_difference)\npaste0 ('standard_deviation: ', standard_deviation)\npaste0 ('geometric mean: ', geometric_mean)", "meta": {"hexsha": "2acbf6079a79d37389b808c35c36fbc58c2781f6", "size": 1182, "ext": "r", "lang": "R", "max_stars_repo_path": "BootcampWithR/ProgrammingBasic.r", "max_stars_repo_name": "giandrea77/RExercises", "max_stars_repo_head_hexsha": "d435e303775b154d4cbbc25f990eb4b23272039d", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "BootcampWithR/ProgrammingBasic.r", "max_issues_repo_name": "giandrea77/RExercises", "max_issues_repo_head_hexsha": "d435e303775b154d4cbbc25f990eb4b23272039d", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "BootcampWithR/ProgrammingBasic.r", "max_forks_repo_name": "giandrea77/RExercises", "max_forks_repo_head_hexsha": "d435e303775b154d4cbbc25f990eb4b23272039d", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.2666666667, "max_line_length": 105, "alphanum_fraction": 0.6759729272, "num_tokens": 334, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9207896802383028, "lm_q2_score": 0.8333245953120233, "lm_q1q2_score": 0.767316687652071}} {"text": "poisson.fun <- function(theta, x, y) {\n # parameters\n lambda1 <- theta[1]\n lambda2 <- theta[2]\n\n # priors\n log.priors <- dgamma(lambda1, .5, 1e-5, log=T) + dgamma(lambda2, .5, 1e-5, log=T)\n\n # likelihood\n log.like <- sum(dpois(x, lambda1, log=T)) + sum(dpois(y, lambda2, log=T))\n\n ll <- log.priors + log.like\n\n ifelse(is.na(ll) | is.nan(ll), -Inf, ll)\n}\n\npoisson.1g.fun <- function(theta, x) {\n # parameters\n lambda <- theta\n\n # priors\n log.priors <- dgamma(lambda, .5, 1e-5, log=T)\n\n # likelihood\n log.like <- sum(dpois(x, lambda, log=T))\n\n ll <- log.priors + log.like\n\n ifelse(is.na(ll) | is.nan(ll), -Inf, ll)\n}\n\nbayes.poisson.test <- function(x, y=NULL, nmc=20000, nbi=20000) {\n if(is.null(y)) {\n theta.init <- (sum(x)+.5)/length(x)\n out <- bayes::mcmc(poisson.1g.fun, theta.init, nmc, nbi, x=x)\n #colnames(out) <- c(\"lambda\")\n } else {\n theta.init <- c((sum(x)+.5)/length(x), (sum(y)+.5)/length(y))\n out <- bayes::mcmc(poisson.fun, theta.init, nmc, nbi, x=x, y=y)\n colnames(out) <- c(\"lambda1\", \"lambda2\")\n }\n return(out)\n}\n", "meta": {"hexsha": "b9872d1318323979eaae916c725e2004404ee34d", "size": 1068, "ext": "r", "lang": "R", "max_stars_repo_path": "R/poi.r", "max_stars_repo_name": "MikeXL/bayes", "max_stars_repo_head_hexsha": "68912c47ae5df94973e960050cdef401676d5acb", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/poi.r", "max_issues_repo_name": "MikeXL/bayes", "max_issues_repo_head_hexsha": "68912c47ae5df94973e960050cdef401676d5acb", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/poi.r", "max_forks_repo_name": "MikeXL/bayes", "max_forks_repo_head_hexsha": "68912c47ae5df94973e960050cdef401676d5acb", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 24.2727272727, "max_line_length": 83, "alphanum_fraction": 0.5861423221, "num_tokens": 400, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9674102542943773, "lm_q2_score": 0.7931059536292271, "lm_q1q2_score": 0.7672588322828352}} {"text": "binomial.fun <- function(theta, x, prior) {\n\n # parameters\n # x[, 1] ... number of success\n # x[, 2] ... number of trials\n\n # priors beta(a, b)\n # flat beta(1, 1)\n # jeffery beta(.5, .5\n #\n # log.priors <- sum(dbeta(theta, prior[1], prior[2], log=T))\n\n # likelihood\n # log.like <- sum(dbinom(x[, 1], x[, 2], theta, log=T))\n\n # ll <- log.priors + log.like\n # posterior is actually another beta(a+y, b+n-y)\n # therefore no need to run full monte carlo, just need to sample from \n ll <- sum(dbeta(theta, prior[1]+sum(x[ ,1]), prior[2]+sum(x[ ,2]) - sum(x[ ,1]), log=T))\n\n ifelse(is.na(ll) | is.nan(ll), -Inf, ll)\n}\n#\n# x is a matrix (series) of success and trials\n# [,1] [,2]\n# [1,] 23 100 100 trials with 23 success\n# [2,] 24 200 200 trials with 24 success\n#\nbayes.binomial.test <- function(x, prior=c(1, 1), nmc=20000, nbi=20000) {\n theta.init <- (sum(x[, 1])+1) / (sum(x[, 2])+2)\n out <- bayes::mcmc(binomial.fun, theta.init, nmc, nbi, x=x, prior=prior)\n return(out)\n}\n", "meta": {"hexsha": "13a632650c69a106d3ce1b4bbdf21177f580c250", "size": 1021, "ext": "r", "lang": "R", "max_stars_repo_path": "R/bino.r", "max_stars_repo_name": "MikeXL/bayes", "max_stars_repo_head_hexsha": "68912c47ae5df94973e960050cdef401676d5acb", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/bino.r", "max_issues_repo_name": "MikeXL/bayes", "max_issues_repo_head_hexsha": "68912c47ae5df94973e960050cdef401676d5acb", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/bino.r", "max_forks_repo_name": "MikeXL/bayes", "max_forks_repo_head_hexsha": "68912c47ae5df94973e960050cdef401676d5acb", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 30.0294117647, "max_line_length": 90, "alphanum_fraction": 0.5719882468, "num_tokens": 376, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9736446479186303, "lm_q2_score": 0.7879312031126512, "lm_q1q2_score": 0.76716499883872}} {"text": "n = c(15,32,18,5,8,29,23,18,1,20,25,22)\r\nE=c( 7.78,26.25,21.39,14.58,8.67,29.25,23.83,16.25,7.56,25.50,20.78,14.17)\r\n# test statistic\r\nXsquare = 0\r\ni=1\r\nwhile(i<=length( n)){\r\n Xsquare=Xsquare+(((n[i]-E[i])^2)/E[i])\r\n i=i+1\r\n}\r\nprint(Xsquare)\r\n# critical value\r\nalpha = 0.05\r\nX.alpha=qchisq(1-alpha,df=6)\r\n# The computed value of xsquare is greater than x.alpha, so we reject the null hypothes\r\n\r\n", "meta": {"hexsha": "ccc05dbc132b4642719b4bf35b9cfc50fe19ab10", "size": 399, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH10/EX10.13/Ex10_13.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH10/EX10.13/Ex10_13.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH10/EX10.13/Ex10_13.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 24.9375, "max_line_length": 88, "alphanum_fraction": 0.634085213, "num_tokens": 177, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9433475746920261, "lm_q2_score": 0.8128673201042492, "lm_q1q2_score": 0.7668164149667503}} {"text": "# Example : 2 Chapter : 6.3 Page No: 314\r\n# Solve Differential equation\r\n\r\n# lambda1,lamda2,lambda3,x1,x2,x3,c1,c2,c3 are computed here.. for remaining details look textbook\r\nA<-matrix(c(1,0,0,1,2,0,1,1,3),ncol=3)\r\nlambda<-eigen(A)$values\r\nx<-round(eigen(A)$vectors)\r\nu<-c(9,7,4)\r\nc<-solve(x,u)\r\nprint(\"Lambda 3 and Lambda 2 and Lambda 1 are\")\r\nprint(lambda)\r\nprint(\"x3 and x2 and x1\")\r\nprint(x)\r\nprint(\"c3,c2 and c1 are\")\r\nprint(c)\r\n#The answer may slightly vary due to rounding off values\r\n#The answers provided in the text book may vary because of the computation process\r\n#Both answers are correct , here it is taken -Ax+b=0 , In the text book it is considered as Ax-b=0\r\n", "meta": {"hexsha": "d583fb2f5fbe1ed1c8a44849a1ea0c333abb6acf", "size": 684, "ext": "r", "lang": "R", "max_stars_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH6/EX6.3.2/Ex6.3_2.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH6/EX6.3.2/Ex6.3_2.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH6/EX6.3.2/Ex6.3_2.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 36.0, "max_line_length": 99, "alphanum_fraction": 0.6988304094, "num_tokens": 223, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9273632916317103, "lm_q2_score": 0.8267117898012104, "lm_q1q2_score": 0.766662166620793}} {"text": "\n# Get data\ndigits.train <- read.table(url(\"http://www.amlbook.com/data/zip/features.train\"))\ndigits.test <- read.table(url(\"http://www.amlbook.com/data/zip/features.test\"))\n\ncolnames(digits.train) <- c(\"digit\", \"symmetry\", \"intensity\")\ncolnames(digits.test) <- c(\"digit\", \"symmetry\", \"intensity\")\n\ndigits.train$digit <- factor(digits.train$digit)\ndigits.test$digit <- factor(digits.test$digit)\n\nlibrary(ggplot2)\n\nggplot(digits.train, aes(x = symmetry, y = intensity, color = digit)) + \n geom_point()\n\nlinearRegression <- function(x, y, lambda, invFn = function(x) solve(x)) {\n # Calculate pseudo inverse\n pseudo = invFn(t(x) %*% x + lambda * diag(ncol(x))) %*% t(x)\n w = pseudo %*% y\n Ein = sum(y != sign(t(w) %*% t(x)))/length(y)\n # error = sum(y != sign(t(t(w) %*% t(x)))) # In case of only one record\n list(w = w, Ein = Ein)\n}\n\nphi.1 <- function(x) as.matrix(cbind(bias = 1, x[,1], x[,2]))\n\nphi.2 <- function(x) as.matrix(cbind(bias = 1, x[,1], x[, 2], x[, 1] * x[,2], x[,1]^2, x[,2]^2))\n\nq7_q8_q9 <- t(sapply(0:9, function(myDigit) {\n lambda = 1\n y.train = ifelse(digits.train$digit == myDigit, 1, -1)\n x.train.1 = phi.1(digits.train[, -1]) # Could be outside the loop\n x.train.2 = phi.2(digits.train[, -1]) # Could be outside the loop\n \n fit.1 <- linearRegression(x.train.1, y.train, lambda)\n fit.2 <- linearRegression(x.train.2, y.train, lambda)\n \n y.test = ifelse(digits.test$digit == myDigit, 1, -1)\n x.test.1 = phi.1(digits.test[, -1])\n x.test.2 = phi.2(digits.test[, -1])\n \n Eout.1 = sum(y.test != sign(t(fit.1$w) %*% t(x.test.1)))/length(y.test)\n Eout.2 = sum(y.test != sign(t(fit.2$w) %*% t(x.test.2)))/length(y.test)\n \n Err.1 = Eout.1 - fit.1$Ein\n Err.2 = Eout.2 - fit.2$Ein\n \n cbind(myDigit, fit.1$Ein, Eout.1, Err.1, \n fit.2$Ein, Eout.2, Err.2, 100*(Eout.2 - Eout.1), Eout.2 <= 0.95 * Eout.1)\n}))\n\ncolnames(q7_q8_q9) <- c(\"Digit\", \"Ein.1\", \"Eout.1\", \"Err.1\",\n \"Ein.2\", \"Eout.2\", \"Err.2\", \"diff\", \"check\")\n\nq7_q8_q9\n\nggplot(as.data.frame(q7_q8_q9), aes(x=Digit)) + \n geom_line(aes(y = Eout.1, color=\"psi1\")) + \n geom_line(aes(y = Eout.2, color = \"psi2\")) \n\n\n# Q10\ndigits.train.sub <- subset(digits.train, digit == 1 | digit == 5)\ndigits.test.sub <- subset(digits.test, digit == 1 | digit == 5)\nmyDigit = 1\n\nrequire(foreach)\nforeach(lambda=c(0.01, 1), .combine = rbind) %do% {\n y.train = ifelse(digits.train.sub$digit == myDigit, 1, -1)\n x.train.2 = phi.2(digits.train.sub[, -1])\n fit.2 <- linearRegression(x.train.2, y.train, lambda)\n \n y.test = ifelse(digits.test.sub$digit == myDigit, 1, -1)\n x.test.2 = phi.2(digits.test.sub[, -1])\n \n Eout.2 = sum(y.test != sign(t(fit.2$w) %*% t(x.test.2)))/length(y.test)\n \n cbind(Ein.2 = fit.2$Ein, Eout.2)\n}\n\n# Q11\nx = rbind(c(1,0), c(0,1), c(0,-1),\n c(-1,0), c(0,2), c(0,-2),\n c(-2,0))\n\ny = c(-1, -1, -1, +1, +1, +1, +1)\n\nplot(x, pch = y+2)\n\nphi <- function(x) as.matrix(cbind(x[,2]^2 - 2 * x[,1] - 1, x[,1]^2 - 2 * x[,2] + 1))\n\nplot(phi(x), pch = y + 2)\n\nabline(-3, 7)\n\nfit <- linearRegression(cbind(1, phi(x)), y, 0)\nabline(-fit$w[1]/fit$w[3], -fit$w[2]/fit$w[3])\n\nw1=-1; w2=1; b = -0.5\nabline(-w1/w2, -b/w2, col = \"red\")\nabline(-b/w2, -w1/w2, col = \"red\")\nabline(w1/w2, b/w2, col = \"red\")\nw1=1; w2=-1; b = -0.5\nabline(-w1/w2, -b/w2, col = \"blue\")\nabline(-b/w2, -w1/w2, col = \"blue\")\nabline(w1/w2, b/w2, col = \"blue\")\nw1=1; w2=1e6; b = -0.5\nabline(-w1/w2, -b/w2, col = \"green\")\nabline(-b/w2, -w1/w2, col = \"green\")\nabline(w1/w2, b/w2, col = \"green\")\nw1=0; w2=1; b = -0.5\nabline(-w1/w2, -b/w2, col = \"purple\")\nabline(-b/w2, -w1/w2, col = \"purple\")\nabline(w1/w2, b/w2, col = \"purple\")\n\n# Got Q11 wrong\n\n# Q12\nrequire(e1071)\nfit <- svm(x, y, \n scale = TRUE, \n kernel = \"polynomial\", degree = 2, gamma = 1, coef0 = 1, cost = 1e16,\n type = \"C-classification\")\n\nfit$tot.nSV\n\n# Q13\nf <- function(x) sign(x[,2] - x[,1] + 0.25 * sin(pi * x[,1]))\nEins <- sapply(1:10000, function(run) {\n x <- cbind(runif(100, -1, 1), runif(100, -1, 1))\n y <- f(x)\n # plot(x, pch=y+2)\n \n fit <- svm(x, y, \n scale = TRUE, \n kernel = \"radial\", gamma = 1.5, cost = 1e16,\n type = \"C-classification\")\n \n #fit$tot.nSV\n #points(x[fit$index,], col='blue', pch=14, lwd=4)\n sum(fit$fitted != y)\n})\n\nsummary(Eins)\n\n# Q14\n# RBF\nphi <- function(gamma, x, k) cbind(bias = 1, \n t(apply(x,1, function(x1) \n apply(k, 1, function(s) \n exp(- gamma * Norm(x1, s)^2)))))\n\n# f <- function(x) sign(tanh(x[,1] - x[,2]))\nk = 12 # 9\ngamma = 1.5\nN <- 100\nruns <- 1000\n\nq14_15 <- sapply(seq(runs), function(run) {\n x.train <- cbind(runif(N, -1, 1), runif(N, -1, 1))\n y.train <- f(x.train)\n fit.svm <- svm(x.train, y.train, \n scale = TRUE, \n kernel = \"radial\", gamma = gamma, cost = 1e16,\n type = \"C-classification\")\n \n # Get centers\n fit.kmeans = kmeans(x.train, k)\n # Get RBF\n x.train.phi = phi(gamma = gamma, x.train, fit.kmeans$centers)\n fit.rbf <- linearRegression(x.train.phi, y.train, 0)\n \n x.test <- cbind(runif(N, -1, 1), runif(N, -1, 1))\n y.test <- f(x.test)\n \n Eout.svm <- sum(y.test != predict(fit.svm, x.test))/length(y.test)\n pred.rbf <- sign(phi(gamma, x.test, fit.kmeans$centers) %*% fit.rbf$w)\n Eout.rbf <- sum(y.test != pred.rbf)/length(y.test)\n \n cbind(Eout.svm, Eout.rbf, Eout.rbf > Eout.svm)\n})\n\n\nsummary(t(q14_15)*100)\nsum(q14_15[3,])*100/runs\n\n# Q16\nq16 <- sapply(seq(runs), function(run) {\n x.train <- cbind(runif(N, -1, 1), runif(N, -1, 1))\n y.train <- f(x.train)\n \n x.test <- cbind(runif(N, -1, 1), runif(N, -1, 1))\n y.test <- f(x.test)\n \n k = 9\n # Get centers\n fit.kmeans = kmeans(x.train, k)\n # Get RBF\n x.train.phi = phi(gamma = gamma, x.train, fit.kmeans$centers)\n fit.rbf.9 <- linearRegression(x.train.phi, y.train, 0)\n \n pred.rbf <- sign(phi(gamma, x.test, fit.kmeans$centers) %*% fit.rbf.9$w)\n Eout.rbf.9 <- sum(y.test != pred.rbf)/length(y.test)\n \n k = 12\n # Get centers\n fit.kmeans = kmeans(x.train, k)\n # Get RBF\n x.train.phi = phi(gamma = gamma, x.train, fit.kmeans$centers)\n fit.rbf.12 <- linearRegression(x.train.phi, y.train, 0)\n \n pred.rbf <- sign(phi(gamma, x.test, fit.kmeans$centers) %*% fit.rbf.12$w)\n Eout.rbf.12 <- sum(y.test != pred.rbf)/length(y.test)\n \n \n cbind(fit.rbf.9$Ein, fit.rbf.12$Ein, Eout.rbf.9, Eout.rbf.12)\n})\n\n\nsummary(t(q16)*100)\n\n\n# Q17\nk = 9\nq17 <- sapply(seq(runs), function(run) {\n x.train <- cbind(runif(N, -1, 1), runif(N, -1, 1))\n y.train <- f(x.train)\n \n x.test <- cbind(runif(N, -1, 1), runif(N, -1, 1))\n y.test <- f(x.test)\n \n gamma = 1.5\n # Get centers\n fit.kmeans = kmeans(x.train, k)\n # Get RBF\n x.train.phi = phi(gamma = gamma, x.train, fit.kmeans$centers)\n fit.rbf.9 <- linearRegression(x.train.phi, y.train, 0)\n \n pred.rbf <- sign(phi(gamma, x.test, fit.kmeans$centers) %*% fit.rbf.9$w)\n Eout.rbf.9 <- sum(y.test != pred.rbf)/length(y.test)\n \n gamma = 2\n # Get centers\n fit.kmeans = kmeans(x.train, k)\n # Get RBF\n x.train.phi = phi(gamma = gamma, x.train, fit.kmeans$centers)\n fit.rbf.12 <- linearRegression(x.train.phi, y.train, 0)\n \n pred.rbf <- sign(phi(gamma, x.test, fit.kmeans$centers) %*% fit.rbf.12$w)\n Eout.rbf.12 <- sum(y.test != pred.rbf)/length(y.test)\n \n \n cbind(fit.rbf.9$Ein, fit.rbf.12$Ein, Eout.rbf.9, Eout.rbf.12)\n})\n\nsummary(t(q17)*100)\nsum(q17[1,]==0)/runs * 100\n\n", "meta": {"hexsha": "5187c1aaab7638dbdb561ccb48ba9dd97bb108d7", "size": 7458, "ext": "r", "lang": "R", "max_stars_repo_path": "Final/Rcode/by_sanealytics/final.r", "max_stars_repo_name": "freeernest/edX-Learning-From-Data-Solutions", "max_stars_repo_head_hexsha": "5cbcf0885b5fdb00c3658d230fc7bb7e20b5cf44", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 79, "max_stars_repo_stars_event_min_datetime": "2015-01-27T11:09:24.000Z", "max_stars_repo_stars_event_max_datetime": "2022-02-05T12:01:35.000Z", "max_issues_repo_path": "Final/Rcode/by_sanealytics/final.r", "max_issues_repo_name": "freeernest/edX-Learning-From-Data-Solutions", "max_issues_repo_head_hexsha": "5cbcf0885b5fdb00c3658d230fc7bb7e20b5cf44", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2018-08-25T05:45:11.000Z", "max_issues_repo_issues_event_max_datetime": "2018-12-04T14:44:32.000Z", "max_forks_repo_path": "Final/Rcode/by_sanealytics/final.r", "max_forks_repo_name": "freeernest/edX-Learning-From-Data-Solutions", "max_forks_repo_head_hexsha": "5cbcf0885b5fdb00c3658d230fc7bb7e20b5cf44", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": 40, "max_forks_repo_forks_event_min_datetime": "2015-04-06T18:43:34.000Z", "max_forks_repo_forks_event_max_datetime": "2021-03-28T18:08:40.000Z", "avg_line_length": 28.6846153846, "max_line_length": 96, "alphanum_fraction": 0.5687851971, "num_tokens": 2904, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9173026573249611, "lm_q2_score": 0.8354835452961425, "lm_q1q2_score": 0.766391276251431}} {"text": "mindistance <- function(vec, df=dfxs) {\r\n ## Function to find distance from vector vec to nearest point in dataframe df\r\n # subtract vec from dataframe column\r\n dif <- sweep(df, 2, vec, \"-\")\r\n # head(dif,2)\r\n # sumsquare each row of dataframe of diferences\r\n sq <- function(x) { sum(x^2) }\r\n difsq <- apply(dif, 1, sq)\r\n # return the minimum distance\r\n mindist <- sqrt( min(difsq) )\r\n return(mindist)\r\n}\r\n\r\nnegative_mindistance <- function(vec, df=dfxs){\r\n mindistance(vec,df) * -1\r\n}\r\n\r\n## Tests of function\r\n\r\n## ## add center point to database for testing\r\n## testdata <- dfxs\r\n## vec <- c(0.5, 0.5, 0.5, 0.5, 0.5, 0.5)\r\n## testdata <- rbind(vec, testdata)\r\n## head(testdata)\r\n## \r\n## ## test to return 0.1\r\n## vec1 <- vec + c(0, 0.1, 0, 0, 0, 0)\r\n## ##vec1\r\n## testanswer <- mindistance(vec1, testdata)\r\n## cat(\"test to return 0.1 = \", testanswer,\"\\n\")\r\n## \r\n## ## test to return 0.14142\r\n## vec1 <- vec + c(0, 0, 0.1, 0, 0.1, 0)\r\n## ##vec1\r\n## testanswer <- mindistance(vec1, testdata)\r\n## cat(\"test to return 0.14142 = \", testanswer,\"\\n\\n\")\r\n## \r\n## ## how about if supply vec from a row in a dataframe and look for min distance from any point in dfxs?\r\n## cat(\"test to use function on vector from dfxs dataframe (same as above but no null row)\\n\")\r\n## vecdf <- data.frame( t( vec ))\r\n## cat(\"vecdf =\\n\")\r\n## vecdf\r\n## cat(\"convert to vector\\n\")\r\n## vec <- as.numeric( vecdf[1,] )\r\n## vec\r\n## mindistance(vec, dfxs)\r\n## \r\n## ## can also use apply to run mindistance function on each row of default dataframe, dfxs\r\n## cat(\"\\ntest to use function on all points in one dataframe to the dfxs dataframe\\n\")\r\n## vecdf <- data.frame(rbind(vec, vec1))\r\n## vecdf\r\n## apply(vecdf, 1, mindistance)\r\n\r\n", "meta": {"hexsha": "9a241fdccdca767c3bfe1dea9b6501ad8b823054", "size": 1735, "ext": "r", "lang": "R", "max_stars_repo_path": "modules/mindistance.r", "max_stars_repo_name": "TECComputing/R-setup", "max_stars_repo_head_hexsha": "f4b5e45c6e2e55fcc6f58f804bb50cea3a697fe0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "modules/mindistance.r", "max_issues_repo_name": "TECComputing/R-setup", "max_issues_repo_head_hexsha": "f4b5e45c6e2e55fcc6f58f804bb50cea3a697fe0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "modules/mindistance.r", "max_forks_repo_name": "TECComputing/R-setup", "max_forks_repo_head_hexsha": "f4b5e45c6e2e55fcc6f58f804bb50cea3a697fe0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-06-16T12:06:21.000Z", "max_forks_repo_forks_event_max_datetime": "2021-06-16T12:06:21.000Z", "avg_line_length": 32.1296296296, "max_line_length": 106, "alphanum_fraction": 0.6103746398, "num_tokens": 550, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9149009596336303, "lm_q2_score": 0.8376199633332891, "lm_q1q2_score": 0.7663393082619124}} {"text": "# Preparing Dataset for the Time Series Analysis\r\n\r\nlibrary(readr)\r\nlibrary(tseries)\r\nlibrary(TSA)\r\nlibrary(dLagM)\r\nlibrary(forecast)\r\nlibrary(car)\r\nlibrary(x12)\r\nlibrary(kableExtra)\r\n\r\n\r\n# Descriptive Analysis function\r\ndescriptive_analysis <- function(ts, object)\r\n{\r\n plot(ts,\r\n ylab = c(paste0(toString(object))),\r\n main = c(paste0(\"Monthly Time Series Plot of \",toString(object))),\r\n type=\"o\")\r\n points(y=ts,x=time(ts), pch=as.vector(season(ts)))\r\n \r\n par(mfrow=c(2,1))\r\n acf(ts,\r\n lag.max = 48,\r\n main = c(paste0(\"ACF plot of \",toString(object))))\r\n \r\n pacf(ts, \r\n lag.max = 48,\r\n main = c(paste0(\"PACF plot of \",toString(object))))\r\n par(mfrow=c(1,1))\r\n \r\n print(adf.test(ts))\r\n print(pp.test(ts))\r\n}\r\n\r\n# Function for Decomposition\r\ndecom <- function(ts)\r\n{\r\n decom.x12 = x12(ts)\r\n plot(decom.x12 , sa=TRUE , trend=TRUE)\r\n \r\n \r\n plotSeasFac(decom.x12)\r\n \r\n \r\n decomposition <- stl(ts, t.window=15, s.window=\"periodic\", robust=TRUE)\r\n plot(decomposition)\r\n}\r\n\r\n\r\nASX_data <- read_csv(\"ASX_data.csv\")\r\nhead(ASX_data)\r\n\r\n\r\n#### ASX ordinaries Price Index\r\n\r\nASX_TS <- ts(ASX_data$`ASX price`, start = c(2004,1), frequency = 12)\r\nclass(ASX_TS)\r\nhead(ASX_TS)\r\n\r\n\r\n#### Gold Price (AUD)\r\n\r\ngold_TS <- ts(ASX_data$`Gold price`, start = c(2004,1), frequency = 12)\r\nclass(gold_TS)\r\nhead(gold_TS)\r\n\r\n\r\n#### Crude Oil (Brent, USD/bbl)\r\n\r\noil_TS <- ts(ASX_data$`Crude Oil (Brent)_USD/bbl`, start = c(2004,1), frequency = 12)\r\nclass(oil_TS)\r\nhead(oil_TS)\r\n\r\n\r\n#### Copper (USD/tonne)\r\n\r\ncopper_TS <- ts(ASX_data$`Copper_USD/tonne`, start = c(2004,1), frequency = 12)\r\nclass(copper_TS)\r\nhead(copper_TS)\r\n\r\n\r\n#### Whole Dataset\r\n\r\nASX_data_TS = ts(ASX_data, start = c(2004,1), frequency = 12)\r\nclass(ASX_data_TS)\r\nhead(ASX_data_TS)\r\n\r\n\r\n\r\n\r\nASX_TS_lambda = BoxCox.lambda(ASX_TS) \r\nASX_TS_lambda\r\n\r\nASX_TSBC = ((ASX_TS^(ASX_TS_lambda)) - 1) / ASX_TS_lambda\r\ndescriptive_analysis(ASX_TSBC,\"ASX ords price Index(Box-cox Transformed)\")\r\n\r\n\r\n\r\ngold_TS_lambda = BoxCox.lambda(gold_TS) \r\ngold_TS_lambda\r\n\r\ngold_TSBC = ((gold_TS^(gold_TS_lambda)) - 1) / gold_TS_lambda\r\ndescriptive_analysis(gold_TSBC,\"gold price(Box-cox Transformed) in AUD\")\r\n\r\n\r\n\r\noil_TS_lambda = BoxCox.lambda(oil_TS) \r\noil_TS_lambda\r\n\r\noil_TSBC = ((oil_TS^(oil_TS_lambda)) - 1) / oil_TS_lambda\r\ndescriptive_analysis(oil_TSBC, \"Crude oil price(Box-cox Transformaed) in USD/bbl\")\r\n\r\n\r\ncopper_TS_lambda = BoxCox.lambda(copper_TS) \r\ncopper_TS_lambda\r\n\r\ncopper_TSBC = ((copper_TS^(copper_TS_lambda)) - 1) / copper_TS_lambda\r\ndescriptive_analysis(copper_TSBC,\"Copper price(Box-cox Transformed) in USD/Tonne\")\r\n\r\n\r\n## Differencing\r\n\r\nASX_TSBC_diff = diff(ASX_TSBC)\r\ndescriptive_analysis(ASX_TSBC_diff,\"ASX price(Bc Transformed-1st diff)\")\r\n\r\ngold_TSBC_diff = diff(gold_TSBC)\r\ndescriptive_analysis(gold_TSBC_diff,\"gold price(BC Transformed-1st diff)\")\r\n\r\noil_TSBC_diff = diff(oil_TSBC)\r\ndescriptive_analysis(oil_TSBC_diff, \"Crude oil price(BC Transformed 1st diff)\")\r\n\r\ncopper_TSBC_diff = diff(copper_TSBC)\r\ndescriptive_analysis(copper_TSBC_diff,\"Copper price(BC Transformed-1st diff)\")\r\n\r\n\r\n## Decomposition\r\ndecom(ASX_TS)\r\n\r\ndecom(gold_TS)\r\n\r\ndecom(oil_TS)\r\n\r\ndecom(copper_TS)\r\n\r\n\r\n# The most accurate and suitable distributed lag model\r\n\r\nASX_scaled= scale(ASX_data_TS)\r\nplot(ASX_scaled, plot.type=\"s\",\r\n col =\tc(\"blue\", \"red\",\"green\",\"black\"), \r\n main= \"ASX ordinaries and gold, oil, copper\") \r\nlegend(\"topleft\",lty=1,col=c(\"blue\",\"red\",\"green\",\"black\"), c(\"ASX(Y)\", \"Gold(X1)\",\"Oil(X2)\",\"Copper(X3)\"))\r\n\r\ncor <- as.data.frame(cor(ASX_data_TS)) %>% round(3)\r\nkbl(cor) %>%\r\n kable_paper()\r\n\r\n\r\n## Finite Distributed Lag Models.\r\n \r\nASX_m = as.data.frame(ASX_data[,c(1,2,3,4)])\r\ncolnames(ASX_m) <- c(\"asx\", \"gold\", \"oil\", \"copper\")\r\nfor ( i in 1:12){\r\n model1.1 = dlm(formula = asx ~ gold + copper, data = data.frame(ASX_m), q = i )\r\n cat(\"q = \", i, \"AIC = \", AIC(model1.1$model), \"BIC = \", BIC(model1.1$model),\"\\n\")\r\n}\r\n\r\n\r\nmodel1 = dlm(formula = asx ~ gold + copper, data = data.frame(ASX_m), q = 12)\r\nsummary(model1$model)\r\ncheckresiduals(model1$model)\r\nvif(model1$model)\r\n\r\n\r\n## Polynomial Distributed Lag Model\r\n\r\nfiniteDLMauto(x = as.vector(ASX_m$copper), y = as.vector(ASX_m$asx), q.min = 1, q.max = 12, k.order = 1,\r\n model.type = \"poly\", error.type =\"AIC\", trace = TRUE)\r\n\r\n\r\n\r\nmodel2 = polyDlm(x = as.vector(ASX_m$copper), y = as.vector(ASX_m$asx), q = 10, k = 1, show.beta = TRUE)\r\nsummary(model2$model)\r\ncheckresiduals(model2$model)\r\nvif(model2$model)\r\n\r\n\r\n## Koyck Distributed Lag Model\r\n\r\nmodel3 = koyckDlm(x = as.vector(ASX_m$copper), y = as.vector(ASX_m$asx))\r\nsummary(model3,diagnostics = TRUE)\r\ncheckresiduals(model3$model)\r\nvif(model3$model)\r\n\r\n\r\n## Autoregressive Distributed Lag Model\r\n\r\nfor (i in 1:5)\r\n{\r\n for(j in 1:5)\r\n { \r\n model4 = ardlDlm(formula = asx ~ gold + copper, data = data.frame(ASX_m),p = i , q = j )\r\n cat(\"p = \", i, \"q =\" , j,\"AIC = \", AIC(model4$model), \"BIC = \", BIC(model4$model), \"\\n\")\r\n }\r\n}\r\n\r\n\r\n# ardlDLM(1,5)\r\n \r\nmodel4_1 = ardlDlm(formula = asx ~ gold + copper, data = data.frame(ASX_m), p = 1 , q = 5)\r\nsummary(model4_1)\r\ncheckresiduals(model4_1$model)\r\nvif(model4_1$model)\r\n\r\n# ardlDLM(2,5)\r\n \r\nmodel4_2 = ardlDlm(formula = asx ~ gold + copper, data = data.frame(ASX_m), p = 2 , q = 5)\r\nsummary(model4_2)\r\ncheckresiduals(model4_2$model)\r\nvif(model4_2$model)\r\n\r\n# ardlDLM(3,5)\r\n \r\nmodel4_3 = ardlDlm(formula = asx ~ gold + copper, data = data.frame(ASX_m), p = 3 , q = 5)\r\nsummary(model4_3)\r\ncheckresiduals(model4_3$model)\r\nvif(model4_3$model)", "meta": {"hexsha": "12a5d249fe17971424afe7be88c283a2d03a4ff6", "size": 5540, "ext": "r", "lang": "R", "max_stars_repo_path": "forecasting_assignment1.r", "max_stars_repo_name": "modihill/forecasting_assignment1", "max_stars_repo_head_hexsha": "32bd719be532749196aea1495abda488035103e6", "max_stars_repo_licenses": ["Unlicense"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "forecasting_assignment1.r", "max_issues_repo_name": "modihill/forecasting_assignment1", "max_issues_repo_head_hexsha": "32bd719be532749196aea1495abda488035103e6", "max_issues_repo_licenses": ["Unlicense"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "forecasting_assignment1.r", "max_forks_repo_name": "modihill/forecasting_assignment1", "max_forks_repo_head_hexsha": "32bd719be532749196aea1495abda488035103e6", "max_forks_repo_licenses": ["Unlicense"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 24.298245614, "max_line_length": 108, "alphanum_fraction": 0.6606498195, "num_tokens": 1817, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9511422199928904, "lm_q2_score": 0.805632181981183, "lm_q1q2_score": 0.7662707820672987}} {"text": "chi2 <- function(a,b,c,d) {\n # Compute the chi^2 statistic for a 2x2 crosstab containing the values\n # [[a, b], [c, d]]\n ooe <- function(o, e) {(o-e)*(o-e) / e}\n tot = 0.0 + a+b+c+d\n a = as.numeric(a)\n b = as.numeric(b)\n c = as.numeric(c)\n d = as.numeric(d)\n (ooe(a, (a+c)*(a+b)/tot)\n + ooe(b, (b+d)*(a+b)/tot)\n + ooe(c, (a+c)*(c+d)/tot)\n + ooe(d, (d+b)*(c+d)/tot))\n}\n\ncorpus.compare <- function(words.x, freq.x=rep(1, length(words.x)), words.y, freq.y=rep(1, length(words.y))) {\n # Compare two corpora, listen relative frequency and chi-squared\n # words should be a vector of character with the words for corpus x and y\n # freq, if given, should be a vector of the same length as words with the counts per word\n # words may be duplicated\n n.x = aggregate(freq.x, list(words.x), FUN=sum)\n colnames(n.x) = c(\"word\", \"freq.x\")\n n.y = aggregate(freq.y, list(words.y), FUN=sum)\n colnames(n.y) = c(\"word\", \"freq.y\")\n result = merge(n.x, n.y, all=T)\n result[is.na(result)] = 0\n result$chi = chi2(result$freq.x, result$freq.y, sum(result$freq.x) - result$freq.x, sum(result$freq.y) - result$freq.y)\n result$over = (result$freq.x / result$freq.y) / (sum(result$freq.x) / sum(result$freq.y))\n result\n}\n\ncorpus.split <- function(aid, words, freq=NULL, pattern, ...) {\n selected.aid = aid[grepl(pattern, words, ...)]\n print(paste(\"Selected\", length(selected.aid),\"/\", length(unique(aid)),\"using pattern\", pattern))\n words.x = words[aid %in% selected.aid]\n freq.x = if (is.null(freq)) NULL else freq[aid %in% selected.aid]\n words.y = words[!(aid %in% selected.aid)]\n freq.y = if (is.null(freq)) NULL else freq[!(aid %in% selected.aid)]\n list(words.x=words.x, freq.x=freq.x, words.y=words.y, freq.y=freq.y) \n}\n\ncorpus.freqs <- function(aid, words, freq) {\n # compute the document frequency for all words\n freqs = aggregate(freq, list(words), FUN=sum)\n docfreqs = aggregate(aid, list(words), FUN=function(x) length(unique(x)))\n result = merge(freqs, docfreqs, by='Group.1')\n colnames(result) <- c(\"word\", \"tf\", \"df\")\n result$df.prop = result$df / length(unique(aid))\n result$idf = log(length(unique(aid)) / result$df)\n result$tfidf = result$tf * result$idf\n result\n}\n", "meta": {"hexsha": "e3ebc196deebf340b502bc0c5c2e4be60674495c", "size": 2201, "ext": "r", "lang": "R", "max_stars_repo_path": "corpus.r", "max_stars_repo_name": "amcat/amcat-r-tools", "max_stars_repo_head_hexsha": "2556c9616824be0a4e93efd606531886473385e6", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2015-02-18T04:45:08.000Z", "max_stars_repo_stars_event_max_datetime": "2015-02-18T04:45:08.000Z", "max_issues_repo_path": "corpus.r", "max_issues_repo_name": "amcat/amcat-r-tools", "max_issues_repo_head_hexsha": "2556c9616824be0a4e93efd606531886473385e6", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "corpus.r", "max_forks_repo_name": "amcat/amcat-r-tools", "max_forks_repo_head_hexsha": "2556c9616824be0a4e93efd606531886473385e6", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 41.5283018868, "max_line_length": 121, "alphanum_fraction": 0.6383462063, "num_tokens": 727, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9372107914029486, "lm_q2_score": 0.8175744739711883, "lm_q1q2_score": 0.7662396197813868}} {"text": "# Example : 1 Chapter : 6.6 Page No: 356\n# Similar matrices are matrices with same eigen values\nA<-matrix(c(0.5,0.5,0.5,0.5),ncol=2)\nAev<-eigen(A)$values\nprint(\"Eigen values of A \")\nprint(Aev)\nLambda<-matrix(c(1,0,0,0),ncol=2)\nLev<-eigen(Lambda)$values\nprint(\"eigen values of lambda matrix\")\nprint(Lev)\nM<-matrix(c(1,1,0,2),ncol=2)\nM1<-solve(M)\nM1AM<-M1%*%A%*%M\nM1AMev<-eigen(M1AM)$values\nprint(\"EIgen values of M-1*A*M\")\nprint(M1AMev)\nprint(\"A and M-1*A*M are similar matrices\")", "meta": {"hexsha": "f385fe2148fc4fe83bfe7557f50f6849c56f0b0f", "size": 485, "ext": "r", "lang": "R", "max_stars_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH6/EX6.6.1/Ex6.6_1.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH6/EX6.6.1/Ex6.6_1.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH6/EX6.6.1/Ex6.6_1.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 28.5294117647, "max_line_length": 54, "alphanum_fraction": 0.6845360825, "num_tokens": 200, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9539660962919971, "lm_q2_score": 0.8031738034238807, "lm_q1q2_score": 0.7662005778962754}} {"text": "sieve <- function(n)\n{\n n <- as.integer(n)\n if(n > 1e6) stop(\"n too large\")\n primes <- rep(TRUE, n)\n primes[1] <- FALSE\n last.prime <- 2L\n for(i in last.prime:floor(sqrt(n)))\n {\n primes[seq.int(2L*last.prime, n, last.prime)] <- FALSE\n last.prime <- last.prime + min(which(primes[(last.prime+1):n]))\n }\n which(primes)\n}\n\nsieve(1000)\n", "meta": {"hexsha": "ae58dfae5d229744367d49ba0b928cb340471480", "size": 360, "ext": "r", "lang": "R", "max_stars_repo_path": "Task/Sieve-of-Eratosthenes/R/sieve-of-eratosthenes.r", "max_stars_repo_name": "djgoku/RosettaCodeData", "max_stars_repo_head_hexsha": "91df62d46142e921b3eacdb52b0316c39ee236bc", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Task/Sieve-of-Eratosthenes/R/sieve-of-eratosthenes.r", "max_issues_repo_name": "djgoku/RosettaCodeData", "max_issues_repo_head_hexsha": "91df62d46142e921b3eacdb52b0316c39ee236bc", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Sieve-of-Eratosthenes/R/sieve-of-eratosthenes.r", "max_forks_repo_name": "djgoku/RosettaCodeData", "max_forks_repo_head_hexsha": "91df62d46142e921b3eacdb52b0316c39ee236bc", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 21.1764705882, "max_line_length": 69, "alphanum_fraction": 0.575, "num_tokens": 126, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9425067179697694, "lm_q2_score": 0.8128673201042492, "lm_q1q2_score": 0.7661329100163379}} {"text": "# Master Thesis Project - Extreme Value Theory\n# We assume that the stock prices follow a geometric\n# Brownian motion (Black-Scholes model). We plot the\n# empirical stock price data as well as the simulated\n# geometric Brownian motions associated to them.\n# Killian Martin--Horgassan\n# 02-06-2015\n\n# Clear the environment\nrm(list=ls())\n\n# Close all already open graphic windows\ngraphics.off()\n\n# Sourcing the auxiliary files\nsource(\"logGrossReturns.r\")\nsource(\"loadStockData.r\")\nsource(\"loadStockData_plain.r\")\nsource(\"meanAndVarianceDF.r\")\n\n\n# Remark : the csv uses the metastock data format \n# 7 columns : - Ticker (identifier of the stock\n# and stockmarket on which it is listed)\n#\t\t\t\t\t - Date (yyyymmdd)\n#\t\t\t\t\t - Open\n#\t\t\t\t\t - High\n#\t\t\t\t\t - Low\n#\t\t\t\t\t - Close\n#\t\t\t\t\t - Volume\n# By default, the highest price is used i.e. column 3.\nCHOICE <- 3\n\n# Loading the original data for the five stocks\ndf_plain <- loadStockData_plain(CHOICE)\n\n# Loading the log-gross returns for the five stocks\ndf <- loadStockData(CHOICE)\n\n# Computing the mean and Variances of the stock\nmeanAndVarDF <- meanAndVarianceDF(df)\n\n# Building the Geometric Brownian motion\n\tN = dim(df)[1]\n\tM = dim(df)[2]\n\tc <- rep(0,N)\n\tgeomBMs <- data.frame(c,c,c,c,c)\n\t\n\tmeans <- meanAndVarDF[1]\n\tvars <- meanAndVarDF[2]\n\t\n\t# Time component\n\ttimeSteps = 0:(N-1)\n\t \n\t# Brownian motion component\n dis = rnorm(N,0,1)\n dis = cumsum(dis)\n \n\n\tfor (i in 1:M) {\n\t\tcoeff1 = (means[[1]])[i] - 0.5*(vars[[1]])[i]\n\t\tgeomBMs[i] <- (df_plain[[i]])[1]*exp(coeff1*timeSteps + sqrt((vars[[1]])[i])*dis)\n\t}\n\n\n\n# Plotting the actual stock prices and the corresponding simulations\nx_label <- \"Weekly measurements\"\ny_label <- \"Prices and simulation\"\ntitle1 <- \"BNP Stock\"\ntitle2 <- \"Carrefour Stock\"\ntitle3 <- \"LVMH Stock\"\ntitle4 <- \"Sanofi Stock\"\ntitle5 <- \"Total Stock\"\n\nquartz()\npng(file = \"actualAndSimulated.png\")\npar(mfrow = c(3,2))\nplot(df_plain[[1]], pch = 1, col = \"black\", type = 'l', xlab = x_label, ylab = y_label, main = title1)\nlines(geomBMs[[1]], col = 'yellow')\nplot(df_plain[[2]], pch = 1, col = \"blue\", type = 'l', xlab = x_label, ylab = y_label, main = title2)\nlines(geomBMs[[2]], col = \"yellow\")\nplot(df_plain[[3]], pch = 1, col = \"green\", type = 'l', xlab = x_label, ylab = y_label, main = title3)\nlines(geomBMs[[3]], col = \"yellow\")\nplot(df_plain[[4]], pch = 1, col = \"purple\", type = 'l', xlab = x_label, ylab = y_label, main = title4)\nlines(geomBMs[[4]], col = \"yellow\")\nplot(df_plain[[5]], pch = 1, col = \"red\", type = 'l', xlab = x_label, ylab = y_label, main = title5)\nlines(geomBMs[[5]], col = \"yellow\")\ndev.off()\ngraphics.off()\n\n# Rescaling the y-axis by computing the maxima and minima\n# and adapting the y-min and y-max\nYmaxima <- c(max(df_plain[[1]],geomBMs[[1]]), max(df_plain[[2]],geomBMs[[2]]),\n\tmax(df_plain[[3]],geomBMs[[3]]), max(df_plain[[4]],geomBMs[[4]]),\n\tmax(df_plain[[5]],geomBMs[[5]]))\nYminima <- c(min(df_plain[[1]],geomBMs[[1]]), min(df_plain[[2]],geomBMs[[2]]),\n\tmin(df_plain[[3]],geomBMs[[3]]), min(df_plain[[4]],geomBMs[[4]]),\n\tmin(df_plain[[5]],geomBMs[[5]]))\n\t\n# Plotting with the y-axes properly scaled\nquartz()\npng(file = \"actualAndSimulatedRescaled.png\")\npar(mfrow = c(3,2))\nplot(df_plain[[1]], pch = 1, col = \"black\", type = 'l', xlab = x_label, ylab = y_label, main = title1, ylim = c(Yminima[1], Ymaxima[1]))\nlines(geomBMs[[1]], col = 'yellow')\nplot(df_plain[[2]], pch = 1, col = \"blue\", type = 'l', xlab = x_label, ylab = y_label, main = title2, ylim = c(Yminima[2], Ymaxima[2]))\nlines(geomBMs[[2]], col = \"yellow\")\nplot(df_plain[[3]], pch = 1, col = \"green\", type = 'l', xlab = x_label, ylab = y_label, main = title3, ylim = c(Yminima[3], Ymaxima[3]))\nlines(geomBMs[[3]], col = \"yellow\")\nplot(df_plain[[4]], pch = 1, col = \"purple\", type = 'l', xlab = x_label, ylab = y_label, main = title4, ylim = c(Yminima[4], Ymaxima[4]))\nlines(geomBMs[[4]], col = \"yellow\")\nplot(df_plain[[5]], pch = 1, col = \"red\", type = 'l', xlab = x_label, ylab = y_label, main = title5,\nylim = c(Yminima[5], Ymaxima[5]))\nlines(geomBMs[[5]], col = \"yellow\")\ndev.off()\ngraphics.off()\n\n\n\n\n\n", "meta": {"hexsha": "f115a4aa0ef9ca60269434041013c54cb869b5ff", "size": 4114, "ext": "r", "lang": "R", "max_stars_repo_path": "r_files_logGrossReturns/simulationFittingGeomBM.r", "max_stars_repo_name": "CillianMH/pdmExtremeValueTheory", "max_stars_repo_head_hexsha": "f7a7504c2eca0c6be665bcfc3d98dfee6c02de41", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "r_files_logGrossReturns/simulationFittingGeomBM.r", "max_issues_repo_name": "CillianMH/pdmExtremeValueTheory", "max_issues_repo_head_hexsha": "f7a7504c2eca0c6be665bcfc3d98dfee6c02de41", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "r_files_logGrossReturns/simulationFittingGeomBM.r", "max_forks_repo_name": "CillianMH/pdmExtremeValueTheory", "max_forks_repo_head_hexsha": "f7a7504c2eca0c6be665bcfc3d98dfee6c02de41", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 33.4471544715, "max_line_length": 137, "alphanum_fraction": 0.6438988819, "num_tokens": 1374, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9314625012602593, "lm_q2_score": 0.822189134878876, "lm_q1q2_score": 0.7658383480832865}} {"text": "## Dale W.R. Rosenthal, 2018\n## You are free to distribute and use this code so long as you attribute\n## it to me or cite the text.\n## The legal disclaimer in _A Quantitative Primer on Investments with R_\n## applies to this code. Use or distribution without these comment lines\n## is forbidden.\n\nbs.call <- function(S,K,rf,T,sigma) {\n d1 <- (log(S/K)+(rf+sigma^2/2)*T)/(sigma*sqrt(T))\n S*pnorm(d1)-K*exp(-rf*T)*pnorm(d1-sigma*sqrt(T))\n}\n\noz.per.year <- 10000\nrf <- 0.03 # 3% interest rates\nwacc <- 0.08 # 8% weighted average cost of capital\ns0 <- 1300\ns0.lt <- 1200\nK <- 1000\nsigma <- 0.3\n\n## annual real options approach, no mean reversion\noz.per.year*((s0-K)/(1+wacc) + bs.call(s0,K,rf,1,sigma)/(1+wacc) +\n sum(bs.call(s0.lt,K,rf,1:8,sigma)/(1+wacc)*exp(-rf)))\n\n## annual real options, assuming mean reversion (approximation)\noz.per.year*((s0-K)/(1+wacc) + bs.call(s0,K,rf,1,sigma)/(1+wacc) +\n sum(bs.call(1200,1000,0.03,1,0.3)/(1+wacc)*exp(-rf*(1:8))))\n\n## quarterly real options, no mean reversion\noz.per.year/4*((s0-K)/(1+wacc)^0.25\n + sum(bs.call(1300,1000,0.03,(1:4)/4,0.3)/(1+wacc)^0.25)\n + sum(bs.call(1300-25*(1:3),1000,0.03,0.25,0.3)/(1+wacc)^0.25*exp(-rf*(5:7)/4))\n + sum(bs.call(1200,1000,0.03,(1:32)/4,0.3)/(1+wacc)^0.25*exp(-rf*(8:39)/4)))\n\n## quarterly real options, assuming mean reversion (approximation)\noz.per.year/4*((s0-K)/(1+wacc)^0.25\n + sum(bs.call(1300,1000,0.03,0.25,0.3)/(1+wacc)^0.25*exp(-rf*(0:3)/4))\n + sum(bs.call(1300-25*(1:4),1000,0.03,0.25,0.3)/(1+wacc)^0.25*exp(-rf*(4:7)/4))\n + sum(bs.call(1200,1000,0.03,0.25,0.3)/(1+wacc)^0.25*exp(-rf*(8:39)/4)))\n", "meta": {"hexsha": "6f5ddc1d6fbdda749c3a31b71b2f592e19f40612", "size": 1637, "ext": "r", "lang": "R", "max_stars_repo_path": "Quantitative Primer/samples/ch21-gold-mine-real-options.r", "max_stars_repo_name": "bmoretz/Quantitative-Investments", "max_stars_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 7, "max_stars_repo_stars_event_min_datetime": "2020-03-26T05:47:30.000Z", "max_stars_repo_stars_event_max_datetime": "2022-02-18T21:50:54.000Z", "max_issues_repo_path": "Quantitative Primer/samples/ch21-gold-mine-real-options.r", "max_issues_repo_name": "bmoretz/Quantitative-Investments", "max_issues_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Quantitative Primer/samples/ch21-gold-mine-real-options.r", "max_forks_repo_name": "bmoretz/Quantitative-Investments", "max_forks_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2020-11-03T09:23:54.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-18T21:50:55.000Z", "avg_line_length": 40.925, "max_line_length": 83, "alphanum_fraction": 0.6212583995, "num_tokens": 661, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9532750360641186, "lm_q2_score": 0.8031738034238806, "lm_q1q2_score": 0.765645536424655}} {"text": "#' @title Binomial distribution simulator\n#'\n#' @param iter The number of iterations to simulate, an integer\n#' @param n The size of the binomial distribution\n#' @param p The probability of success\n#'\n#' @return A barplot of the binomial distribution\n#' @export\n#'\n#' @importFrom grDevices rainbow\n#' @importFrom graphics barplot\n#'\n#' @examples\n#' \\dontrun{mybin(iter = 10000, n = 20, p = 0.7)}\nmybinomial=function(iter=100,n=10, p=0.5){\n # make a matrix to hold the samples\n #initially filled with NA's\n sam.mat=matrix(NA,nrow=n,ncol=iter, byrow=TRUE)\n #Make a vector to hold the number of successes in each trial\n succ=c()\n for( i in 1:iter){\n #Fill each column with a new sample\n sam.mat[,i]=sample(c(1,0),n,replace=TRUE, prob=c(p,1-p))\n #Calculate a statistic from the sample (this case it is the sum)\n succ[i]=sum(sam.mat[,i])\n }\n #Make a table of successes\n succ.tab=table(factor(succ,levels=0:n))\n #Make a barplot of the proportions\n barplot(succ.tab/(iter), col=rainbow(n+1), main=\"Binomial simulation\", xlab=\"Number of successes\")\n succ.tab/iter\n}\n", "meta": {"hexsha": "2c337aec679f332795e0943031488f5cd6d5cbe1", "size": 1082, "ext": "r", "lang": "R", "max_stars_repo_path": "R/mybinomial.r", "max_stars_repo_name": "sam-irl/MATH4753bird0023", "max_stars_repo_head_hexsha": "3414fb54d8fd3bdcae2f8214cf192a3e5789898e", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/mybinomial.r", "max_issues_repo_name": "sam-irl/MATH4753bird0023", "max_issues_repo_head_hexsha": "3414fb54d8fd3bdcae2f8214cf192a3e5789898e", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/mybinomial.r", "max_forks_repo_name": "sam-irl/MATH4753bird0023", "max_forks_repo_head_hexsha": "3414fb54d8fd3bdcae2f8214cf192a3e5789898e", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 32.7878787879, "max_line_length": 100, "alphanum_fraction": 0.6959334566, "num_tokens": 333, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9532750373915658, "lm_q2_score": 0.8031737963569016, "lm_q1q2_score": 0.7656455307540512}} {"text": "## See Bayesian Choice, pg. 181\nposterior_ccdf <- function(n0, m){\n if(n0 < 1 || m < 1 || n0 < m) stop(\"Something is wrong, check your parameters\")\n require(VGAM)\n lnum <- log(VGAM::zeta(x = 2, shift = n0))\n ldenom <- log(VGAM::zeta(x = 2, shift = m))\n return(exp(lnum - ldenom)) \n}\nposterior_ccdf <- Vectorize(posterior_ccdf)\napproximate_posterior_ccdf <- function(n0, m){\n m/n0\n}\napproximate_posterior_ccdf <- Vectorize(approximate_posterior_ccdf)\n\nobs.tram.number <- 100\n\nk <- 10\n\nN0s <- obs.tram.number:(k*obs.tram.number)\n\nps <- posterior_ccdf(n0 = N0s, m = obs.tram.number)\napp.ps <- approximate_posterior_ccdf(n0 = N0s, m = obs.tram.number)\n\nplot(N0s, 1-ps, type = \"l\", lwd = 3, \n main = \"CDF of N given T\",\n xlab = expression(n[0]), ylab = expression(Pr(N >= n[0])))\nlines(N0s, 1-app.ps, col = 2, lwd = 2, lty = 2)\nlegend(x=\"bottomright\",\n legend = c(\"Exact\", \"Approximate\"),\n col = 1:2, lty = 1:2, lwd = 2, bty = 'n')\nabline(h = 1/2, lty = 2)\nabline(v = 2*obs.tram.number, lwd = 2, col = 2, lty = 2)", "meta": {"hexsha": "5e795a926a8b4c0e91e6322867e7064983dace6c", "size": 1036, "ext": "r", "lang": "R", "max_stars_repo_path": "code/tramcar_problem.r", "max_stars_repo_name": "lucasmoschen/BayesianStatisticsCourse", "max_stars_repo_head_hexsha": "79fe17dd71fa9638ae4865c8e75eeb0f814d2ccb", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 6, "max_stars_repo_stars_event_min_datetime": "2021-03-17T17:39:29.000Z", "max_stars_repo_stars_event_max_datetime": "2022-02-15T23:40:56.000Z", "max_issues_repo_path": "code/tramcar_problem.r", "max_issues_repo_name": "anhnguyendepocen/BayesianStatisticsCourse", "max_issues_repo_head_hexsha": "79fe17dd71fa9638ae4865c8e75eeb0f814d2ccb", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 6, "max_issues_repo_issues_event_min_datetime": "2021-03-24T01:28:22.000Z", "max_issues_repo_issues_event_max_datetime": "2022-02-16T20:49:10.000Z", "max_forks_repo_path": "code/tramcar_problem.r", "max_forks_repo_name": "anhnguyendepocen/BayesianStatisticsCourse", "max_forks_repo_head_hexsha": "79fe17dd71fa9638ae4865c8e75eeb0f814d2ccb", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2021-05-26T16:28:02.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-23T12:33:26.000Z", "avg_line_length": 32.375, "max_line_length": 82, "alphanum_fraction": 0.6254826255, "num_tokens": 397, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9284088005554476, "lm_q2_score": 0.8244619263765707, "lm_q1q2_score": 0.7654377081709057}} {"text": "setwd('/Users/demg/Projects/FA/Course III/ECONOMETRICS/task4')\ndata <- read.table('./AG.txt', dec=',', header=TRUE)\ngetwd()\n#install.packages('lmtest')\n#install.packages(\"ggiraphExtra\")\nlibrary(lmtest)\nlibrary(ggiraphExtra)\n\nx <- data$x\ny <- data$y\nx\ny\n\n\n\n#линейная модель \nm1<-lm(y~x,data=data) \nm1\nsm1<-summary(m1) \nsm1\nA1 <- (sum(abs(sm1$residuals/y))/length(y))*100\n\nggPredict(m1, interactive = TRUE)\n#данная модель значима\n#критерий Стьюдента\n#H0 отвергается, коэффициенты значимы\n\n#показательная модель\nm2<-lm(log10(y)~x,data=data) \nm2 \nsm2=summary(m2) \nsm2\n\nA2 <- (sum(abs(sm2$residuals/log10(y)))/length(log10(y)))*100\nggPredict(m2, interactive = TRUE)\n#данная модель значима\n#критерий Стьюдента\n#H0 отвергается, коэффициенты значимы\n\n#степенная модель\nx1<-log10(x)\ny1<-log10(y)\nm3<-lm(y1~x1,data=data)\nm3\nsm3=summary(m3)\nsm3\n\nA3 <- (sum(abs(sm3$residuals/y1))/length(y1))*100\nggPredict(m3, interactive = TRUE)\n#данная модель значима\n\n#гиперболическая модель\n#критерий Стьюдента\n#H0 отвергается, коэффициенты значимы\n\nx2<-1/x\nm4<-lm(y~x2,data=data) \nm4\nsm4=summary(m4) \nsm4\n\nA4 <- (sum(abs(sm4$residuals/y))/length(y))*100\nggPredict(m4, interactive = TRUE)\n\n#Линейная\nprint(sm1$sigma)\nprint(sm1$r.squared)\nprint(sm1$fstatistic)\nprint(A1)\n\n\n#Показательная\nprint(sm2$sigma)\nprint(sm2$r.squared)\nprint(sm2$fstatistic)\nprint(A2)\n\n#степенная\nprint(sm3$sigma)\nprint(sm3$r.squared)\nprint(sm3$fstatistic)\nprint(A3)\n\n#гиперболическая\nprint(sm4$sigma)\nprint(sm4$r.squared)\nprint(sm4$fstatistic)\nprint(A4)\n\n#данная модель значима\n#критерий Стьюдента\n#H0 не отвергается, коэффициенты незначимы\n\n#Отчет\n#у гиперболической модели самый маленький коэффициент детерминации, а у показательной коэффициент\n#R-squared: 0.6878791 (ближе всего к 1), значит,качество данной модели лучшее среди всех остальных", "meta": {"hexsha": "fe3efb267af2d1dd0cc27ae65453f560551e989f", "size": 1795, "ext": "r", "lang": "R", "max_stars_repo_path": "Course III/ECONOMETRICS/task4/all.r", "max_stars_repo_name": "GeorgiyDemo/FA", "max_stars_repo_head_hexsha": "641a29d088904302f5f2164c9b3e1f1c813849ec", "max_stars_repo_licenses": ["WTFPL"], "max_stars_count": 27, "max_stars_repo_stars_event_min_datetime": "2019-08-18T20:54:27.000Z", "max_stars_repo_stars_event_max_datetime": "2022-02-22T02:39:45.000Z", "max_issues_repo_path": "Course III/ECONOMETRICS/task4/all.r", "max_issues_repo_name": "GeorgiyDemo/FA", "max_issues_repo_head_hexsha": "641a29d088904302f5f2164c9b3e1f1c813849ec", "max_issues_repo_licenses": ["WTFPL"], "max_issues_count": 217, "max_issues_repo_issues_event_min_datetime": "2019-09-22T14:43:25.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T13:49:18.000Z", "max_forks_repo_path": "Course III/ECONOMETRICS/task4/all.r", "max_forks_repo_name": "GeorgiyDemo/FA", "max_forks_repo_head_hexsha": "641a29d088904302f5f2164c9b3e1f1c813849ec", "max_forks_repo_licenses": ["WTFPL"], "max_forks_count": 42, "max_forks_repo_forks_event_min_datetime": "2019-09-18T11:36:28.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-19T18:43:00.000Z", "avg_line_length": 18.6979166667, "max_line_length": 99, "alphanum_fraction": 0.7498607242, "num_tokens": 750, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9678992960608886, "lm_q2_score": 0.7905303087996143, "lm_q1q2_score": 0.7651537294019436}} {"text": "#' Probability of path choices using logit model.\r\n#'\r\n#' This function calculates probabilities for selection of each path on the network based on set of path disutilities (costs). The function uses a logit random utility model.\r\n#' @param u Vector of utlities on each path\r\n#' @param ODpair Vector indicating the OD pair serviced by each route.\r\n#' @param theta The logit parameter. Defaults to 1.\r\n#' @return Vector of route choice probabilities\r\n#' @keywords path route probability\r\n#' @examples\r\n#' A <- matrix(c(0,1,0,0,1,0,0,0,0,1,1,0,0,0,1,0,0,0,0,1,1,0,0,0,0,0,0,1),ncol=4,byrow=T)\r\n#' ODpair <- c(1,1,2,2)\r\n#' Alpha <- rep(10,7)\r\n#' Beta <- rep(2,7)\r\n#' pow <- rep(4,7)\r\n#' path_flow <- c(10,20,15,15)\r\n#' x <- A%*%path_flow\r\n#' u <- PathCost(x,A,Alpha,Beta)\r\n#' LogitPathProb(u,ODpair,theta=0.7)\r\n#' @export\r\n\r\nLogitPathProb <- function(u,ODpair,theta=1){\r\n\tu <- u - rep(tapply(u,ODpair,min),table(ODpair))\r\n\tp1 <- exp(-theta*u)\r\n\tp.sums <- tapply(p1,ODpair,sum)\r\n\tp.sums <- rep(p.sums,unname(table(ODpair)))\r\n\tp1/p.sums\r\n}\r\n", "meta": {"hexsha": "97893d5757a8959152606b17b1477d84154fc118", "size": 1036, "ext": "r", "lang": "R", "max_stars_repo_path": "R/LogitPathProb.r", "max_stars_repo_name": "MartinLHazelton/transportation", "max_stars_repo_head_hexsha": "ba690828d2e24b492677c41a7b659712382ccec0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/LogitPathProb.r", "max_issues_repo_name": "MartinLHazelton/transportation", "max_issues_repo_head_hexsha": "ba690828d2e24b492677c41a7b659712382ccec0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/LogitPathProb.r", "max_forks_repo_name": "MartinLHazelton/transportation", "max_forks_repo_head_hexsha": "ba690828d2e24b492677c41a7b659712382ccec0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 37.0, "max_line_length": 175, "alphanum_fraction": 0.6592664093, "num_tokens": 353, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9304582593509315, "lm_q2_score": 0.8221891283434876, "lm_q1q2_score": 0.7650126652157411}} {"text": "y1bar=25.1\r\ny2bar=23.5\r\ny3bar=37.8\r\n\r\nMSE=10.278\r\nsigma=sqrt(MSE)\r\n\r\n# crtical value\r\nalpha = 0.025\r\nz.alpha=qt(1-alpha,df=15)\r\n\r\n# For panels 2 and 3, we have nt = 10 observations per panel, thus confidence interval will be\r\nn=10\r\nerror=sigma*z.alpha*sqrt(2/n)\r\n# thus confidence interval will be\r\nleft_i=(y3bar-y2bar)-error\r\nright_i=(y3bar-y2bar)+error\r\nprint(\"confidence interval is\")\r\nprint(left_i)\r\nprint(right_i)", "meta": {"hexsha": "540752c49419e4632661cf0d39b8ab57de38f3eb", "size": 419, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH14/EX14.11/Ex14_11.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH14/EX14.11/Ex14_11.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH14/EX14.11/Ex14_11.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 20.95, "max_line_length": 95, "alphanum_fraction": 0.7136038186, "num_tokens": 147, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9252299570920386, "lm_q2_score": 0.8267118004748677, "lm_q1q2_score": 0.7648985236808438}} {"text": "## Load some packages that will be useful\nlibrary(mgcv) # load the MGCV package with Simon Wood's gam() functions\nlibrary(readr) # Hadley Wickham's package for reading in data easily\nlibrary(ggplot2) # for plotting with ggplot\nlibrary(ggfortify) # for autoplot\n\n##################################################################################################\n## We'll first examine the bias-variance tradeoff in a simplified form with a small exercise.\n## If you remember, this tradeoff is one of the concepts behind finding the optimal amount of smoothing.\n## We'll fit linear regressions to parts of the data, increasing the number of parts from 1 to 10.\n##################################################################################################\n\n# First, read in the bioluminescence data.\n# Sources is the number of bioluminescent plankton seen in each water sample\n# SampleDepth is the depth of the water sample, in m\n# Station is the ID of the location at which multiple water samples were taken\nISIT <- read_tsv(url('https://github.com/aeda2021/2021_master/raw/main/raw-data/ISIT.txt')) # tsv for tab-separated values\n\n# Subset it to one station. This is what we'll work with for now.\nISITsub <- subset(ISIT, Station == 8)\n\n# Plot the data\nggplot(ISITsub, aes(x=SampleDepth, y=Sources)) +\n\tgeom_point()\n\n# Now you can fit a linear regression to the ISITsub dataset, with Sources as the response and SampleDepth as the explanatory variable\n# Please call the output \"mod1\", as I've started to fill in for you\nmod1 <- lm(Sources ~ SampleDepth, data=ISITsub)\n\n# Q1: What was your code for fitting a linear regression of Sources vs. SampleDepth?\n\n## mod1 <- lm(Sources ~ SampleDepth, data=ISITsub)\n\n# We'll predict the mean response and confidence intervals from this model and save the output\nISITsub$mod1 <- predict(mod1)\nISITsub$mod1lwr <- predict(mod1, interval='confidence', level=0.95)[,'lwr']\nISITsub$mod1upr <- predict(mod1, interval='confidence', level=0.95)[,'upr']\n\n# Now plot the linear model fit to the full dataset on top of the data\nggplot(ISITsub, aes(x=SampleDepth, y=Sources)) +\n\tgeom_point() +\n\tgeom_line(aes(y=mod1)) + \n\tgeom_ribbon(aes(ymin=mod1lwr, ymax=mod1upr), alpha=0.3)\n\n# Q2: Use your skills from earlier in this course and evaluate this linear model (autoplot may be useful here). How does this fit look to you? Does a linear regression look reasonable? Any well-justified answer is appropriate. \n\n## Visually you can see that the linear model is not a great fit\n\nautoplot(mod1)\n\n## From autoplot()'s QQ plot we can see that the residuals don't look normal, and the sign and magnitude of the\n## residuals still show a pattern when plotted against the fitted values. The variance does seem to be pretty\n## homogeneous, however. It also looks like some data-points (represented in the bottom right hand corner of the\n## residuals vs leverage plot, eg. 20, 17 & 24) are having an outsized effect on the model fit.\n\n\n# For comparison, let's fit linear models to two halves of the data. This involves a fair bit of coding in R, so please ask for help understanding the code where things are confusing. \n# First, we have to find the halves of the data\nquants2 <- quantile(ISITsub$SampleDepth, probs=seq(0, 1, by=0.5)) # define the ends and the half-way point in the data with the quantile function\nISITsub$split2 <- cut(ISITsub$SampleDepth, breaks=quants2, include.lowest=TRUE, labels=1:2) \n\n# Q3: In your own words, what does the cut() function do? How are we using it here?\n\n## It looks like cut creates a new column that assigns each row to one of the quantiles (1 & 2 in this case)\n\n# Next, let's fit a linear model to each subset (half) of the data. We do this in a loop to make it easier.\nmod2s <- vector('list', length=2) # A list to hold each of our models in a single, convenient object\nISITsub$mod2 <- ISITsub$mod2lwr <- ISITsub$mod2upr <- NA # Initialize the variables we'll use and fill with NA\nfor(i in 1:length(mod2s)){ # Loop through each model\n\tmod2s[[i]] <- lm(Sources ~ SampleDepth, data=ISITsub[ISITsub$split2==i,]) # Fit a linear regression to the appropriate subset of the data. Now see why we made the split2 vector?\n\tISITsub$mod2[ISITsub$split2==i] <- predict(mod2s[[i]]) # Now predict from that model. Notice we're only predicting for part of the data.\n\tISITsub$mod2lwr[ISITsub$split2==i] <- predict(mod2s[[i]], interval='confidence', level=0.95)[,'lwr'] # Same for the confidence intervals\n\tISITsub$mod2upr[ISITsub$split2==i] <- predict(mod2s[[i]], interval='confidence', level=0.95)[,'upr']\n}\n\n# Plot the data, the 1-model fit, and the 2-model fit\n# There will be an odd 3rd line segment connecting the end of the first model fit to the beginning of the second model fit. Just pretend it's not there.\nggplot(ISITsub, aes(x=SampleDepth, y=Sources)) +\n\tgeom_point() +\n\tgeom_line(aes(y=mod1)) +\n\tgeom_ribbon(aes(ymin=mod1lwr, ymax=mod1upr), alpha=0.3) +\n\tgeom_line(aes(y=mod2, color='red')) +\n\tgeom_ribbon(aes(ymin=mod2lwr, ymax=mod2upr), alpha=0.3, fill='red')\n\n\n# Q4: Has the fit between the model and the data improved? What's the downside of continuing the split the data into finer and finer chunks and fitting more models?\n\n## It does look better, the average distance between points and the line are definitely smaller now than they\n## were for the linear model.\n\n# Now, it's your turn. Please fit 10 linear regression models. I'd recommend using the 2-model code above as a guide and tweaking it.\n\nquants <- quantile(ISITsub$SampleDepth, probs=seq(0, 1, by=0.1))\nISITsub$split <- cut(ISITsub$SampleDepth, breaks=quants, include.lowest=TRUE, labels=1:10)\n\nmods <- vector('list', length=10) # A list to hold each of our models in a single, convenient object\nISITsub$mods <- ISITsub$modslwr <- ISITsub$modsupr <- NA # Initialize the variables we'll use and fill with NA\nfor(i in 1:length(mods)){ # Loop through each model\n mods[[i]] <- lm(Sources ~ SampleDepth, data=ISITsub[ISITsub$split==i,]) # Fit a linear regression to the appropriate subset of the data. Now see why we made the split2 vector?\n ISITsub$mods[ISITsub$split==i] <- predict(mods[[i]]) # Now predict from that model. Notice we're only predicting for part of the data.\n ISITsub$modslwr[ISITsub$split==i] <- predict(mods[[i]], interval='confidence', level=0.95)[,'lwr'] # Same for the confidence intervals\n ISITsub$modsupr[ISITsub$split==i] <- predict(mods[[i]], interval='confidence', level=0.95)[,'upr']\n}\n\n# Now plot the 10 models on top of the data and on top of the 1- and 2-model fits. The plot with the data, 1-model, and 2-model fit is probably a useful guide here.\n\nggplot(ISITsub, aes(x=SampleDepth, y=Sources)) +\n geom_point() +\n geom_line(aes(y=mod1)) +\n geom_ribbon(aes(ymin=mod1lwr, ymax=mod1upr), alpha=0.3) +\n geom_line(aes(y=mod2, color='red')) +\n geom_ribbon(aes(ymin=mod2lwr, ymax=mod2upr), alpha=0.3, fill='red')+\n geom_line(aes(y=mods, color='blue'))+\n geom_ribbon(aes(ymin=modslwr, ymax=modsupr), alpha=0.3, fill='blue')\n\n\n# Q5: Compare your 10-model fit to the 1-model fit. Which model's predictions are furthest from the observed data? Which model has the widest confidence bounds? How does this (or does this not) illustrate the bias-variance tradeoff?\n\n## The 10-model fit goes through almost all the points, and goes very close to the others. The 1-model fit's predictions\n## are the furthest from the observed data. The confidence interval on the 10 model fit is very large in some places.\n## This demonstrates that as you improve fit by adding complexity to the model, you also increase the variance around \n## the predictions and thereby decrease certainty in the predictions. \n\n####################################################\n## Now you'll fit some GAMs and evaluate your models\n####################################################\n#install.packages(\"maps\") # if needed\nlibrary(maps) # has map data in it\n\n# load the data\nspdata <- readRDS(url('https://github.com/aeda2021/2021_master/raw/main/raw-data/gadusmorhua.rds')) # load the spdata data.frame with abundance and environmental data from cod surveys\nspdata$presfit01 <- as.numeric(spdata$presfit) # make a vector that's nice for plotting\nspdata <- spdata[order(spdata$presfit01),] # order the data from absent to present for ease of plotting\n\n# examine the data\nhead(spdata) # look at the dataset\nsummary(spdata)\n\n# make a map of the data\nworld <- map_data('world')\n\nggplot() + \n\tgeom_polygon(data=world, aes(x=long, y=lat, group=group), color='black', fill=NA) + # the map\n\txlim(-100, -45) + \n\tylim(23, 62) +\n\tgeom_point(data=spdata, aes(x=lon, y=lat, color=presfit, alpha=0.1), size=0.01) # the data points. note that because the dataframe is sorted from absent to present, the presences are plotted on top of the absences\n\n\n# Q6: Based on the map, do you think cod prefer warmer or cooler waters? Why do you think that?\n\n## According to the map, cod site occupancy is much more common in the cold waters of New England and Atlantic\n## Canada.\n\n\n# Q7: Plot cod presence/absence (the presfit vector) vs. the bottom temperature (SBT.actual). At what range of temperatures have cod been observed?\n\nggplot(spdata, aes(y=SBT.actual, group=presfit01)) +\n geom_boxplot()\n\n\n# Q8: Fit a GAM for presfit against SBT.actual. Check the model. Does it look like the assumptions have been met? Why or why not?\n\ngam1 <- gam(presfit01 ~ s(SBT.actual), data=spdata)\ngam.check(gam1)\n\nplot(gam1)\n\n## Those look weird. The histogram of residuals looks bimodal, and everything else is two equidistant lines,\n## because the data is binary.\n\n\n# Q9: Fit a new GAM with a more appropriate error structure and save it as \"mod2\". The gam() function takes the same family= argument as does glm(). Which error structure and link function did you choose?\n\nmod2 <- gam(presfit01 ~ s(SBT.actual), data=spdata, family='binomial')\n\nsummary(mod2)\n\n## I used the binomial error distribution because of the binary nature of the outcome data, and left the link\n## family as the default 'logit'.\n\n# Q10: Check your mod2 GAM. Does it look like the assumptions have been met? Make sure to read the text output as well as look at the graphs. If something doesn't look right, what would you do to fix it?\n\ngam.check(mod2)\n\ncheck_model(mod2)\n\nplot(mod2, ylim=c(-100,1000))\n\n## The the QQ plot looks much better. The others still look a little funky, including the histogram of residuals\n## which is still bimodal. \n\n# Q11: Interpret your mod2 GAM (summary function). How much deviance is explained? Is the SBT.actual term significant at alpha=0.05? How wiggly do you expect the smooth fit to be?\n\nsummary(mod2)\n\n## The GAM explains 26.5% of the deviance. The SBT.actual interaction is highly significant, (so yes, significant at alpha = 0.05).\n## My first instinct was that there was no reason for the fit to be wiggly given what appears to be a straightforward\n## threshold type relationship between temperature and presense of cod. However, seeing an edf of about 9 made me unsure\n## (Zuur says 10ish edf is usually pretty wiggly, iirc). Because I already plotted the model, though, I can see\n## that it is not very wiggly!\n\n# Now let's make predictions from our last model (mod2) and plot them.\nnd <- data.frame(SBT.actual = seq(-5,30, by=0.5)) # make a data.frame of new explanatory variables\nnd$mod2 <- predict(mod2, newdata=nd, type='response') # predict on the scale of the response\nnd$mod2se <- predict(mod2, newdata=nd, type='response', se.fit=TRUE)$se.fit # get the standard errors of the fit\n\nggplot(spdata, aes(x=SBT.actual, y=presfit01)) +\n\tgeom_point() +\n\tgeom_line(data=nd, aes(x=SBT.actual, y=mod2, color='red')) +\n\tgeom_ribbon(data=nd, aes(x=SBT.actual, ymin=mod2-mod2se, ymax=mod2+mod2se), alpha=0.3, fill='red', inherit.aes=FALSE)\n\n\n\n# Q12: Does the fit look realistic? Why or why not? Does it look overfit? Why or why not?\n\n## I suspect that the model might be overfit. Without knowing the ecology of cod very well or diving into the \n## data much deeper, it seems odd to me that there is a wiggle in the line between SBT = 1 and SBT = 6ish...\n## I would have though the true relationship to be more monotonically decreasing in this interval. However\n## there may be some ecological explanation that I'm not aware of... closer inspection of the data may give a \n## hint here.\n\n\n\n# Q13: This dataset is actually a concatenation of seven different surveys which each have slightly different abilities to catch cod. Fit a new GAM that includes a categorical predictor for survey (the region vector). Based on AIC, which model would you choose? How confident would you be?\n\nmod3 <- gam(presfit01 ~ s(SBT.actual) + factor(region), data=spdata, family='binomial')\nsummary(mod3)\nAIC(mod2, mod3)\n\n## The model with region as a factor explains more of the deviance (33%) and has a lower AIC (delta AIC = 800),\n## Such a large delta AIC makes me very confident that the model with region as a factor is a better choice. \n", "meta": {"hexsha": "983e2fab652b7c138c705da5422e2060cdac8eac", "size": 12945, "ext": "r", "lang": "R", "max_stars_repo_path": "scripts/9_GAMs.r", "max_stars_repo_name": "aeda2021/aldercotte_andrew", "max_stars_repo_head_hexsha": "68309fad74372a4170fbff3f944d4278818c659f", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "scripts/9_GAMs.r", "max_issues_repo_name": "aeda2021/aldercotte_andrew", "max_issues_repo_head_hexsha": "68309fad74372a4170fbff3f944d4278818c659f", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2021-03-02T02:06:25.000Z", "max_issues_repo_issues_event_max_datetime": "2021-03-02T02:06:25.000Z", "max_forks_repo_path": "scripts/9_GAMs.r", "max_forks_repo_name": "aeda2021/aldercotte_andrew", "max_forks_repo_head_hexsha": "68309fad74372a4170fbff3f944d4278818c659f", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 55.7974137931, "max_line_length": 289, "alphanum_fraction": 0.7252993434, "num_tokens": 3505, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9252299509069106, "lm_q2_score": 0.8267117855317474, "lm_q1q2_score": 0.7648985047417031}} {"text": "births <- read.table('birth.txt',header=T)\r\n\r\n# fit a loess regression\r\n\r\nbirth.lo <- loess(netherlands~year, data=births)\r\nplot(birth$year,predict(birth.lo))\r\n\r\n# the span = argument to loess() is the smoothing parameter\r\n# higher = smoother (more like an overall quadratic)\r\n\r\n# compare predicted values with those from a quadratic model\r\n\r\nbirth.lm2 <- lm(netherlands~year + I(year^2), data=births)\r\n# the I() bit is to tell R to evaluate the formula inside\r\n# an alternative is to compute year2 in the births data frame\r\n# births$year2 <- births$year^2\r\n# birth.lm2 <- lm(netherlands~year + year2, data=births)\r\n\r\nplot(birth$year, predict(birth.lm2))\r\nlines(birth$year,predict(birth.lo))\r\n\r\n# would be nice to use anova() to compare the two fits, but\r\n# anova can only compare loess() to loess() or lm() to lm()\r\n\r\n# trick loess into giving you a quadratic regression\r\n\r\nbirth.lo2 <- loess(netherlands~year, data=births, span=100)\r\nanova(birth.lo2, birth.lo)\r\n\r\n# trick loess into giving you a linear regression\r\nbirth.lo1 <- loess(netherlands~year, data=births, span=100, degree=1)\r\nanova(birth.lo1, birth.lo)\r\n\r\n# The mgcv library provides gam() which gives you smoothing splines\r\n# and generalized additive models (covered in 511)\r\n\r\n\r\n# Breusch-Pagan test, need to assemble by specific computations\r\n\r\n# just the linear regression\r\nbirth.lm <- lm(netherlands~year,data=births)\r\n\r\nesq <- (45/0.00006542)*resid(birth.lm)^2\r\n# need to replace 45 by N, 0.00006542 by SSE\r\n\r\nbp <- lm(esq~births$year)\r\nsummary(bp)\r\n# gives you the information for the Breush-Pagan test\r\n\r\n\r\n# the cut() function breaks a continuous variable into groups\r\nyeargroup <- cut(birth$year,breaks=seq(1949,1994,5))\r\n\r\n# seq(1949, 1994, 5) gives 1949, 1954, 1959, ...\r\n# breaks includes the lowest break in the first group\r\n# so the first group includes 1949, 1950, 1951, 1952, and 1953.\r\n# 1954 goes into the second group\r\n\r\n# the result of cut() is a factor\r\n\r\n\r\n\r\n", "meta": {"hexsha": "ecfc1c2bd773adec888ed5d980664609df3c0d01", "size": 1947, "ext": "r", "lang": "R", "max_stars_repo_path": "RFrontEndSolution/Tests Repo/Rscripts All (163 files)/births2.r", "max_stars_repo_name": "AlexandrosPlessias/CompilerFrontEndForRLanguage", "max_stars_repo_head_hexsha": "71e3e60476f6f83b05cc97c625265edbde086341", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "RFrontEndSolution/Tests Repo/Rscripts All (163 files)/births2.r", "max_issues_repo_name": "AlexandrosPlessias/CompilerFrontEndForRLanguage", "max_issues_repo_head_hexsha": "71e3e60476f6f83b05cc97c625265edbde086341", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "RFrontEndSolution/Tests Repo/Rscripts All (163 files)/births2.r", "max_forks_repo_name": "AlexandrosPlessias/CompilerFrontEndForRLanguage", "max_forks_repo_head_hexsha": "71e3e60476f6f83b05cc97c625265edbde086341", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 30.9047619048, "max_line_length": 70, "alphanum_fraction": 0.7118644068, "num_tokens": 555, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8840392725805823, "lm_q2_score": 0.8652240860523327, "lm_q1q2_score": 0.7648920716529034}} {"text": "# Recursive function to find factorial\nrecursive.factorial <- function(x) {\nif (x == 0) return (1)\nelse return (x * recursive.factorial(x-1))\n}\n", "meta": {"hexsha": "c5a4b0b216ed9160e6f3255e817f9b1db971effe", "size": 157, "ext": "r", "lang": "R", "max_stars_repo_path": "factorial_recursion/factorial_recursion.r", "max_stars_repo_name": "hpissei/hacktoberfest", "max_stars_repo_head_hexsha": "1851a8845a71df3ac919ca650c07ce778ec5da47", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2020-02-08T07:11:32.000Z", "max_stars_repo_stars_event_max_datetime": "2020-02-08T07:11:32.000Z", "max_issues_repo_path": "factorial_recursion/factorial_recursion.r", "max_issues_repo_name": "hpissei/hacktoberfest", "max_issues_repo_head_hexsha": "1851a8845a71df3ac919ca650c07ce778ec5da47", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 2, "max_issues_repo_issues_event_min_datetime": "2020-01-19T14:40:27.000Z", "max_issues_repo_issues_event_max_datetime": "2020-01-19T14:42:51.000Z", "max_forks_repo_path": "factorial_recursion/factorial_recursion.r", "max_forks_repo_name": "hpissei/hacktoberfest", "max_forks_repo_head_hexsha": "1851a8845a71df3ac919ca650c07ce778ec5da47", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.1666666667, "max_line_length": 52, "alphanum_fraction": 0.6433121019, "num_tokens": 41, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9381240142763573, "lm_q2_score": 0.8152324938410784, "lm_q1q2_score": 0.7647891796907182}} {"text": "# ************************************************\n### simon munzert\n### maximum likelihood estimation\n# ************************************************\n\nsource(\"packages.r\")\nsource(\"functions.r\")\n\n\n### Writing functions in R -----------------------\n\n# R is a functional programming lanugage, i.e. it provides many tools for the creation and manipulation of functions\n# you can do virtually anything with functions: assign them to variables, store them in lists, pass them as arguments to other functions, ...\n# very helpful in obeying the \"don't repeat yourself\" a.k.a. DRY principle\n\nf <- function(x) x^2\nf\nf(3)\n\n# function that returns the mean of a vector\nmy_mean <- function(my_vector) {\n mean <- sum(my_vector)/length(my_vector) \n mean\n}\nmy_mean(c(1, 2, 3))\nmy_mean\n\n# another function that finds the remainder after division (\"modulo operation\")\nremainder <- function(num = 10, divisor = 4) {\n remain <- num %% divisor\n remain\n}\nremainder()\nargs(remainder)\n\n## let's study the \"functions.r\" file now!\n\n\n### Exercise: Functions --------------------------\n# 1. program a function ultimateAnswer() that always returns the number 42!\n# 2. program a function normalize() that produces normalizes a numeric vector x to mean(x) = 0 and sd(x) = 1!\n\n\n\n### Probability distributions in R -----------\n\n# for an overview of implemented distributions, see\n?Distributions\n\n## the Normal distribution\n\n# rnorm() performs random draws from the distribution\ny <- rnorm(1000, mean = 0, sd = 1) \nplot(y)\nplot(density(y))\n\n# dnorm() gives the density of the distribution\ndnorm(0, mean = 0, sd = 1) \nz_scores <- seq(-3, 3, by = .1)\n\ndvalues <- dnorm(z_scores)\nplot(z_scores, dvalues, type = \"l\", main = \"pdf of the Standard Normal\", xlab = \"Z score\") \n\n# pnorm() gives the distribution function\npnorm(0)\npnorm(-1)\npnorm(1.96)\npnorm(1.96, lower.tail = FALSE)\n\npvalues <- pnorm(z_scores)\nplot(z_scores, pvalues, type = \"l\", main = \"cdf of the Standard Normal\", xlab= \"Z score\", ylab=\"Probability Density\") \n\n## the Binomial distribution\np <- 0.5\nn <- 100\nsize <- 5\ntmp <- rbinom(n, size, p)\ntable(tmp)\nplot(table(tmp), xlab = \"Sum of 1 in N\", ylab = \"Occurrence in n = 100\")\ntext(4.5, c(27, 24, 21), c(paste0(\"n = \", n), paste0(\"p = \", p), paste0(\"N = \", size)))\n\n\n\n## Example 1: Coin flips ----------------------\n\n# get 100 random draws from a binomial distribution with p = .4 --> the estimate we're actually interested in\nset.seed(1234)\nflips <- rbinom(n = 100, size = 1, prob = .4)\ntable(flips)\n\n# define likelihood function\nbinom_loglik <- function(x, p) { # x: vector of results/observed 0s and 1s, p: probability of success \n llik <- sum(dbinom(x, size = 1, prob = p, log = TRUE)) # calculate log likelihood with pdf for binomial distribution\n return(-llik) # return the negative log likelihood \n}\n\n# visually identify parameter value for which negative likelihood is minimized (= likelihood is maximized)\nllks <- vector()\nprobs <- seq(0, 1, .01)\nfor (i in seq_along(probs)) {\n llks[i] <- -sum(dbinom(flips, size = 1, prob = probs[i], log = TRUE))\n}\nplot(probs, -llks, type = \"l\")\nabline(v = probs[which.min(llks)], col = \"red\", lty = 2)\n\n# numerically optimize log-likelihood\nresult <- optim(par = .5, fn = binom_loglik, x = flips, method = 'Brent', lower = 0, upper = 1)\nresult\n# par: initial values of parameter to be estimated, we assume a fair coin\n# fn: function to be minimized\n# lower/upper: since probability paramenter can only be within the unit interval\n\n\n\n## Example 2: Linear model ---------------------\n\n# prepare data, run OLS\ndata(\"wage1\")\nwage_ols <- lm(wage ~ educ, data = wage1)\nsummary(wage_ols)\ny <- wage1$wage\nX <- cbind(1, wage1$educ)\n\n# define likelihood function...\n# ... but how? Here are three options:\n # 1. minimizing the sum of squared residuals (not an acutal ML estimate)\n # 2. maximizing the log-likelihood for normally distributed residuals\n # 3. maximizing the log-likelihood for normally distributed DVs\n\n# 1. Squared residuals\nols <- function(y, X, b) { \n res <- y - X %*% b # calculate residuals\n return(sum(res^2, na.rm = TRUE))\n}\n# this function calculates the sum of squared residuals\n# OLS is defined to return coefficients that give the smallest possible\n# sum of squared residuals\n\n# 2. normally distributed residuals\nnormal_loglik <- function(theta, y, X) {\n b <- theta[-length(theta)] # b's\n sigma <- theta[length(theta)] # sigma\n res <- y - X %*% b # residuals\n return(-sum(dnorm(res, mean = 0, sd = sigma, log = TRUE), na.rm = TRUE))\n}\n# implies the following assumption on the distribution of e:\n# y = f(X, b) + e with e ~ N(0, sigma)\n\n# 3. normally distributed y\nnormal2_loglik <- function(theta, y, X) {\n b <- theta[-length(theta)] # b's\n sigma <- theta[length(theta)] # sigma\n yhat <- X %*% b # predicted values for y \n return(-sum(dnorm(y, mean = yhat, sd = sigma, log = TRUE), na.rm = TRUE))\n}\n# an equivalent formulation is\n# y ~ f(theta, sigma) with theta = g(X, b)\n\n\n# OLS solution\nresult_ols <- optim(par = c(1, 1), fn = ols, y = y, X = X, method = \"BFGS\")\nresult_ols\n\n# optimize log-likelihoods\nresult_normal <- optim(par = c(1, 1, 1), fn = normal_loglik, y = y, X = X, method = \"BFGS\")\nresult_normal\n\nresult_normal2 <- optim(par = c(1, 1, 1), fn = normal2_loglik, y = y, X = X, method = \"BFGS\")\nresult_normal2\n\n# compare again with OLS\nsummary(wage_ols)\n\n\n\n## Assessing estimation uncertainty ---------------------\n\nresult <- optim(par = c(1, 1, 1), fn = normal_loglik, y = y, X = X, hessian = TRUE) # set hessian = TRUE to optain Hessian matrix, which contains the second-order partial derivates\n\ninv_hess <- solve(result$hessian) # take the inverse of the Hessian to get the Fisher information matrix\n\nsigma <- sqrt(diag(inv_hess)) # the square root of the diagonals are then the standard errors\n\nestimates_df <- data.frame(params = result$par,\n ci95lo = result$par - 1.96 * sigma,\n ci95hi = result$par + 1.96 * sigma)\nrownames(estimates_df) <- c(\"beta_0\", \"beta_1\", \"sigma2\")\nestimates_df\n\n\n\n\n\n\n", "meta": {"hexsha": "58d0023d436087f002704d649d6d030d135f6bff", "size": 6024, "ext": "r", "lang": "R", "max_stars_repo_path": "code/07-maximum-likelihood-estimation.r", "max_stars_repo_name": "simonmunzert/stats-II-hertie-2017", "max_stars_repo_head_hexsha": "f577db8b0b5f2599e7896907233ef6871d793253", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "code/07-maximum-likelihood-estimation.r", "max_issues_repo_name": "simonmunzert/stats-II-hertie-2017", "max_issues_repo_head_hexsha": "f577db8b0b5f2599e7896907233ef6871d793253", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "code/07-maximum-likelihood-estimation.r", "max_forks_repo_name": "simonmunzert/stats-II-hertie-2017", "max_forks_repo_head_hexsha": "f577db8b0b5f2599e7896907233ef6871d793253", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2017-09-18T08:04:57.000Z", "max_forks_repo_forks_event_max_datetime": "2018-03-22T08:28:12.000Z", "avg_line_length": 30.8923076923, "max_line_length": 180, "alphanum_fraction": 0.6552124834, "num_tokens": 1718, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8856314738181875, "lm_q2_score": 0.863391602943619, "lm_q1q2_score": 0.7646467777972047}} {"text": "# Guía del fichero: https://rpubs.com/probestaunal/tablas\n\n######################\n# ANÁLISIS GRÁFICO #\n######################\n\n# graficar las frecuencias relativas\nnj <- c(145, 2415, 3456, 852, 459, 157, 130)\nnames(nj) <- 0:6\nbarplot(nj)\n\n# graficar las frecuencias relativas\nhj <- prop.table(nj)\nbarplot(hj)\n\n\n##################################################################\n# DISTRIBUCIÓN DE FRECUENCIAS #\n##################################################################\n# Considerar el siguiente conjunto de datos asociados con el #\n# nivel educativo de una muestra de empleados (Bachillerato (B), #\n# Pregrado (P), Maestría (M), y Doctorado (D)). Elaborar la #\n# tabla de frecuencias correspondiente. #\n# #\n# B, D, M, B, B, P, B, M, B, B, B, P, B, M, B, B, M, B, M, B, B, #\n# B, B, B, B, B, P, B, B, B, B, M, B, P, B, B, M, B, B, B, D, B, #\n# M, B, P, B, B, B, P, P #\n##################################################################\n\n# datos\nedu <- c(\"B\", \"D\", \"M\", \"B\", \"B\", \"P\", \"B\", \"M\", \"B\", \"B\", \"B\", \"P\", \"B\", \"M\", \n \"B\", \"B\", \"M\", \"B\", \"M\", \"B\", \"B\", \"B\", \"B\", \"B\", \"B\", \"B\", \"P\", \"B\", \n \"B\", \"B\", \"B\", \"M\", \"B\", \"P\", \"B\", \"B\", \"M\", \"B\", \"B\", \"B\", \"D\", \"B\", \n \"M\", \"B\", \"P\", \"B\", \"B\", \"B\", \"P\", \"P\")\n# tamaño de la muestra\nn <- length(edu)\nprint(n)\n\n# frecuencias absolutas\nnj <- table(edu)\nnj <- nj[c(1, 4, 3, 2)]\nprint(nj)\n\n# frecuencias relativas\nhj <- nj/n\nprint(hj)\n\n# frecuencias absolutas acumuladas\nNj <- cumsum(nj)\nprint(Nj)\n\n# frecuencias relativas acumuladas\nHj <- cumsum(hj)\nprint(Hj)\n\n##################################################################################################\n# VARIABLES CUANTITATIVAS #\n##################################################################################################\n# Considerar el siguiente conjunto de datos asociados con el peso (en kg) de una #\n# muestra de materiales. Elaborar la distribución de frecuencias correspondiente. #\n# #\n# 103.1, 82.1 , 106.2, 100.9, 91.8, 96.1 , 126.9, 119.8, 93.1 , 86.8, 75.2 , 93.0, 82.3 , 94.8, #\n# 64.2 , 105.3, 108.0, 86.3 , 81.8, 138.1, 92.5, 66.3 , 66.6 , 142.2, 96.5 , 74.8, 95.4 , 100.1, #\n# 81.9 , 112.0, 116.8, 103.2, 66.1, 60.4 , 78.7 #\n##################################################################################################\n\n# datos\npeso<- c(103.1, 82.1, 106.2, 100.9, 91.8, 96.1, 126.9, 119.8, 93.1, 86.8, 75.2, 93.0, \n 82.3, 94.8, 64.2, 105.3, 108.0, 86.3, 81.8, 138.1, 92.5, 66.3, 66.6, 142.2, \n 96.5, 74.8, 95.4, 100.1, 81.9, 112.0, 116.8, 103.2, 66.1, 60.4, 78.7)\n# tamaño de la muestra\nn <- length(peso)\nprint(n)\n\n# numero de intervalos\nm <- round(1 + 3.3*log(n, base = 10), 2)\nprint(m)\n\n# rango\nR <- max(peso) - min(peso)\nprint(R)\n\n# amplitud\na <- R/m\nprint(a)\n\n# limites\nlim <- min(peso) + (0:m)*a\nprint(lim)\n# frecuencias absolutas\nnj <- table(cut(x = peso, breaks = lim, include.lowest = T))\nprint(nj)\n\n# frecuencias relativas\nhj <- nj/n\nprint(hj)\n\n# frecuencias absolutas acumuladas\nNj <- cumsum(nj)\nprint(Nj)\n\n# frecuencias relativas acumuladas\nHj <- cumsum(hj)\nprint(Hj)\n", "meta": {"hexsha": "c38d0b239bfc073ac714d72d474e5866023530c8", "size": 3491, "ext": "r", "lang": "R", "max_stars_repo_path": "02.tablas/tablas.r", "max_stars_repo_name": "devHectorGa/UNALProbabilidadEstadistica", "max_stars_repo_head_hexsha": "1cd472cc1b39daa8a9b81d40ec128d3d168af0a5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "02.tablas/tablas.r", "max_issues_repo_name": "devHectorGa/UNALProbabilidadEstadistica", "max_issues_repo_head_hexsha": "1cd472cc1b39daa8a9b81d40ec128d3d168af0a5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "02.tablas/tablas.r", "max_forks_repo_name": "devHectorGa/UNALProbabilidadEstadistica", "max_forks_repo_head_hexsha": "1cd472cc1b39daa8a9b81d40ec128d3d168af0a5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 33.2476190476, "max_line_length": 98, "alphanum_fraction": 0.4122028072, "num_tokens": 1213, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8933093975331751, "lm_q2_score": 0.8558511396138365, "lm_q1q2_score": 0.7645398659065176}} {"text": "f1 <- function(x) dnorm(x)\nf2 <- function(x) dcauchy(x)\nf3 <- function(x) dt(x, df = 1)\nf4 <- function(x) dt(x, df = 5)\nf5 <- function(x) dt(x, df = 30)\n\npar(mfrow = c(1, 2))\ncurve(f1, -5, 5, xlab = expression(x), ylab = \"Densidade\", lwd = 2)\ncurve(f2, lwd = 2, col = \"grey50\", add = TRUE)\ncurve(f3, lwd = 2, col = \"red\", lty = 2, add = TRUE)\ncurve(f4, lwd = 2, col = \"blue\", lty = 3, add = TRUE)\ncurve(f5, lwd = 2, col = \"red\", lty = 4, add = TRUE)\n\ncurve(f1, 2, 5, xlab = expression(x), ylab = \"Densidade\", lwd = 2)\ncurve(f2, lwd = 3, col = \"grey50\", add = TRUE)\ncurve(f3, lwd = 3, col = \"red\", lty = 2, add = TRUE)\ncurve(f4, lwd = 3, col = \"blue\", lty = 3, add = TRUE)\ncurve(f5, lwd = 3, col = \"red\", lty = 4, add = TRUE)\n\nlegend(x = \"topright\",\n legend = c(\n \"N(0,1)\",\n \"Cauchy\",\n \"T(1)\",\n \"T(5)\",\n \"T(30)\"\n ),\n col = c(\"black\", \"grey50\", \"red\", \"blue\", \"red\", \"blue\"),\n lty = c(1, 1, 2, 3, 4, 5),\n lwd = 2,\n bty = 'n')", "meta": {"hexsha": "bddf50bd228ea11331e182dc628f4a5fe36f0118", "size": 999, "ext": "r", "lang": "R", "max_stars_repo_path": "code/plots_t_Student.r", "max_stars_repo_name": "jlduim/Statistical_Inference_BSc", "max_stars_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 33, "max_stars_repo_stars_event_min_datetime": "2020-08-03T15:42:28.000Z", "max_stars_repo_stars_event_max_datetime": "2021-11-30T15:43:10.000Z", "max_issues_repo_path": "code/plots_t_Student.r", "max_issues_repo_name": "jlduim/Statistical_Inference_BSc", "max_issues_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 23, "max_issues_repo_issues_event_min_datetime": "2020-08-16T23:02:47.000Z", "max_issues_repo_issues_event_max_datetime": "2021-11-07T14:34:43.000Z", "max_forks_repo_path": "code/plots_t_Student.r", "max_forks_repo_name": "jlduim/Statistical_Inference_BSc", "max_forks_repo_head_hexsha": "6dfa2441c0b09bfe39a68367a242a81d76c41778", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 10, "max_forks_repo_forks_event_min_datetime": "2020-08-13T00:53:42.000Z", "max_forks_repo_forks_event_max_datetime": "2021-12-10T07:35:56.000Z", "avg_line_length": 32.2258064516, "max_line_length": 67, "alphanum_fraction": 0.4904904905, "num_tokens": 432, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9489172659321807, "lm_q2_score": 0.8056321889812553, "lm_q1q2_score": 0.7644782941150507}} {"text": "# ......................................................................................\n# ...............................Cvičení 1 - Kombinatorika..............................\n# ..................Adéla Vrtková, Michal Béreš, Martina Litschmannová..................\n# ......................................................................................\n\n# Nezobrazuje-li se vám text korektně, nastavte File \\ Reopen with Encoding... na UTF-8\n# Pro zobrazení obsahu skriptu použijte CTRL+SHIFT+O\n# Pro spouštění příkazů v jednotlivých řádcích použijte CTRL+ENTER\n\n# * Variace ####\n# \n# V(n,k) - variace bez opakování, první argument bude celkový počet entit, druhý\n# argument velikost výběru\n\n\n# funkce se vytváří příkazem fucntion, je to objekt jehož jméno je dáno až proměnnou \n# do které tento objekt přiřadím\nvariace = function(n,k) # zde zadávám počet parametrů a jejich jména\n{ # celé tělo funkce je uzavřeno mezi závorkami {...}\n citatel = factorial(n) # faktoriál v originálním Rku existuje tak jej použijeme\n jmenovatel = factorial(n-k)\n return(citatel/jmenovatel) # to co funkce vrátí se dává do příkazu return(...)\n}\n\n# V*(n,k) - variace s opakováním\n\n\nvariace_opak = function(n,k)\n{\n return(n^k)\n}\n\n# * Permutace ####\n# \n# P(n)=V(n,n) - permutace\n\n\npermutace = function(n)\n{\n return(variace(n,n))\n}\n\n# P*(n1,n2,n3,....,nk) - permutace s opakováním, vstup bude vektor s jednotlivými počty\n# unikátních entit\n\n\npermutace_opak = function(vec_n) # vec_n je vektro počtů hodnot př.: vec_n = c(2,2,2,4,3)\n{\n n = sum(vec_n) # spočteme kolik máme hodnot celkem\n res_temp=factorial(n) #jejich faktoriál = hodnota v čitateli\n # jednoduchý cyklus začíná příkazem for, pak v závorkách následuje název iterátoru a z \n # jakého seznamu bude brán\n for(pocet in vec_n) # pocet je iterátor a postupně bude nabývat hodnot z vektoru vec_n\n {\n # postupně dělíme faktoriálem každého počtu unikátních entit\n res_temp=res_temp/factorial(pocet) \n }\n return(res_temp)\n}\n\n# * Kombinace ####\n# \n# C(n,k) - kombinace\n\n\nkombinace = function(n,k)\n{\n return(choose(n,k)) # funkce for kombinace už existuje v Rku a jmenuje se choose\n}\n\n# C*(n,k) - kombinace s opakováním\n\n\nkombinace_opak = function(n,k)\n{\n return(choose(n+k-1,k)) # použijeme známý vzorec\n}\n\n# Úlohy na cvičení ####\n# \n# * Příklad 1. ####\n# \n# V prodejně mají k dispozici tři typy zámků. Pro otevření prvního\n# zámku je nutno zmáčknout čtyři z deseti tlačítek označených číslicemi 0 až 9. (Na\n# pořadí nezáleží - tlačítka zůstávají zmáčknuta.)\n# Druhý zámek se otevře pokud zmáčkneme šest tlačítek z deseti.\n# Pro otevření třetího zámku je nutno nastavit správnou kombinaci\n# na čtyřech kotoučích. Který z těchto zámků nejlépé chrání před\n# zloději?\n\n\nz1=kombinace(10,4)\nz2=kombinace(10,6)\nz3=variace_opak(10,4)\npaste(\"pocet kombinaci: \",z1,\",\",z2,\",\",z3)\npaste(\"pradvedepodobnost nahodnehootevreni: \",1/z1,\",\",1/z2,\",\",1/z3)\n\n# * Příklad 2. ####\n# \n# V prodejně nabízejí dva druhy zamykání kufříku. První kufřík se zamyká šifrou, která\n# se skládá\n# z šesti číslic. Druhý kufřík se zamyká dvěma zámky, které se otevírají současně. Šifra\n# každého\n# z nich se skládá ze tří číslic. Určete pro každý kufřík pravděpodobnost otevření\n# zlodějem při\n# prvním pokusu. Který typ zámku je bezpečnější?\n\n\nz1=variace_opak(10,6);\nz2=variace_opak(10,3)*variace_opak(10,3);\nz2_v2=variace_opak(10,3)+variace_opak(10,3);\npaste(\"pocet kombinaci: \",z1,\",\",z2,\",druha varianta - \",z2_v2)\n\n# * Příklad 3. ####\n# \n# V urně je 40 koulí - 2 červené a 38 bílých. Z urny náhodně vytáhneme 2 koule. S jakou\n# pravděpodobností budou obě červené?\n\n\npoc_moz=kombinace(40,2);\npoc_priz=kombinace(2,2);\nprob=poc_priz/poc_moz;\npaste(\"pravdepodobnost je: \",prob)\n\n# * Příklad 4. ####\n# \n# Student si měl ke zkoušce připravit odpovědi na 40 otázek. Na dvě otázky, které mu dal\n# zkoušející, neuměl odpovědět a tak řekl „To mám smůlu! To jsou jediné dvě otázky, na\n# které neumím odpovědět.“ S jakou pravděpodobností mluví pravdu?\n\n\n\n\n# * Příklad 5. ####\n# \n# Test z chemie žák složí, pokud v seznamu 40 chemických sloučenin podtrhne jediné dva\n# aldehydy, které v seznamu jsou. Jaká je pravděpodobnost, že test složí žák, který\n# provede výběr\n# sloučenin náhodně?\n\n\n\n\n# * Příklad 6. ####\n# \n# Ze zahraničí se vracela skupina 40 turistů a mezi nimi byli 2 pašeráci. Na hranici\n# celník 2 turisty\n# vyzval k osobní prohlídce a ukázalo se, že oba dva jsou pašeráci. Zbylí turisté na to\n# reagovali:\n# „Celník měl opravdu štěstí!“, „Pašeráky někdo udal!“, . . .. Jak se postavit k těmto\n# výrokům?\n# Je oprávněné podezření, že pašeráky někdo udal?\n\n\n\n\n# * Příklad 7. ####\n# \n# Z urny se třemi koulemi, dvěma červenými a jednou bílou, budou současně vybrány dvě\n# koule.\n# Student a učitel uzavřou sázku. Pokud budou obě koule stejné barvy, vyhraje student.\n# Pokud\n# budou mít koule různou barvu, vyhraje učitel. Je hra férová? Jaké jsou\n# pravděpodobnosti výhry\n# učitele a studenta?\n\n\n# funkce combn vyrobí kombinace o předepsané velikosti - první parametr je vektor hodnot, druhý velikost výběru\ncombn(c('cerna','cerna','cervena'),2)\n\n# * Příklad 8. ####\n# \n# \n# Hra popsaná v příkladu 7 nebyla férová. Jakou kouli (červenou nebo bílou) musíme do\n# urny přidat, aby hra férová byla?\n\n\ncombn(c('cerna','cerna','cerna','cervena'),2)\ncombn(c('cerna','cerna','cervena','cervena'),2)\n\n# * Příklad 9. ####\n# \n# Chcete hrát Člověče nezlob se, ale ztratila se hrací kostka. Čím a jak lze nahradit\n# hrací kostku,\n# máte-li k dispozici hrací karty (balíček 32 karet) a 4 různobarevné kuličky?\n\n\n\n\n# * Příklad 10. ####\n# \n# Chcete hrát Člověče nezlob se, ale ztratila se hrací kostka. Jak lze nahradit hrací\n# kostku, máte-li\n# k dispozici 3 různobarevné kuličky?\n\n\n\n\n# * Příklad 11. ####\n# \n# V prodejně vozů Škoda mají v měsíci únoru prodejní akci. Ke standardnímu vybavení\n# nabízejí\n# 3 položky z nadstandardní výbavy zdarma. Nadstandardní výbava zahrnuje 7 položek:\n# - tempomat, vyhřívání sedadel, zadní airbagy, xenonová světla, stropní okénko,\n# bezpečnostní\n# zámek převodovky, speciální odolný metalízový lak.\n# \n# Kolik možností má zákazník, jak zvolit 3 položky z nadstandardní výbavy?\n\n\nkombinace(7,3)\n\n# * Příklad 12. ####\n# \n# Při zkoušce si do 5. řady sedlo 12 studentů. Zkoušející chce určit sám, jak tyto\n# studenty v řadě\n# rozesadit.\n# - Kolik je možností jak studenty rozesadit?\n# - Student Brahý žádá, aby mohl sedět na kraji a odejít dříve, aby stihl vlak. Kolik je\n# možností jak studenty rozesadit, chce-li zkoušející vyhovět požadavku studenta\n# Brahého?\n# - Kolik je možností jak studenty rozesadit, nesmějí-li Pažout a Horáček sedět vedle\n# sebe?\n\n\n#a\npermutace(12)\nprazdnych_sedadel=8\npermutace_opak(c(1,1,1,1,1,1,1,1,1,1,1,1,prazdnych_sedadel))\n#b\n1*permutace(11)+permutace(11)*1\n#c\nvedle_sebe=permutace(11)+permutace(11)\npermutace(12)-vedle_sebe\n\n# * Příklad 13. ####\n# \n# Kolik anagramů lze vytvořit ze slova STATISTIKA?\n\n\nstatistika=c(2,3,2,2,1)\npermutace_opak(statistika)\n\n# * Příklad 14. ####\n# \n# V Tescu dostali nové zboží – 6 druhů chlapeckých trik. Od každého druhu mají alespoň 7\n# kusů.\n# Maminka chce synovi koupit 4 trika. Kolik je možností, jak je vybrat\n# - mají-li být všechna různá?\n# - připouští-li, že mohou být všechna stejná?\n\n\n#a\nkombinace(6,4)\n#b\nkombinace_opak(6,4)\n\n# * Příklad 15. ####\n# Kolik hesel délky 5 můžeme vytvořit ze znaků abecedy\n# - nejsou-li rozlišována velká a malá písmena?\n# - jsou-li rozlišována velká a malá písmena?\n\n\n#a\nvariace_opak(26,5)\n#b\nvariace_opak(52,5)\n\n\n\n", "meta": {"hexsha": "f42918038d959ebcf53ce84aebf5996f94e0adba", "size": 7505, "ext": "r", "lang": "R", "max_stars_repo_path": "CV1/cv_ulohy_ze_sbirky/cv1.r", "max_stars_repo_name": "Atheloses/VSB-S8-PS", "max_stars_repo_head_hexsha": "fdef214f8169094b6366ce0489f92ef20b460702", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "CV1/cv_ulohy_ze_sbirky/cv1.r", "max_issues_repo_name": "Atheloses/VSB-S8-PS", "max_issues_repo_head_hexsha": "fdef214f8169094b6366ce0489f92ef20b460702", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "CV1/cv_ulohy_ze_sbirky/cv1.r", "max_forks_repo_name": "Atheloses/VSB-S8-PS", "max_forks_repo_head_hexsha": "fdef214f8169094b6366ce0489f92ef20b460702", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 27.6937269373, "max_line_length": 111, "alphanum_fraction": 0.6942038641, "num_tokens": 3341, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9546474162199107, "lm_q2_score": 0.8006920020959544, "lm_q1q2_score": 0.7643785509888501}} {"text": "#The built-in standard deviation function applies the Bessel correction. To reverse this, we can apply an uncorrection.\n#If na.rm is true, missing data points (NA values) are removed.\n reverseBesselCorrection <- function(x, na.rm=FALSE)\n {\n if(na.rm) x <- x[!is.na(x)]\n len <- length(x)\n if(len < 2) stop(\"2 or more data points required\")\n sqrt((len-1)/len)\n }\n testdata <- c(2,4,4,4,5,5,7,9)\n reverseBesselCorrection(testdata)*sd(testdata) #2\n", "meta": {"hexsha": "050ff0c212dbb16f4edd263ce8a194aa927e609b", "size": 453, "ext": "r", "lang": "R", "max_stars_repo_path": "Task/Standard-deviation/R/standard-deviation-1.r", "max_stars_repo_name": "djgoku/RosettaCodeData", "max_stars_repo_head_hexsha": "91df62d46142e921b3eacdb52b0316c39ee236bc", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Task/Standard-deviation/R/standard-deviation-1.r", "max_issues_repo_name": "djgoku/RosettaCodeData", "max_issues_repo_head_hexsha": "91df62d46142e921b3eacdb52b0316c39ee236bc", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Standard-deviation/R/standard-deviation-1.r", "max_forks_repo_name": "djgoku/RosettaCodeData", "max_forks_repo_head_hexsha": "91df62d46142e921b3eacdb52b0316c39ee236bc", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 37.75, "max_line_length": 120, "alphanum_fraction": 0.6931567329, "num_tokens": 140, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9196425311777929, "lm_q2_score": 0.8311430415844384, "lm_q1q2_score": 0.7643544905335226}} {"text": "sample_size=c(6,6,6,6,6)\r\n \r\n# l=y1bar-(y2bar+y3bar+y4bar+y5bar)/4 \r\n \r\n# thus we identify a1 = 4, a2 = -1, a3 =-1, a4 = -1 , a5=-1 \r\na=c(4,-1,-1,-1,-1)\r\n \r\ntest=0\r\ni=1\r\nwhile(i<=length(sample_size)){\r\n test=test+a[i]^2\r\n i=i+1\r\n}\r\nprint(test)\r\ny1bar=1.175\r\ny2bar=1.293\r\ny3bar=1.328\r\ny4bar=1.415\r\ny5bar=1.500\r\nl=4*y1bar-y2bar-y3bar-y4bar-y5bar\r\nprint(l)\r\n# we can obtain the sum of squares associated with the contrast from\r\nSSC1=(sample_size[1]*(l^2))/test\r\nprint(SSC1)\r\n\r\na=c(0,1,1,-1,-1)\r\ntest=0\r\ni=1\r\nwhile(i<=length(sample_size)){\r\n test=test+a[i]^2\r\n i=i+1\r\n} \r\nl=0*y1bar+y2bar+y3bar-y4bar-y5bar\r\n# we can obtain the sum of squares associated with the contrast from\r\nSSC2=(sample_size[2]*(l^2))/test\r\nprint(SSC2)\r\n\r\na=c(0,1,-1,0,0)\r\ntest=0\r\ni=1\r\nwhile(i<=length(sample_size)){\r\n test=test+a[i]^2\r\n i=i+1\r\n} \r\nl=0*y1bar+y2bar-y3bar+0*y4bar+0*y5bar\r\n# we can obtain the sum of squares associated with the contrast from\r\nSSC3=(sample_size[2]*(l^2))/test\r\nprint(SSC3)\r\n\r\na=c(0,0,0,1,-1)\r\ntest=0\r\ni=1\r\nwhile(i<=length(sample_size)){\r\n test=test+a[i]^2\r\n i=i+1\r\n} \r\nl=0*y1bar+0*y2bar+0*y3bar+y4bar-y5bar\r\n# we can obtain the sum of squares associated with the contrast from\r\nSSC4=(sample_size[2]*(l^2))/test\r\nprint(SSC4)\r\n\r\n", "meta": {"hexsha": "1466a0f019c4573cd31ab2068c2c1efb4a1b3ccb", "size": 1233, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH9/EX9.3/Ex9_3.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH9/EX9.3/Ex9_3.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH9/EX9.3/Ex9_3.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 19.8870967742, "max_line_length": 69, "alphanum_fraction": 0.6431467964, "num_tokens": 511, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9219218370002789, "lm_q2_score": 0.828938806208442, "lm_q1q2_score": 0.764216786980505}} {"text": "x = c(-3, -1, 1, 3, 5, 7)\ny = c(14, 4, 2, 8, 22, 44)\n\nn = length(x)\n\nnum = sum(x * y) - sum(x) * sum(y) / n\nden = sum(x * x) - sum(x) * sum(x) / n\n\nB1 = num / den\nB0 = (sum(y) - (B1 * sum(x))) / n\n\npng('images/disp_diagram.png')\nplot(x, y)\ndev.off()\n\nB0\nB1\n\nprint('For x = 0 predicted value is')\nprint(B1 * 0 + B0)\n\nprint('For x = 2 predicted value is')\nprint(B1 * 2 + B0)\n", "meta": {"hexsha": "7b7a1892eea7f074f9934ae836a6d1f49b1d1268", "size": 373, "ext": "r", "lang": "R", "max_stars_repo_path": "Tasks/CP6-Ex2/CP6-Ex2.r", "max_stars_repo_name": "2kodevs/Statistics-Tasks", "max_stars_repo_head_hexsha": "264dc6287c9a2d1b7118fd48c40f54e26fc18b42", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Tasks/CP6-Ex2/CP6-Ex2.r", "max_issues_repo_name": "2kodevs/Statistics-Tasks", "max_issues_repo_head_hexsha": "264dc6287c9a2d1b7118fd48c40f54e26fc18b42", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 4, "max_issues_repo_issues_event_min_datetime": "2020-04-09T14:27:47.000Z", "max_issues_repo_issues_event_max_datetime": "2020-04-16T18:31:14.000Z", "max_forks_repo_path": "Tasks/CP6-Ex2/CP6-Ex2.r", "max_forks_repo_name": "2kodevs/Statistics-Tasks", "max_forks_repo_head_hexsha": "264dc6287c9a2d1b7118fd48c40f54e26fc18b42", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 15.5416666667, "max_line_length": 38, "alphanum_fraction": 0.5201072386, "num_tokens": 173, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.960361158630024, "lm_q2_score": 0.7956580927949807, "lm_q1q2_score": 0.7641191278699428}} {"text": "softmax <- function (x) {\n m <- max(x)\n exps <- exp(x - m)\n s <- sum(exps)\n return(exps / s)\n}\n", "meta": {"hexsha": "5845847b01755aaa5568353a0340dcf97911967a", "size": 107, "ext": "r", "lang": "R", "max_stars_repo_path": "m2cgen/interpreters/r/softmax.r", "max_stars_repo_name": "Symmetry-International/m2cgen", "max_stars_repo_head_hexsha": "3157e0cbd5bd1ee7e044a992223c60224e2b7709", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2161, "max_stars_repo_stars_event_min_datetime": "2019-01-13T02:37:56.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-30T13:24:09.000Z", "max_issues_repo_path": "m2cgen/interpreters/r/softmax.r", "max_issues_repo_name": "Symmetry-International/m2cgen", "max_issues_repo_head_hexsha": "3157e0cbd5bd1ee7e044a992223c60224e2b7709", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 380, "max_issues_repo_issues_event_min_datetime": "2019-01-17T15:59:29.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T20:59:20.000Z", "max_forks_repo_path": "m2cgen/interpreters/r/softmax.r", "max_forks_repo_name": "Symmetry-International/m2cgen", "max_forks_repo_head_hexsha": "3157e0cbd5bd1ee7e044a992223c60224e2b7709", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 201, "max_forks_repo_forks_event_min_datetime": "2019-02-13T19:06:44.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-12T09:45:46.000Z", "avg_line_length": 15.2857142857, "max_line_length": 25, "alphanum_fraction": 0.4579439252, "num_tokens": 37, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9399133531922387, "lm_q2_score": 0.8128673087708699, "lm_q1q2_score": 0.7640248378871791}} {"text": "library(Biodem)\nm <- matrix(c(3,2,2,1), nrow=2)\nmtx.exp(m, 0)\n# [,1] [,2]\n# [1,] 1 0\n# [2,] 0 1\nmtx.exp(m, 1)\n# [,1] [,2]\n# [1,] 3 2\n# [2,] 2 1\nmtx.exp(m, 2)\n# [,1] [,2]\n# [1,] 13 8\n# [2,] 8 5\nmtx.exp(m, 3)\n# [,1] [,2]\n# [1,] 55 34\n# [2,] 34 21\nmtx.exp(m, 10)\n# [,1] [,2]\n# [1,] 1346269 832040\n# [2,] 832040 514229\n", "meta": {"hexsha": "8ba930b22e9004939786c54ad76e7e8f50bd563a", "size": 389, "ext": "r", "lang": "R", "max_stars_repo_path": "Task/Matrix-exponentiation-operator/R/matrix-exponentiation-operator.r", "max_stars_repo_name": "LaudateCorpus1/RosettaCodeData", "max_stars_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Matrix-exponentiation-operator/R/matrix-exponentiation-operator.r", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Matrix-exponentiation-operator/R/matrix-exponentiation-operator.r", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 16.9130434783, "max_line_length": 31, "alphanum_fraction": 0.35218509, "num_tokens": 221, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9511422241476943, "lm_q2_score": 0.8031737963569016, "lm_q1q2_score": 0.7639325110440507}} {"text": "#' The Epanechnikov kernel\n#' @param R vector of distances to convert to weights\n#' @param bw bandwidth of the kernel\n#' @return vector of kernel weights, given by \\eqn{1 - (R / bw)^2} if \\eqn{R < bw}; otherwise 0\n#' @export\nepanechnikov = function(R, bw) {\n ifelse( R < bw, 1-(R/bw)**2, 0)\n}\n\n#' The cubic kernel\n#' @param d vector of distances to convert to weights\n#' @param bw bandwidth of the kernel\n#' @return vector of kernel weights, given by \\eqn{1 - (7 * (d / bw)^2 - 8.75 * (d / bw)^3 + 3.5 * (d / bw)^5 - 0.75 * (d / bw)^7} if \\eqn{d < bw}; otherwise 0\n#' @export\ncubic = function(d, bw) {\n ifelse(d\n # 2, 0, 0, 0\n # 0, 1, 1, 0\n # 0, 0, 1, 1\n # 0, 0, 0, 1\n puts\n \n #------------------------------------------------------------\n m = M4[\n [3, 1, -1, 1],\n [-3, -1, 3, -1],\n [-2, -2, 0, 0],\n [0, 0, -4, 2]\n ]\n jf, pt, qt, field, modulus = m.jordan_form_info\n print \"extention = \"; p modulus #=> [a^2 + 4]\n jf.display; puts #=>\n # 2, 1, 0, 0\n # 0, 2, 0, 0\n # 0, 0, a, 0\n # 0, 0, 0, -a\n \n m = m.convert_to(jf.type)\n p jf == pt * m * qt #=> true\n \n #------------------------------------------------------------\n m = M4[\n [-1, 1, 2, -1],\n [-5, 3, 4, -2],\n [3, -1, 0, 1],\n [5, -2, -2, 0]\n ]\n jf, pt, qt, field, modulus = m.jordan_form_info\n print \"extention = \"; p modulus #=> [a^3 + 3a - 1, b^2 + ab + a^2 + 3]\n jf.display; puts #=>\n # 2, 0, 0, 0\n # 0, a, 0, 0\n # 0, 0, b, 0\n # 0, 0, 0, -b - a\n \n m = m.convert_to(jf.type)\n p jf == pt * m * qt #=> true\n ----------$ sample-jordanform01.rb\n=end\n", "meta": {"hexsha": "7441df448c4549dc74f8c3b47586d96cd036a64c", "size": 1264, "ext": "rd", "lang": "R", "max_stars_repo_path": "doc-ja/sample-jordanform01.rb.v.rd", "max_stars_repo_name": "kunishi/algebra-ruby2", "max_stars_repo_head_hexsha": "ab8e3dce503bf59477b18bfc93d7cdf103507037", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 6, "max_stars_repo_stars_event_min_datetime": "2015-04-25T17:00:02.000Z", "max_stars_repo_stars_event_max_datetime": "2021-07-08T02:59:44.000Z", "max_issues_repo_path": "work/consider/algebra-0.72/doc-ja/sample-jordanform01.rb.v.rd", "max_issues_repo_name": "rubyworks/stick", "max_issues_repo_head_hexsha": "7e89d1a1ade1db085ddfecf19f774f0ba9bc2b70", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2017-03-10T14:02:43.000Z", "max_issues_repo_issues_event_max_datetime": "2017-03-10T14:02:43.000Z", "max_forks_repo_path": "doc-ja/sample-jordanform01.rb.v.rd", "max_forks_repo_name": "kunishi/algebra-ruby2", "max_forks_repo_head_hexsha": "ab8e3dce503bf59477b18bfc93d7cdf103507037", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.5714285714, "max_line_length": 72, "alphanum_fraction": 0.3393987342, "num_tokens": 614, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9314625050654263, "lm_q2_score": 0.8198933315126792, "lm_q1q2_score": 0.7636998964572381}} {"text": "# Example : 2.5A Chapter : 2.5 Pageno : 87\n# Inverse of difference matrix is Sum matrix\nA<-matrix(c(1,-1,0,0,1,-1,0,0,1),ncol=3)\nA1<-solve(A)\nprint(\"Inverse of the difference matrix is singular \")\nprint(A1)\n", "meta": {"hexsha": "73cd57291df90ff16226ef527606517bf25af3d1", "size": 211, "ext": "r", "lang": "R", "max_stars_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH2/EX2.5.a/Ex2_2.5A.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH2/EX2.5.a/Ex2_2.5A.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH2/EX2.5.a/Ex2_2.5A.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 30.1428571429, "max_line_length": 54, "alphanum_fraction": 0.6777251185, "num_tokens": 81, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9314625069680098, "lm_q2_score": 0.8198933271118221, "lm_q1q2_score": 0.7636998939179203}} {"text": "euclidean <- function(a, b) {\n return (sqrt(sum((a - b) ^ 2)))\n}\n\nkNN <- function(dataset, points, k, dist = euclidean) {\n answer <- array(dim=c(length(points[,1])))\n \n for (i in 1:length(points[,1])) {\n distance <- array(dim=dim(dataset)[1])\n for (j in 1:dim(dataset)[1]) {\n distance[j] <- dist(dataset[j, 3:4], points[i,])\n }\n sortedDataset <- dataset[order(distance),]\n \n classesCount <- c(0, 0, 0)\n names(classesCount) = unique(iris$Species)\n for (j in 1:k) {\n classesCount[sortedDataset$Species[j]] <- classesCount[sortedDataset$Species[j]] + 1\n }\n answer[i] = names(which.max(classesCount))[1]\n }\n \n return (answer)\n}\n\nfast_cvloo_knn <- function() {\n maxK <- length(iris[,1]) - 1\n classes = unique(iris$Species)\n \n ans <- rep(x = 0, times = maxK)\n for (i in 1:length(iris[,1])) {\n # for (i in 1:10) {\n cat(\"\\r\", \"Processing sample \", i, \" of \", length(iris[,1]))\n dataset <- iris[-i,]\n # print(dataset)\n distance <- array(dim=c(length(dataset[,1])))\n for (j in 1:(length(dataset[,1]))) {\n distance[j] <- euclidean(dataset[j, 3:4], iris[i, 3:4])\n }\n sortedDataset <- dataset[order(distance),]\n \n classesCount <- rep(x = 0, times = length(classes))\n names(classesCount) = classes\n for (j in 1:maxK) {\n classesCount[sortedDataset$Species[j]] <- classesCount[sortedDataset$Species[j]] + 1\n \n classForCurrentK = names(which.max(classesCount))[1]\n if (classForCurrentK == iris$Species[i]) {\n ans[j] = ans[j] + 1\n }\n }\n \n }\n cat(\"\\n\")\n for (i in 1:length(ans)) {\n \n ans[i] = ans[i] / length(iris[,1] - 1)\n }\n \n return (ans)\n}\n\npar(mfrow=c(1,2), pty=\"s\")\n# LOO CV, looking for the best k\nstats <- fast_cvloo_knn()\nplot(1:(length(iris[,1]) - 1), stats, type=\"l\", xlab=\"k\", ylab=\"Accuracy\")\n\nmaxPoint = which(stats == max(stats))\npoints((1:(length(iris[,1]) - 1))[maxPoint], stats[maxPoint], pch = 19, col = \"red\")\n\nbestK <- which.max(stats)\ncat(\"Best K =\", bestK, \"\\n\")\n\n# k-NN demo\nz <- array(dim=c(10, 2))\nfor (i in 1:length(z[,1])) {\n z[i,] = c(runif(1, min = 1, max = 7), runif(1, min = 0, max = 2.5))\n}\n\nprint(z)\n\nresult <- kNN(iris, z, 5)\n\ncolors <- c(\"setosa\" = \"blue\", \"virginica\" = \"red\", \"versicolor\" = \"green\")\nplot(iris[, 3:4], bg = colors[paste(iris$Species)], pch=23, asp=1)\npoints(z[,1], z[,2], bg = colors[result], pch = 22)", "meta": {"hexsha": "607c461f8c0b5c858dcc44f7860f20c782af9119", "size": 2381, "ext": "r", "lang": "R", "max_stars_repo_path": "1 - Nearest neighbors algorithm/knn.r", "max_stars_repo_name": "shadowusr/ml-course", "max_stars_repo_head_hexsha": "5e336dc47ed9dff71877e830a4d67afd8a23a8a1", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "1 - Nearest neighbors algorithm/knn.r", "max_issues_repo_name": "shadowusr/ml-course", "max_issues_repo_head_hexsha": "5e336dc47ed9dff71877e830a4d67afd8a23a8a1", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "1 - Nearest neighbors algorithm/knn.r", "max_forks_repo_name": "shadowusr/ml-course", "max_forks_repo_head_hexsha": "5e336dc47ed9dff71877e830a4d67afd8a23a8a1", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 27.6860465116, "max_line_length": 90, "alphanum_fraction": 0.5728685426, "num_tokens": 806, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9449947163538935, "lm_q2_score": 0.8080672181749422, "lm_q1q2_score": 0.7636192516341093}} {"text": "## Dale W.R. Rosenthal, 2018\n## You are free to distribute and use this code so long as you attribute\n## it to me or cite the text.\n## The legal disclaimer in _A Quantitative Primer on Investments with R_\n## applies to this code. Use or distribution without these comment lines\n## is forbidden.\n\nrf <- 0.02 # 2% interest rates\nnum.sims <- 100000 # 100,000 simulations\ns0 <- 90 # underlier price at t=0\ns.bar <- 95\nK <- 102 # strike price\nsigma <- 0.25 # volatility of underlier log-returns\nT <- 2 # 2 years = option expiry\ntau <- 1 # mid-life of one-year bond\nlambda <- 2 # mean reversion rate; 2 => half-life = ln(2)/2 = 0.35 years\n\n## arithmetic Brownian motion; normal underlier price\nw1 <- rnorm(num.sims) # simulated W_T values\nsigma.abm <- sigma*s0 # rescale volatility for initial prife level\ns.sim.abm <- s0 + rf*T + sigma.abm*sqrt(T)*w1\nopt.payoff.abm <- pmax(s.sim.abm - K, 0)\nopt.value.abm <- mean(opt.payoff.abm)*exp(-rf*T)\n\n## geometric Brownian motion; normal underlier log-returns\nw2 <- rnorm(num.sims) # simulated W_T values\ns.sim.gbm <- s0*exp((rf-sigma^2/2)*T + sigma*sqrt(T)*w2)\nopt.payoff.gbm <- pmax(s.sim.gbm - K, 0)\nopt.value.gbm <- mean(opt.payoff.gbm)*exp(-rf*T)\n\n## Ornstein-Uhlenbeck process for underlier price\nw3 <- rnorm(num.sims) # simulated W_T values\ns.sim.ou <- s.bar + exp(-lambda*T)*(s0-s.bar) + sigma*s.bar*\n sqrt((1-exp(-2*lambda*T))/(2*lambda))*w3\nopt.payoff.ou <- pmax(s.sim.ou - K, 0)\nopt.value.ou <- mean(opt.payoff.ou)*exp(-rf*T)\n\n## Brownian bridge; two-year bond maturing at 100\n## option is struck at 102 in year 1\n## FYI: vol of 0.25 is very high for a two-year bond\nw4 <- rnorm(num.sims) # simulated W_tau values\ns.bar.bb <- s0 + (100-s0)*tau/T\ns.sim.bb <- s.bar.bb + sigma*s.bar.bb*sqrt(tau/T*(T-tau)/T)*w4\nopt.payoff.bb <- pmax(s.sim.bb - K, 0)\nopt.value.bb <- mean(opt.payoff.bb)*exp(-rf*tau)\n", "meta": {"hexsha": "6c7b0c28df89fd5c87356afaf90f359ff7d230c2", "size": 1860, "ext": "r", "lang": "R", "max_stars_repo_path": "Quantitative Primer/samples/ch21-option-simulating.r", "max_stars_repo_name": "bmoretz/Quantitative-Investments", "max_stars_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 7, "max_stars_repo_stars_event_min_datetime": "2020-03-26T05:47:30.000Z", "max_stars_repo_stars_event_max_datetime": "2022-02-18T21:50:54.000Z", "max_issues_repo_path": "Quantitative Primer/samples/ch21-option-simulating.r", "max_issues_repo_name": "bmoretz/Quantitative-Investments", "max_issues_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Quantitative Primer/samples/ch21-option-simulating.r", "max_forks_repo_name": "bmoretz/Quantitative-Investments", "max_forks_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2020-11-03T09:23:54.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-18T21:50:55.000Z", "avg_line_length": 40.4347826087, "max_line_length": 73, "alphanum_fraction": 0.6768817204, "num_tokens": 628, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9566342049451596, "lm_q2_score": 0.7981867849406659, "lm_q1q2_score": 0.763572780409447}} {"text": "# Plot of generator function for frank cupola\nlibrary(copula)\nu= seq(0.000001, 1, length=500)\nfrank = iPsi(copula=archmCopula(family=\"frank\", param=1), u)\nplot(u, frank, type=\"l\", lwd=3, ylab=expression(phi(u)))\nabline(h=0)\nabline(v=0)\n\n## Scatter plot of 9 bivariate frank copulas\nset.seed(5640)\ntheta = c(-100, -50, -10, -1, 0, 5, 20, 50, 500)\npar(mfrow=c(3,3), cex.axis=1.2, cex.lab=1.2, cex.main=1.2)\nfor(i in 1:9){\n U= rCopula(n=200, copula=archmCopula(family=\"frank\", param=theta[i]))\n plot(U, xlab=expression(u[1]), ylab=expression(u[2]), \n main=eval(substitute(expression(paste(theta, \" = \", j)),\n list(j = as.character(theta[i])))))\n}", "meta": {"hexsha": "3f8112fdc5673e7590732b854b427c09f6b33a8e", "size": 694, "ext": "r", "lang": "R", "max_stars_repo_path": "chapter_8_copulas_markdown_files/archim_copula.r", "max_stars_repo_name": "emoen/Statistics-and-Data-Analysis-for-Financial-Engineering-Copulas", "max_stars_repo_head_hexsha": "e7a0d7bfb570ebd2778a5b40005dcb18dff383e1", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "chapter_8_copulas_markdown_files/archim_copula.r", "max_issues_repo_name": "emoen/Statistics-and-Data-Analysis-for-Financial-Engineering-Copulas", "max_issues_repo_head_hexsha": "e7a0d7bfb570ebd2778a5b40005dcb18dff383e1", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "chapter_8_copulas_markdown_files/archim_copula.r", "max_forks_repo_name": "emoen/Statistics-and-Data-Analysis-for-Financial-Engineering-Copulas", "max_forks_repo_head_hexsha": "e7a0d7bfb570ebd2778a5b40005dcb18dff383e1", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 38.5555555556, "max_line_length": 82, "alphanum_fraction": 0.621037464, "num_tokens": 255, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9362850057480346, "lm_q2_score": 0.8152324915965392, "lm_q1q2_score": 0.7632899580804503}} {"text": "\nbirthday = function(k)\n{\n\tprod = 1\n\tfor(i in (365-k+1):365)\n\t{\n\t\tprod = prod*i\n\t}\n\t\n\treturn (1-prod/(365^k))\n}\n\nnum_people = c(2:50)\nprobability = c()\nfor(i in 1:length(num_people))\n{\n\tres = birthday(num_people[i])\n\tprobability = cbind(probability, res)\n}\n\nplot(num_people, probability, type=\"l\", xlab=\"number of people\", ylab=\"probability of birthday match\")\nabline(h = 0.5, col=\"red\", lty=\"dashed\")\ntitle(\"Birthday problem\")", "meta": {"hexsha": "6306598f62b62b64a8d7b183820a44ff95a088f6", "size": 428, "ext": "r", "lang": "R", "max_stars_repo_path": "files/stat345/birthday_problem_R_code.r", "max_stars_repo_name": "anastasiiakim/anastasiiakim.github.io", "max_stars_repo_head_hexsha": "83aad58339ba629dd4e63ffb833d1ec5a172ad12", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2020-05-03T03:36:07.000Z", "max_stars_repo_stars_event_max_datetime": "2021-01-21T14:15:29.000Z", "max_issues_repo_path": "files/stat345/birthday_problem_R_code.r", "max_issues_repo_name": "anastasiiakim/anastasiiakim.github.io", "max_issues_repo_head_hexsha": "83aad58339ba629dd4e63ffb833d1ec5a172ad12", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "files/stat345/birthday_problem_R_code.r", "max_forks_repo_name": "anastasiiakim/anastasiiakim.github.io", "max_forks_repo_head_hexsha": "83aad58339ba629dd4e63ffb833d1ec5a172ad12", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2020-05-15T06:27:06.000Z", "max_forks_repo_forks_event_max_datetime": "2020-05-15T06:27:06.000Z", "avg_line_length": 18.6086956522, "max_line_length": 102, "alphanum_fraction": 0.6612149533, "num_tokens": 138, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9304582497090322, "lm_q2_score": 0.8198933381139645, "lm_q1q2_score": 0.7628765203296152}} {"text": "crime_rate=c(876,578,718,388,562,971,698,298,673,537,642,856,376,508,529,393,354,735,811,504,807,719,464,410,491,557,771,685,448,571,189,661,877,563,647,447,336,526,624,605,496,296,628,481,224,868,804,210,421,435,291,393,605,341,352,374,267,684,685,460,466,498,562,739,562,817,690,720,758,731,480,559,505,703,809,706,631,626,639,585,570,928,516,885,751,561,1020,592,814,843)\r\n \r\nlower_quartile= 464.5\r\nupper_quartile=718.5 # calculated in previous example\r\n \r\niqr=IQR(crime_rate)\r\n\r\nlower_inner_fence= lower_quartile - (1.5*iqr)\r\nupper_inner_fence= upper_quartile + (1.5*iqr)\r\nlower_outer_fence= lower_quartile - (3*iqr)\r\nupper_outer_fence= upper_quartile +(3*iqr)\r\nprint(lower_inner_fence)\r\nprint(upper_inner_fence)\r\nprint(lower_outer_fence)\r\nprint(upper_outer_fence)\r\n\r\n", "meta": {"hexsha": "26d93a898d45711ec3200b6b24b7589896660af9", "size": 773, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH3/EX3.14/Ex3_14.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH3/EX3.14/Ex3_14.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH3/EX3.14/Ex3_14.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 45.4705882353, "max_line_length": 375, "alphanum_fraction": 0.7645536869, "num_tokens": 301, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9252299529686201, "lm_q2_score": 0.824461932846258, "lm_q1q2_score": 0.7628168753517609}} {"text": "#number of trials\r\nn<-5\r\n# the probability of success when one person is selected from the population is\r\nz<-0.9\r\n# probability that exactly one person in the sample of five households is unemployed.\r\n\r\ny<-4\r\nprobability_forexactone_unemployed<-(factorial(n))/(factorial(y)*factorial(n-y))*(z^y)*(1-z)^(n-y)\r\nprint(probability_forexactone_unemployed)\r\n# the probability of one or fewer being unemployed\r\nprobability_foroneorfew_unemployed=((factorial(n))/(factorial(4)*factorial(n-4))*(z^4)*(1-z)^(n-4))+((factorial(n))/(factorial(5)*factorial(n-5))*(z^5)*(1-z)^(n-5))\r\nprint(probability_foroneorfew_unemployed)", "meta": {"hexsha": "16a912ec50f87ac1124fa228017cc65f040b931f", "size": 614, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH4/EX4.9/Ex4_9.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH4/EX4.9/Ex4_9.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH4/EX4.9/Ex4_9.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 51.1666666667, "max_line_length": 165, "alphanum_fraction": 0.7394136808, "num_tokens": 177, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9648551546097942, "lm_q2_score": 0.79053032607222, "lm_q1q2_score": 0.7627472599861428}} {"text": "##########################\n# SECTION 2.13: INDEXING #\n##########################\n\n# open dataset\nlibrary(dslabs)\ndata('murders')\n\n# define population, total and state\npopulation <- murders$population\ntotal <- murders$total\nstate <- murders$state\n\n# ------------------------\n# Subsetting with logicals\n# ------------------------\n\n# calculating murders rate per population\nrate <- total / population * 100000\n\n# which state have murder rates inferior than 0.71?\nindex <- rate < 0.71\nindex\nstate[index]\n\n# logical operators are integers, also. we can sum up them!\n# hence, how many state have murder rates inferior than 0.71?\nsum(index)\n\n# ------------------------\n# Logical operators\n# ------------------------\n\n# the logical operator AND (&) return return TRUE when both\n# of the given conditions are true.\n\n# select state with murder rates equal or inferior than 1.2\n# and located on the west:\nsafe <- rate <= 1.0\nwest <- murders$region == 'West'\nindex <- safe & west\nstate[index]\n\n# ------------------------\n# Which, match and %in%\n# ------------------------\n\n# The function `which` tells us which entries of a logical vector are TRUE.\n# We can acess the murder rate of California:\nind <- which(state == \"California\")\nrate[ind]\n\n# The `match` function tells us which indexes of a second vector match each of the entries of a first vector.\n# Say we wish to subsect the states vector, containing only New York, Florida and Texas:\nind <- match(c(\"New York\", \"Florida\", \"Texas\"), state)\nind\n\n# Thus, we can look at the rates of these states:\nrate[ind]\n\n# The `%in%` operator is kinda like the same in python: it tells us whether or not each element of a first vector is in a second.\n# Let’s imagine you are not sure if Boston, Dakota, and Washington are states. You can find out like this:\nc(\"Boston\", \"Dakota\", \"Washington\") %in% state\n", "meta": {"hexsha": "1bdd4fc51f1ca29461405f301f0dda71ad94ecc5", "size": 1834, "ext": "r", "lang": "R", "max_stars_repo_path": "edx/harvardx_ph125/chapter_02/02-13_indexing.r", "max_stars_repo_name": "pbittencourt/datasciencestudies", "max_stars_repo_head_hexsha": "85f0b2a4366fe7c6daa5628ed4bd2994355963c0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "edx/harvardx_ph125/chapter_02/02-13_indexing.r", "max_issues_repo_name": "pbittencourt/datasciencestudies", "max_issues_repo_head_hexsha": "85f0b2a4366fe7c6daa5628ed4bd2994355963c0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "edx/harvardx_ph125/chapter_02/02-13_indexing.r", "max_forks_repo_name": "pbittencourt/datasciencestudies", "max_forks_repo_head_hexsha": "85f0b2a4366fe7c6daa5628ed4bd2994355963c0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 28.65625, "max_line_length": 129, "alphanum_fraction": 0.6423118866, "num_tokens": 427, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.905989822921759, "lm_q2_score": 0.8418256472515683, "lm_q1q2_score": 0.7626854690844435}} {"text": "confidence_interval <- function(vector, interval) {\r\n # Standard deviation of sample\r\n vec_sd <- sd(vector)\r\n # Sample size\r\n n <- length(vector)\r\n # Mean of sample\r\n vec_mean <- mean(vector)\r\n # Error according to t distribution\r\n error <- qt((interval + 1)/2, df = n - 1) * vec_sd / sqrt(n)\r\n # Confidence interval as a vector\r\n ans <- c(\"lower\" = vec_mean - error, \"upper\" = vec_mean + error)\r\n return(ans)\r\n}\r\nvector <- c(2.7, 2.4, 1.9, 2.6, 2.4, 1.9, 2.3,\r\n 2.2, 2.5 ,2.3 ,1.8, 2.5, 2.0 ,2.2 )\r\nconfidence_interval(vector, 0.95)\r\n ", "meta": {"hexsha": "0305c2b6b6571d46bb04fa45fbd047a6a192e428", "size": 558, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH5/EX5.17/Ex5_17.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH5/EX5.17/Ex5_17.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH5/EX5.17/Ex5_17.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 32.8235294118, "max_line_length": 67, "alphanum_fraction": 0.5967741935, "num_tokens": 197, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9465966717067252, "lm_q2_score": 0.8056321913146127, "lm_q1q2_score": 0.7626087509182081}} {"text": "skew=function(x)\n{\n\tn = length(x)\n\tnfact = n/((n - 1) * (n - 2))\n\txm = mean(x)\n\txv = sqrt(var(x))\n\tskw = sum((x - xm)^3)\n\tskew = (nfact * skw)/xv^3\n\tskew\n}\n", "meta": {"hexsha": "b4ba4864d1272ed0df7034f090f2945238b29972", "size": 156, "ext": "r", "lang": "R", "max_stars_repo_path": "labs/tutorial/skew.r", "max_stars_repo_name": "rcquan/qmssviz", "max_stars_repo_head_hexsha": "28ac552dc59c248f087f4e41dd5445269817bfa1", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-03-14T04:47:23.000Z", "max_stars_repo_stars_event_max_datetime": "2017-03-14T04:47:23.000Z", "max_issues_repo_path": "labs/tutorial/skew.r", "max_issues_repo_name": "rcquan/qmssviz", "max_issues_repo_head_hexsha": "28ac552dc59c248f087f4e41dd5445269817bfa1", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2016-10-04T16:48:09.000Z", "max_issues_repo_issues_event_max_datetime": "2016-10-04T16:54:36.000Z", "max_forks_repo_path": "labs/tutorial/skew.r", "max_forks_repo_name": "rcquan/qmssviz", "max_forks_repo_head_hexsha": "28ac552dc59c248f087f4e41dd5445269817bfa1", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 5, "max_forks_repo_forks_event_min_datetime": "2015-01-26T19:11:27.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-01T18:16:13.000Z", "avg_line_length": 14.1818181818, "max_line_length": 30, "alphanum_fraction": 0.4935897436, "num_tokens": 74, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9465966717067252, "lm_q2_score": 0.8056321866478979, "lm_q1q2_score": 0.7626087465007114}} {"text": "# Mean and Standard Deviation of the Binomial Probability Distribution \r\n#number of trials\r\nn<-1218\r\n# the probability of success of single event is\r\nz<-0.5\r\nMean<-n*z\r\nprint(Mean)\r\nstandard_deviation=sqrt(n*z*(1-z))\r\nprint(standard_deviation)\r\n# survey of 1,218 customersrevealsthat 516 would add the new service\r\nobserved_valueof_y=516\r\n# y = 516 is more than (3 * standard_deviation), or 52.35, less than Mean\r\n# thus the observed number of customers in sample who would add the new service is too small\r\nprint(\" Consequently, the company concluded that offering the new service was not a good idea\")\r\n\r\n", "meta": {"hexsha": "b840f3eb059f394bec1d4355bfab28ce3c764faf", "size": 609, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH4/EX4.11/Ex4_11.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH4/EX4.11/Ex4_11.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH4/EX4.11/Ex4_11.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 38.0625, "max_line_length": 96, "alphanum_fraction": 0.7586206897, "num_tokens": 156, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9615338101862455, "lm_q2_score": 0.7931059511841119, "lm_q1q2_score": 0.7625981871234455}} {"text": "#### deterministic L Matrices ####\ndetermL <- function(typeL, m, n, k ) {\n # returns a deterministic L Matrix as described in Ledermann et al (2011)\n #\n # Steps:\n # 1. find pre image v\n # 2. get GS image w\n # 3. select n last columns of w\n # \n # Example\n # ==========\n # l = detemL('Ledermann',10,2)\n # \n # Parameters\n # ==========\n # m : int\n # number of rows in l\n # n : int\n # number of columns in l\n # k : int\n # additional parameter for Type I,II,III L matrices\n # \n # Output\n # ==========\n # l : numeric (two dimensional array)\n # deterministic L Matrix\n \n ## Assertion\n if (!any(typeL==c('Ledermann', 'TypeI','TypeII', 'TypeIII','Type I','Type II','Type III','I','II', 'III'))) { \n stop(sprintf(\"unkown type %s for type of deterministic L Matrix\", typeL))}\n if (nargs() < 3) {\n stop(\"not enough input arguments\")}\n if (!m%%1==0) {\n stop(sprintf(\"%f is not an integer value\", m))}\n if (!n%%1==0) {\n stop(sprintf(\"%f is not an integer value\", n))}\n if (!typeL=='Ledermann' & !nargs()==4){\n stop(\"L Matrices of Type I-III need an additional integer parameter k\")}\n \n ## find pre-image\n # Ledermann\n if (typeL %in% c('Ledermann')){\n v = matrix(0, m, m-1)\n for (c in 1:m-1) {\n v[c,c] = 1\n v[c+1,c] = -1\n }\n \n # Type I\n } else if (typeL %in% c('TypeI', 'Type I', 'I')){\n if (!(2*k <= m+1-n)) {\n stop(\" relation 2*k <= m+1-n not fullfilled see Ledermann 2011\")\n }\n v <- matrix(0, m, m+1-2*k)\n for (c in 1:(m+1-2*k)) {\n v[c:(c+2*k-1), c] <- rep(c(1,-1),k)\n }\n \n # Type II \n } else if (typeL %in% c('TypeII', 'Type II', 'II')){\n if (!(m-k >= n)) {\n stop(\" relation m-k < n not fullfilled see Ledermann 2011\")\n }\n v <- matrix(0, m, m-k)\n for (c in 1:(m-k)) {\n v[c:(c+k-1), c] <- rep(1,k)\n v[c+k, c] <- -k\n }\n # Type III \n } else if (typeL %in% c('TypeIII', 'Type III', 'III')){\n if (!(m-2 >= n)) {\n stop(\" relation m-2 >= n not fullfilled see Ledermann 2011\")\n }\n v <- matrix(0, m, m-2)\n for (c in 1:(m-2)) {\n v[c, c] <- k\n v[c+1, c] <- -1\n v[c+2, c] <- 1-k\n }\n }\n \n ## get GS image w\n w <- gramSchmidt(l)$Q\n \n ## select n last columns of w\n return(w[ , (ncol(w)-(n-1)):ncol(w)])\n}\n\n#### data-specific L Matrices ####\ndataL <- function(y) {\n # returns a data-specific L Matrix as described in Ledermann et al (2011)\n # Steps:\n # 1. de-mean\n # 2. orthogonalize with GS\n # \n # Example\n # ==========\n # l = dataL(y)\n # \n # Parameters\n # ==========\n # y : numeric (tow dimensional array)\n # original sample\n # \n # Output\n # ==========\n # l : numeric (two dimensional array)\n # data-specific L Matrix\n \n ## Assertion\n if (!ncol(y)prob) \n elem <- 0\n else\n elem <- 1\n} \n\nrf <-apply(rf,1:2,set_tree,0.5)\n\nrf\n\nimage(rf,asp=1,axes=F,col=c(\"white\",\"black\"))\n\nimage(rf)\n\ngenerate_rf <- function(sideDim,p)\n{\n rf <- matrix(runif(sideDim*sideDim),ncol=sideDim)\n rf <-apply(rf,1:2,set_tree,p)\n #image(rf,asp=1,axes=F,col=c(\"white\",\"black\"))\n return(rf)\n}\n\ngenerate_rf(100,0.4)\n\ngenerate_rf(100,0.5)\n\nrf <- generate_rf(10,0.5)\n\nrf\n\nrf[1,] <- 2\n\nfor(j in 1:ncol(rf))\n{\n \n if( rf[1,j]==2 & rf[2,j]==1)\n rf[2,j] <- 2\n}\n\nrf\n\nfor(i in 2:nrow(rf))\n for(j in 1:ncol(rf))\n {\n if( rf[i-1,j]==2 & rf[i,j]==1)\n rf[i,j] <- 2\n }\n\n\nimage(rf,asp=1,axes=F,col=c(\"white\",\"black\",\"red\"))\n\nfor(i in 2:nrow(rf))\n for(j in 2:(ncol(rf)-1))\n {\n if( (rf[i-1,j]==2 || rf[i-1,j-1]==2 || \n rf[i-1,j+1]==2) && rf[i,j]==1)\n rf[i,j] <- 2\n }\n\n\nimage(rf,asp=1,axes=F,col=c(\"white\",\"black\",\"red\"))\n\n# This function only propagate the fire in one direction\n#\nfire_rf <- function(rf) {\n dimi=nrow(rf)\n dimj=ncol(rf)-1\n rf[1,] <- 2\n for(i in 2:dimi)\n for(j in 2:dimj)\n {\n if((rf[i-1,j]==2 || rf[i-1,j-1]==2 || rf[i-1,j+1]==2) && (rf[i,j]==1))\n rf[i,j] <- 2\n }\n image(rf,asp=1,axes=F,col=c(\"white\",\"green\",\"red\"))\n return(rf)\n}\n\nrf <- generate_rf(100,0.5)\n\nrf1 <- fire_rf(rf)\n\nimage(rf1,asp=1,axes=F,col=c(\"white\",\"green\",\"red\"))\n\ncountBurned <- function(rf)\n{\n bur <-0\n dimi=nrow(rf)\n dimj=ncol(rf)\n \n for(i in 2:dimi)\n for(j in 1:dimj)\n {\n if(rf1[i,j]==2 )\n bur <- bur + 1\n }\n return(bur/((dimi-1)*dimj))\n}\n\nrf <- generate_rf(100,0.4)\nrf1 <- fire_rf(rf)\ncountBurned(rf1)\n\n# Make a plot of the proportion of burned \n# sites versus p (probability of tree establishment)\n#\n\npp <- seq(0.1,.9,0.05)\npropBurned <- pp\nfor(i in 1:length(pp) )\n{\n rf <- generate_rf(200,pp[i])\n rf1 <- fire_rf(rf)\n propBurned[i] <- countBurned(rf1)\n} \n \nplot(propBurned ~ pp)\n\ndf <- data.frame(pp,propBurned)\n\nrequire(ggplot2)\n\nggplot(df,aes(x=pp,y=propBurned))+geom_line()\n\n## Infection in 1 dimension\n#\n# Now we have to propagate the infection\n# there are two possibilities: contagion with \n# probability lambda or recuperation with \n# probability mu\n#\n# dim_in: is the size of the infection\n# time_in: is the time \n#\nsimulate_inf <- function(lambda,mu,dim_in,time_in){\n \n inf<-matrix(0,time_in,dim_in)\n inf[1,] <- ifelse(runif(dim_in)>0.5,1,0)\n for(i in 1:(time_in-1))\n for(j in 2:(dim_in-1))\n {\n if(inf[i,j]==0){\n \n if(inf[i,j-1]==1){\n inf[i+1,j] <- ifelse(runif(1)<=lambda,1,0)\n }\n else if(inf[i,j+1]==1 ){\n inf[i+1,j] <- ifelse(runif(1)<=lambda,1,0)\n }\n }\n else\n {\n inf[i+1,j] <- ifelse(runif(1)<=mu,0,1)\n }\n }\n image(inf,asp=1,axes=F,col=c(\"grey\",\"brown\")) \n}\n\nsimulate_inf(.4,.3,50,100)", "meta": {"hexsha": "d471649af145cb74d4c474f2b6a86675e8ce54d8", "size": 3025, "ext": "r", "lang": "R", "max_stars_repo_path": "R/curso_R4.r", "max_stars_repo_name": "lsaravia/MultifractalsInR", "max_stars_repo_head_hexsha": "1dfe51dbd49f370551c45fd16fd37f4ce040b2ca", "max_stars_repo_licenses": ["CC-BY-3.0"], "max_stars_count": 3, "max_stars_repo_stars_event_min_datetime": "2015-08-11T04:34:37.000Z", "max_stars_repo_stars_event_max_datetime": "2017-03-17T12:25:35.000Z", "max_issues_repo_path": "R/curso_R4.r", "max_issues_repo_name": "lsaravia/MultifractalsInR", "max_issues_repo_head_hexsha": "1dfe51dbd49f370551c45fd16fd37f4ce040b2ca", "max_issues_repo_licenses": ["CC-BY-3.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/curso_R4.r", "max_forks_repo_name": "lsaravia/MultifractalsInR", "max_forks_repo_head_hexsha": "1dfe51dbd49f370551c45fd16fd37f4ce040b2ca", "max_forks_repo_licenses": ["CC-BY-3.0"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2017-03-17T12:26:28.000Z", "max_forks_repo_forks_event_max_datetime": "2020-02-11T20:31:32.000Z", "avg_line_length": 17.1875, "max_line_length": 76, "alphanum_fraction": 0.5666115702, "num_tokens": 1157, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8774767810736693, "lm_q2_score": 0.8688267830311354, "lm_q1q2_score": 0.762375328884752}} {"text": "diabetes <- matrix(c(326,160,8,64), nrow=2) \r\ncolnames(diabetes) <- c(\"DiabNO\", \"DiabYes\") \r\nrownames(diabetes) <- c(\"StressNO\", \"StressYes\") \r\nTableDiabetes <- as.table(diabetes)\r\n\r\nDfBiabetes <- as.data.frame(TableDiabetes) \r\n\r\nLogModel <- glm(Var2 ~ Var1, weights = Freq, data = DfBiabetes, family = binomial(logit))\r\nsummary(LogModel)\r\n\r\nPx0=(exp(-3.7075))/(1+exp(-3.7075))\r\nPx0\r\nPx1=(exp(-3.7075+2.7912))/(1+exp(-3.7075+2.7912))\r\nPx1\r\n\r\nOddsx0=exp(-3.7075)\r\nOddsx0\r\nOddsx1=exp(2.7912-3.7075)\r\nOddsx1\r\n\r\nOR = exp(2.7912-3.7075)/exp(-3.7075)\r\nOR\r\n\r\nBeta = LogModel$coefficient[1]\r\nAlpha = LogModel$coefficient[2]\r\nBeta\r\nAlpha\r\n\r\nP0 <- exp(LogModel$coefficient[1]) / (1 + exp(LogModel$coefficient[1]))\r\nP1 <- exp(LogModel$coefficient[1] + LogModel$coefficient[2]) / (1 + exp(LogModel$coefficient[1]+LogModel$coefficient[2]))\r\nP0\r\nP1\r\n\r\nodds0 <- P0 / (1 - P0)\r\nodds1 <- P1 / (1 - P1)\r\nodds0\r\nodds1\r\n\r\nOR1 <- odds1 / odds0\r\nOR1 \r\n\r\nOR2 <- (TableDiabetes[1,1]*TableDiabetes[2,2]) / (TableDiabetes[1,2]*TableDiabetes[2,1])\r\nOR2\r\n", "meta": {"hexsha": "8e326775988b217afe516f80ee050c896143cd3e", "size": 1028, "ext": "r", "lang": "R", "max_stars_repo_path": "Chapter04/SimpleLogisticRegression.r", "max_stars_repo_name": "kumaranil02/Analytics", "max_stars_repo_head_hexsha": "faa2aae1f52764a1dc45ae2ccd9f20abfd612318", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 11, "max_stars_repo_stars_event_min_datetime": "2018-07-03T03:31:01.000Z", "max_stars_repo_stars_event_max_datetime": "2021-08-30T11:46:16.000Z", "max_issues_repo_path": "Chapter04/SimpleLogisticRegression.r", "max_issues_repo_name": "kumaranil02/Analytics", "max_issues_repo_head_hexsha": "faa2aae1f52764a1dc45ae2ccd9f20abfd612318", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2021-09-25T20:32:32.000Z", "max_issues_repo_issues_event_max_datetime": "2021-10-01T10:51:27.000Z", "max_forks_repo_path": "Chapter04/SimpleLogisticRegression.r", "max_forks_repo_name": "kumaranil02/Analytics", "max_forks_repo_head_hexsha": "faa2aae1f52764a1dc45ae2ccd9f20abfd612318", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 15, "max_forks_repo_forks_event_min_datetime": "2018-03-05T05:48:24.000Z", "max_forks_repo_forks_event_max_datetime": "2021-11-10T12:58:27.000Z", "avg_line_length": 23.3636363636, "max_line_length": 122, "alphanum_fraction": 0.6527237354, "num_tokens": 412, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9643214491222695, "lm_q2_score": 0.7905303285397349, "lm_q1q2_score": 0.7623253519925409}} {"text": "# Define a general vector\nv <- c(1, 1, 2, 3, 5, 8, 13, 21)\n\n# In R, operations on vector occurs *element-wise*:\nv3 <- v * 3\nv3\n\n# Two vectors of the same length can be operated\na <- c(1, 2, 3, 4)\nb <- c(4, 8, 12, 16)\nsoma <- a + b\nsoma\ndiferenca <- a - b\ndiferenca\nmultiplication <- a * b\nmultiplication\ndivision <- a / b\ndivision\n", "meta": {"hexsha": "155dd3552aea311325e9efe1c203a2633d3870a6", "size": 331, "ext": "r", "lang": "R", "max_stars_repo_path": "edx/harvardx_ph125/chapter_02/vector_arithmetics.r", "max_stars_repo_name": "pbittencourt/datasciencestudies", "max_stars_repo_head_hexsha": "85f0b2a4366fe7c6daa5628ed4bd2994355963c0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "edx/harvardx_ph125/chapter_02/vector_arithmetics.r", "max_issues_repo_name": "pbittencourt/datasciencestudies", "max_issues_repo_head_hexsha": "85f0b2a4366fe7c6daa5628ed4bd2994355963c0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "edx/harvardx_ph125/chapter_02/vector_arithmetics.r", "max_forks_repo_name": "pbittencourt/datasciencestudies", "max_forks_repo_head_hexsha": "85f0b2a4366fe7c6daa5628ed4bd2994355963c0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 17.4210526316, "max_line_length": 51, "alphanum_fraction": 0.6223564955, "num_tokens": 140, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8947894689081711, "lm_q2_score": 0.8519527963298946, "lm_q1q2_score": 0.7623183901628577}} {"text": "library(deSolve)\n\ndiffeq <- function (t, state, f_params) {\n # State variables\n # ---------------\n # u: rabbits\n # v: foxes\n with(\n as.list(c(state, f_params)), {\n du = a*u - b*u*v\n dv = -c*v + d*b*u*v\n \n return(list(c(du, dv)))\n }\n )\n}\n\nf_params <- c(a = 1.0, b = 0.1, c = 1.5, d = 0.75)\nstate <- c(u = 10, v = 5)\nt <- seq(0, 18, by = 0.01)\n\nout <- as.data.frame(ode(func = diffeq, y = state, parms = f_params, times = t))\n\nmatplot(out[,-1], type = \"l\", xlab = \"Time\", ylab = \"Population\")\nlegend(\"topright\", c(\"Rabbits\", \"Foxes\"), lty = c(1,2), col = c(1,2), box.lwd = 0)", "meta": {"hexsha": "44f33cd9b15a6dc99044f677d0f4697e0c541b2d", "size": 649, "ext": "r", "lang": "R", "max_stars_repo_path": "R/test_deSolve.r", "max_stars_repo_name": "camrepo/ode_solver", "max_stars_repo_head_hexsha": "facb6d026440db51b3052e7a6b88184d749b5be0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2021-03-07T10:33:32.000Z", "max_stars_repo_stars_event_max_datetime": "2021-08-28T17:29:25.000Z", "max_issues_repo_path": "R/test_deSolve.r", "max_issues_repo_name": "camrepo/ode_solver", "max_issues_repo_head_hexsha": "facb6d026440db51b3052e7a6b88184d749b5be0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/test_deSolve.r", "max_forks_repo_name": "camrepo/ode_solver", "max_forks_repo_head_hexsha": "facb6d026440db51b3052e7a6b88184d749b5be0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-04-15T02:33:12.000Z", "max_forks_repo_forks_event_max_datetime": "2021-04-15T02:33:12.000Z", "avg_line_length": 25.96, "max_line_length": 82, "alphanum_fraction": 0.469953775, "num_tokens": 240, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9674102542943774, "lm_q2_score": 0.7879311981328135, "lm_q1q2_score": 0.7622527207521387}} {"text": "## Author: Sergio García Prado\n## Title: Statistical Inference - Non parametric Tests - Exercise 11\n\nrm(list = ls())\n\nn <- 40 - 1 # due to there was one tie\n# 39\n\nV <- 242\n\n(V.mean <- n * (n + 1) / 4)\n# 390\n\n(V.var <- n * (n + 1) * (2 * n + 1) / 24)\n# 5135\n\n## Asymptotic pvalue (with continuity correction)\n2 * (1 - pnorm(abs(V + 0.5 * sign(V.mean - V) - V.mean) / sqrt(V.var)))\n# 0.039555378139781\n\n## Exact\n2 * (1 - psignrank(V - (V.mean < V), n, lower.tail = V.mean < V))\n# 0.0385776563234685\n", "meta": {"hexsha": "de0b9c9026e5eb480eb6f240112e91151e8b02fc", "size": 498, "ext": "r", "lang": "R", "max_stars_repo_path": "statistical-inference/non-parametric/exercise-11.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "statistical-inference/non-parametric/exercise-11.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "statistical-inference/non-parametric/exercise-11.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 20.75, "max_line_length": 71, "alphanum_fraction": 0.5803212851, "num_tokens": 194, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9579122768904644, "lm_q2_score": 0.7956581000631542, "lm_q1q2_score": 0.762170662257837}} {"text": "## Dexter Barrows\n## dbarrows.github.io\n## McMaster University\n## 2016\n\n## ymat: \tContains the initial conditions where:\n# \t\t\t- rows are locations\n# \t\t\t- columns are S, I, R\n## pars: \tContains the parameters: global values for R0, r, N, eta, berr\n## T: \t\tThe stop time. Since 0 in included, there should be T+1 time steps in the simulation\n## neinum:\tNumber of neighbors for each location, in order\n## neibmat: Contains lists of neighbors for each location\n#\t\t\t- rows are parent locations (nodes)\n# \t\t\t- columns are locations each parent is attached to (edges)\nStocSSIRstan <- function(ymat, pars, T, steps, neinum, neibmat, berrmat, bmatlim) {\n\n\t## number of locations\n nloc <- dim(ymat)[1]\n\n ## storage\n ## dims are locations, (S,I,R,B), times\n # output array\n out <- array(NA, c(nloc, 4, T+1), dimnames = list(NULL, c(\"S\",\"I\",\"R\",\"B\"), NULL))\n # temp storage\n BSI <- numeric(nloc)\n rI <- numeric(nloc)\n\n ## extract parameters\n R0 <- pars[['R0']]\n r <- pars[['r']]\n N <- pars[['N']]\n eta <- pars[['eta']]\n berr <- pars[['berr']]\n phi <- pars[['phi']]\n\n B0 <- rep(R0*r/N, nloc)\n\n ## state vectors\n S <- ymat[,'S']\n I <- ymat[,'I']\n R <- ymat[,'R']\n B <- B0\n\n ## assign starting to output matrix\n out[,,1] <- cbind(ymat, B0)\n\n h <- 1 / steps\n\n for ( i in 1:(T*steps) ) {\n\n \tif (i <= bmatlim) {\n\t\t B <- exp( log(B) + eta*(log(B0) - log(B)) + berrmat[,i])\n\t } else {\n\t B <- exp( log(B) + eta*(log(B0) - log(B)) + rnorm(nloc, 0, berr) )\n\t }\n \n\n for (loc in 1:nloc) {\n \tn <- neinum[loc]\n \tsphi <- 1 - phi*(n/(n+1))\n \tophi <- phi/(n+1)\n \tnBIsum <- B[neibmat[loc,1:n]] %*% I[neibmat[loc,1:n]]\n \tBSI[loc] <- S[loc]*( sphi*B[loc]*I[loc] + ophi*nBIsum )\n }\n\n rI <- r*I\n\n dS <- -BSI\n dI <- BSI - rI\n dR <- rI\n\n S <- S + h*dS\n I <- I + h*dI\n R <- R + h*dR\n\n if (i %% steps == 0)\n out[,,i/steps+1] <- cbind(S,I,R,B)\n\n }\n\n\treturn(out)\n\n}\n\n### Suggested parameters\n#\n# T <- 60\n# i_infec <- 5\n# steps <- 7\n# N <- 500\n# sigma <- 10\n#\n# pars <- c(R0 = 3.0, # new infected people per infected person\n# r = 0.1, # recovery rate\n# N = 500, # population size\n# eta = 0.5, # geometric random walk\n# berr = 0.5, # Beta geometric walk noise\n# \t\t\tphi = 0.5 )\t # interconnectivity degree", "meta": {"hexsha": "f446a8a3ad1e00f4dbb506df2557483ee4a1a5e7", "size": 2459, "ext": "r", "lang": "R", "max_stars_repo_path": "code/sir-functions/StocSSIRstan.r", "max_stars_repo_name": "dbarrows/epidemic-forecasting", "max_stars_repo_head_hexsha": "a0865fa20c992dc4159e79bb332500e3ff2357ae", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "code/sir-functions/StocSSIRstan.r", "max_issues_repo_name": "dbarrows/epidemic-forecasting", "max_issues_repo_head_hexsha": "a0865fa20c992dc4159e79bb332500e3ff2357ae", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "code/sir-functions/StocSSIRstan.r", "max_forks_repo_name": "dbarrows/epidemic-forecasting", "max_forks_repo_head_hexsha": "a0865fa20c992dc4159e79bb332500e3ff2357ae", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 25.0918367347, "max_line_length": 92, "alphanum_fraction": 0.5079300529, "num_tokens": 844, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9489172630429475, "lm_q2_score": 0.8031737963569014, "lm_q1q2_score": 0.7621454805868046}} {"text": "#\n# Exemplo 2\n#\n\n# Série de MacLaurin para a exponencial de x\n# para x=3 até n=4 (A série de MacLaurin é a\n# mesma série de Taylor desenvolvida em torno\n# de 0).\nx <- 3\nmaclaurin <- 1 + x\nmaclaurin <- maclaurin + x^2 / factorial(2)\nmaclaurin <- maclaurin + x^3 / factorial(3)\nmaclaurin <- maclaurin + x^4 / factorial(4)\n\nmaclaurin\n# valor real da exponencial de x\nexp(x)", "meta": {"hexsha": "ad80aff14b5a530c39b76e7dc56ffc21ff59cc47", "size": 370, "ext": "r", "lang": "R", "max_stars_repo_path": "src/r/aula4/exemplo2.r", "max_stars_repo_name": "EduardoJM/anotacoes-matematica-aplicada", "max_stars_repo_head_hexsha": "75eaa8548ec01cc596e40dc4699fbef06001f20d", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "src/r/aula4/exemplo2.r", "max_issues_repo_name": "EduardoJM/anotacoes-matematica-aplicada", "max_issues_repo_head_hexsha": "75eaa8548ec01cc596e40dc4699fbef06001f20d", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "src/r/aula4/exemplo2.r", "max_forks_repo_name": "EduardoJM/anotacoes-matematica-aplicada", "max_forks_repo_head_hexsha": "75eaa8548ec01cc596e40dc4699fbef06001f20d", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 21.7647058824, "max_line_length": 45, "alphanum_fraction": 0.6864864865, "num_tokens": 148, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9294404077216356, "lm_q2_score": 0.8198933337131076, "lm_q1q2_score": 0.7620419943745618}} {"text": "library(SAGx) ## for gap statistic\nlibrary(cluster) ## for hierarchical cluster, k-mean cluster & silhouette width\nlibrary(Hmisc) ## for error bar plot\n\nset.seed(7) ## for random number later\nx1 <- c(rnorm(20, sd = .05), \n rnorm(20, mean = 1, sd = .05),\n rnorm(20, mean = 2.5, sd= .05))\n\n## x1 dimension with 3 clusters\nx2 <- 4+c(rnorm(20, sd = 0.5),\n rnorm(20, mean = 10, sd = 1.0), \n rnorm(20, mean = 10, sd = 1))\n\n## x2 dimension with 3 clusters\nplot(x1,x2) ## scatter plot of the data\n\ndat = cbind(x1, x2) ## combine two vectors into one data matrix\nhc0 = hclust(dist(dat), method = \"ave\")\n## hierarchical clustering (hc) with average linkage\nplot(hc0) ## plot the dendrogram of the hc result\n\n# Using gap statistic to determine k in HC - 1\nk = 6 ## check all possible numbers of clusters, 2~6\ngap = rep(0, k) ## initialize the gap statistics\nse = rep(0, k) ## initialize the standard error\nfor (i in 2:k) {\n mem = cutree(hc0, i) ## get the cluster membership by using “cuttree” on the object of hier. cluster. \n result=gap(dat, class=mem) \n ## get the gapstatistics\n gap[i] = result[1] ## extract the gap stat values se[i]=result[2] ## and the s.e. values\n}\n\nerrbar(1:k, gap, gap - se, gap + se, xlab = \"Number of clusters\") ## error bar plot\nlines(1:k, gap) ## connect them\n\n# Using silhouette width to determine k in HC\nk = 6\nsil = rep(0,k)\nfor (i in 2:k){\n mem = cutree(hc0, i)\n aa = silhouette(mem, dist(dat))\n sil[i] = mean(aa[,3])\n}\nplot(1:k, sil)\nlines(1:k, sil)\n\nkm = kmeans(dat, centers = 2)\nmem = km$cluster\nplot(x1, x2, col = mem+1)\n\n# Use gap statistic to determine k in K-means\nk = 6 ## check all possible numbers of clusters, 2~6\ngap = rep(0,k) ## initialize the gap statistics\nse = rep(0, k) ## initialize the standard error\nfor (i in 2:k) {\n km = kmeans(dat, centers = i)\n mem = km$cluster\n result = gap(dat, class = mem) ## get the gap statistics\n gap[i] = result[1] ## extract the gap stat values se[i]=result[2] ## and the s.e. values\n}\n\nerrbar(1:k, gap, gap-se, gap+se, xlab=\"Number of clusters\") ## error bar plot\nlines(1:k, gap) ## connect them\n\n# Use silhouette width to determine k in K-means\nk = 6\nsil = rep(0, k)\nfor (i in 2:k) {\n km = kmeans(dat, centers = i)\n mem = km$cluster\n aa = silhouette(mem, dist(dat))\n sil[i] = mean(aa[,3])\n}\nplot(1:k, sil)\nlines(1:k, sil)\n\n# How about just let k=3 for both HC and K- means, and check\nhc0 = hclust(dist(dat))\nmem = cutree(hc0, 3)\nplot(x1, x2, col = mem)\n\nkm = kmeans(dat, 3)\nmem = km$cluster\nplot(x1, x2, col = mem)\n\n# revisit the data ...\nplot(x1, x2)\nplot(x1, x2, xlim = c(-0.2, 16), ylim = c(-0.2, 16))\n\n# Scaling needed\nx1.sc = x1/sd(x1)\nx2.sc = x2/sd(x2)\ndat.sc = cbind(x1.sc, x2.sc)\nhc1 = hclust(dist(dat.sc), \"ave\")\nplot(hc1)\n\n# For the scaled data, perform HC and gap\nK = 6\ngap = rep(0, k)\nse = rep(0, k)\n\nfor (i in 2:k) {\n mem = cutree(hc1, i)\n result = gap(dat.sc, class = mem)\n gap[i] = result[1]\n se[i]=result[2]\n}\nerrbar(1:k, gap, gap-se, gap+se, xlab=\"Number of clusters\")\nmem3 = cutree(hc1, 3)\nplot(x1, x2, col = mem3)\nlines(1:k, gap)\n\n# For the scaled data, perform Kmeans and gap \nk = 6\ngap = rep(0,k)\nse = rep(0,k)\nfor (i in 2:k) {\n km = kmeans(dat.sc, centers = i)\n mem = km$cluster\n result = gap(dat.sc, class = mem)\n gap[i] = result[1]\n se[i] = result[2]\n}\n\nerrbar(1:k, gap, gap-se, gap+se, xlab=\"Number of clusters\")\nlines(1:k, gap)\n\n# For the scaled data, perform Kmeans and silhouette width\nk = 6\nsil = rep(0, k)\nfor (i in 2:k) {\n km = kmeans(dat.sc, centers=i)\n mem = km$cluster\n aa = silhouette(mem, dist(dat.sc))\n sil[i] = mean(aa[,3])\n}\nplot(1:k, sil)\nlines(1:k, sil)\n\nkm = kmeans(dat.sc, centers = 3)\nmem3 = km$cluster\n# What???? K-means is sensitive to seeds initialization\nplot(x1, x2, col=mem3)\n\n# Recommend: Hybrid ... (hierarchical+kmeans)\n# Use the seeds info from HC result\nhc = hclust(dist(dat.sc), method = \"ave\")\nmem = cutree(hc, 3)\nc1 = tapply(x1.sc, mem, mean)\nc2 = tapply(x2.sc, mem, mean)\n\n# then do kmeans clustering:\nkm = kmeans(dat.sc, centers = cbind(c1, c2))\nplot(x1, x2, col=km$cluster)\n", "meta": {"hexsha": "d5db2416a9f992bb70d815e410b61d4fc5d7a0b2", "size": 4089, "ext": "r", "lang": "R", "max_stars_repo_path": "clustering/cluster.r", "max_stars_repo_name": "kyclark/abe516", "max_stars_repo_head_hexsha": "755d9c49fc2f66159c57e5eb623908ae1640c0b8", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "clustering/cluster.r", "max_issues_repo_name": "kyclark/abe516", "max_issues_repo_head_hexsha": "755d9c49fc2f66159c57e5eb623908ae1640c0b8", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "clustering/cluster.r", "max_forks_repo_name": "kyclark/abe516", "max_forks_repo_head_hexsha": "755d9c49fc2f66159c57e5eb623908ae1640c0b8", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.2115384615, "max_line_length": 104, "alphanum_fraction": 0.6331621423, "num_tokens": 1453, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.945801274759925, "lm_q2_score": 0.8056321819811829, "lm_q1q2_score": 0.7619679447054227}} {"text": "#' Calculation of significance level alpha_n\n#'\n#' For a given sample size n and the significance level alpha (alpha is the\n#' probability for minimum one observation to fall into the outlier region)\n#' the probability alpha_n for an individual observation to fall into the\n#' outlier region is calculated.\n#' @param n A sample size\n#' @param alpha A significance level, default value 0.05\n#' @return alpha_n\n#' @keywords alpha_n\n#' @export\n#' @examples\n#' get_alpha_n(1) # returns alpha_n = 0.05 since sample size n = 1 and default value of alpha is 0.05\n#'\n#' get_alpha_n(1, 0.1) # returns alpha_n = 0.1 since sample size n = 1\n\nget_alpha_n <- function(n, alpha = 0.05) {\n if(alpha <= 0 | 1 <= alpha){\n stop(paste(\"alpha not beteen 0 and 1\"));\n }\n if(any(n <= 0)){\n stop(paste(\"Sample size n not positive\"));\n }\n return(1 - (1 - alpha)^(1 / n));\n}\n\n#' Robust estimates for location-scale families of distributions\n#'\n#' The robust estimates of the scale (Q_n) and location parameters for\n#' location-scale families of distributions.\n#' Implemented distributions: normal, gumbel, cauchy, laplace, logistic\n#' @param x A sample\n#' @param distribution The distribution name\n#' @return ret The list structure with location and scale - the estimates of location and scale parameters.\n#' @keywords robust estimator\n#' @export\n#' @examples\n#' x <- rnorm(100)\n#' estimates <- get_robust_estimates(x)\n#' estimates$location\n#' estimates$scale\n#'\n#' x <- rcauchy(100)\n#' estimates <- get_robust_estimates(x, \"cauchy\")\n#' estimates\n#'\n#' x <- rlogis(100)\n#' estimates <- get_robust_estimates(x, \"logis\")\n#' estimates\n#'\n\nget_robust_estimates <- function(x, distribution = \"norm\") {\n require(\"robustbase\");\n\n if(!(distribution %in% c(\"norm\", \"logis\", \"cauchy\", \"gumbel\",\n \"laplace\", \"lnorm\", \"extII\"))){\n stop(paste(\"given distribution is supported yet\"));\n }\n\n n <- length(x);\n mu <- NA;\n sigma <- NA;\n\n if(distribution == \"lnorm\") {\n x <- log(x);\n }\n\n k_const <- switch (distribution,\n norm = 2.22191445,\n logis = 1.307883,\n cauchy = 1.2071068,\n gumbel = 1.957615,\n extII = 1.957615,\n laplace = 1.9305030,\n lnorm = 2.22191445\n )\n\n sigma <- Qn(x, constant = k_const);\n med <- median(x);\n mu <- switch (distribution,\n norm = med,\n logis = med,\n cauchy = med,\n laplace = med,\n gumbel = med - 0.3665129*sigma,\n extII = med + 0.3665129*sigma,\n lnorm = med\n )\n\n ret <- list(location=mu, scale=sigma)\n return(ret);\n}\n\n\n#' constant b_n\n#'\n#' The calculation of the constant b_n necessary for BP test\n#' @param n A sample size\n#' @param m An estimate of location parameter mu (default value (theoretical) 0)\n#' @param s An estimate of shape parameter sigma (default value (theoretical) 1)\n#' @param distribution The distribution name\n#' @param alternative The choice of alternative\n#' @return ret The b_n value\n#' @keywords b_n constant\n#' @export\n#' @examples\n#' get_bn(100, distribution = \"norm\")\n#'\nget_bn <- function(n, m = 0, s = 1, distribution = \"norm\", alternative = \"greater\") {\n\n bn <- NA;\n if(!(alternative %in% c(\"greater\", \"less\", \"two.sided\"))){\n stop(paste(\"Choose alternative from greater/less/two.sided\"));\n }\n\n if(!(distribution %in% c(\"norm\", \"logis\", \"cauchy\", \"gumbel\",\n \"laplace\", \"lnorm\", \"extII\"))){\n stop(paste(\"given distribution is supported yet\"));\n }\n\n if(n < 3){\n stop(paste(\"Sample size is not sufficient\"));\n }\n\n if(alternative == \"greater\" | alternative == \"less\") {\n if(distribution == \"norm\") {\n bn <- m + s*qnorm((n-1)/n);\n } else if(distribution == \"gumbel\") {\n bn <- m - s*log(-log(1-1/n));\n } else if(distribution == \"extII\") {\n bn <- m + s*log(log(n));\n } else if(distribution == \"logis\") {\n bn <- m + s*log(n-1);\n } else if(distribution == \"cauchy\") {\n bn <- m + s*n/pi;\n } else if(distribution == \"lnorm\") {\n bn <- exp(m + s*qnorm((n-1)/n))\n } else if(distribution == \"laplace\") {\n bn <- m + s*log(n/2);\n }\n } else { ## two.sided alternative\n if(distribution == \"norm\") {\n bn <- m + s*qnorm(1-1/(2*n));\n } else if(distribution == \"logis\") {\n bn <- m + s*log(2*n-1);\n } else if(distribution == \"cauchy\") {\n bn <- m + s*2*n/pi;\n } else if(distribution == \"laplace\") {\n bn <- m + s*log(n);\n } else if(distribution == \"lnorm\") {\n bn <- m + s*log(n);\n } else if(distribution == \"gumbel\") {\n bn1 <- m + s*log(log(n));\n bn2 <- m - s*log(-log(1-1/n));\n bn <- c(bn2, bn1)\n } else if(distribution == \"extII\") {\n bn1 <- m + s*log(log(n));\n bn2 <- m - s*log(-log(1-1/n));\n bn <- c(bn2, bn1)\n }\n }\n return(bn);\n}\n\n\n#' constant a_n\n#'\n#' The calculation of the constant a_n nessisary for BP test\n#' @param n A sample size\n#' @param m An estimate of location parameter mu (default value (theoretical) 0)\n#' @param s An estimate of shape parameter sigma (default value (theoretical) 1)\n#' @param distribution The distribution name\n#' @param alternative The choice of alternative\n#' @return ret The a_n value\n#' @keywords a_n constant\n#' @export\n#' @examples\n#' get_an(100, distribution = \"norm\")\n#'\n#'\nget_an <- function(n, m = 0, s=1, distribution = \"norm\", alternative = \"greater\"){\n an <- NA;\n\n if(!(alternative %in% c(\"greater\", \"less\", \"two.sided\"))){\n stop(paste(\"Choose alternative from greater/less/two.sided\"));\n }\n\n if(!(distribution %in% c(\"norm\", \"logis\", \"cauchy\", \"gumbel\",\n \"laplace\", \"lnorm\", \"extII\"))){\n stop(paste(\"given distribution is supported yet\"));\n }\n\n if(n < 3){\n stop(paste(\"Sample size is not sufficient\"));\n }\n\n\n if(alternative == \"greater\" | alternative == \"less\") {\n if(distribution == \"norm\") {\n an <- s/qnorm(1 - 1/n)\n } else if(distribution == \"gumbel\") {\n an <- -s/((n-1)*log(1-1/n))\n } else if(distribution == \"extII\") {\n an <- s/log(log(n))\n #an <- s/exp(-log(log(n)))\n } else if(distribution == \"logis\") {\n an <- s*n/(n-1);\n } else if(distribution == \"cauchy\") {\n an <- s*n/pi;\n } else if(distribution == \"lnorm\") {\n bn <- get_bn(n, m, s, distribution);\n an <- s*bn/(n*dnorm(qnorm(1 - 1/n)))\n } else if(distribution == \"laplace\") {\n an <- s;\n }\n } else {\n if(distribution == \"norm\") {\n an <- s/qnorm(1 - 1/(2*n))\n } else if(distribution == \"logis\") {\n an <- s*4*n/(2*n-1);\n } else if(distribution == \"cauchy\") {\n an <- s*2*pi/(2*n*(sin(pi/(2*n)))^2);\n } else if(distribution == \"laplace\") {\n an <- 2*s;\n } else if(distribution == \"lnorm\") {\n bn <- get_bn(n, m, s, distribution);\n an <- s*bn/(n*dnorm(qnorm(1 - 1/(2*n))))\n } else if(distribution == \"gumbel\") {\n an1 <- s/(log(n))\n an2 <- -s/((n-1)*log(1-1/n))\n an <- c(an2, an1)\n } else if(distribution == \"extII\") {\n an1 <- s/(log(n))\n an2 <- -s/((n-1)*log(1-1/n))\n an <- c(an2, an1)\n }\n }\n return(an);\n}\n\n#' Critical values of BP test\n#'\n#' The method with estimated aproximations of critical values.\n#' For two.sided alternatives the exact approximations were provided.\n#' For less common configurations the simulation is applied and exact critical value is calculated.\n#' @param n A sample size\n#' @param s A upper limit (default s=5)\n#' @param alpha The significance level (default: 0.05)\n#' @param distribution The distribution name\n#' @param alternative The choice of alternative (\"two.sided\"/\"greater\"/\"less\")\n#' @param gen_num The number of simulations to used in order to calculate p-value.\n#' @return ret The critical value of statistics U\n#' @keywords BP critical values\n#' @export\n#' @examples\n#' get_critical(100)\n#'\n#'\nget_critical <- function(n, s = 5, alpha = 0.05, distribution = \"norm\", alternative = \"two.sided\", gen_num = 10000) {\n critical <- NA;\n\n if (alternative == \"two.sided\") {\n if (distribution == \"norm\") {\n if(alpha == 0.05) {\n if (s == 5) {\n critical <- 0.9853\n return(critical)\n }\n }\n } else if (distribution == \"logis\") {\n if(alpha == 0.05) {\n if (s == 5) {\n x <- log(log(log(log(n))));\n if(n %% 2 == 1) {\n critical <- 1 - (0.010536 -0.006989 * x)\n }else {\n critical <- 1 - (0.005306 -0.018044 * x)\n }\n return(critical)\n }\n }\n } else if (distribution == \"laplace\") {\n if(alpha == 0.05) {\n if (s == 5) {\n x <- log(log(log(log(n))));\n if(n %% 2 == 1) {\n critical <- 1 - (0.009657 -0.006613 * x)\n }else {\n critical <- 1 - (0.006819 -0.013780 * x)\n }\n return(critical)\n }\n }\n } else if (distribution == \"gumbel\") {\n if(alpha == 0.05) {\n if (s == 5) {\n x <- log(log(log(log(n))));\n if(n %% 2 == 1) {\n critical <- 1 - (0.005755 -0.002166 * x)\n }else {\n critical <- 1 - ( 0.00302 -0.00840 * x)\n }\n return(critical)\n }\n }\n } else if (distribution == \"cauchy\") {\n if(alpha == 0.05) {\n if (s == 5) {\n x <- log(log(log(log(n))));\n if(n %% 2 == 1) {\n critical <- 1 - ( 0.009183 -0.003114 * x)\n }else {\n critical <- 1 - (0.008783 -0.004095 * x)\n }\n return(critical)\n }\n }\n }\n }\n\n if(is.na(critical)){\n r_samples <- switch(distribution,\n \"norm\" = lapply(rep(n, gen_num), rnorm),\n \"cauchy\" = lapply(rep(n, gen_num), rcauchy),\n \"logis\" = lapply(rep(n, gen_num), rlogis),\n \"laplace\" = lapply(rep(n, gen_num), rlaplace),\n \"lnorm\" = lapply(rep(n, gen_num), rlnorm),\n \"gumbel\" = lapply(rep(n, gen_num), rgumbel),\n \"extII\" = lapply(rep(n, gen_num), rextII)\n )\n statistics <- lapply(r_samples, bp_statistic, distribution = distribution, alternative=alternative, s = s)\n ms <- lapply(statistics, function(X){return(X$Test_statistic_U)})\n critical <- quantile(unlist(ms), 1-alpha)[[1]]\n\n #warning(\"At given s, alpha and alternative, exact critical values is not implemented.\n # Rough approximation is used insted.\")\n #critical <- (1-alpha)^(1/s)\n }\n return(critical)\n\n}\n\n#' Main BP statistic\n#'\n#' The calculation of the value of the BP test statistic U.\n#' @param data A given data\n#' @param distribution The distribution name\n#' @param alternative The choice of alternative\n#' @return ret The value of the statistic U\n#' @keywords BP statistic\n#' @export\n#' @examples\n#' x <- rnorm(100)\n#' get_main_bp_statistic(x)\n#'\n#'\nget_main_bp_statistic <- function(data, distribution = \"norm\",\n alternative = \"two.sided\") {\n bp <- bp_statistic(data, distribution, alternative)\n return(bp$Test_statistic_U)\n}\n\n#' p-value of BP test\n#'\n#' The use simulation and for given conditions calculate exact p-value.\n#' Since simulation is used it might take few minutes.\n#' @param statistic_val A given BP statistics value\n#' @param n The size of the sample\n#' @param distribution The distribution name\n#' @param alternative The chooise of alternative\n#' @param gen_num The number of simulations to used in order to calculate p-value.\n#' @return ret The p-value of given BP statistics\n#' @keywords BP p-value\n#' @export\n#' @examples\n#' x <- rnorm(100)\n#' bp <- bp_statistic(x)\n#' get_pvalue(bp$Test_statistic_U, 100)\n#'\nget_pvalue <- function(statistic_val, n, distribution = \"norm\", alternative = \"two.sided\", gen_num = 1e4) {\n r_samples <- switch(distribution,\n \"norm\" = lapply(rep(n, gen_num), rnorm),\n \"cauchy\" = lapply(rep(n, gen_num), rcauchy),\n \"logis\" = lapply(rep(n, gen_num), rlogis),\n \"laplace\" = lapply(rep(n, gen_num), rlaplace),\n \"lnorm\" = lapply(rep(n, gen_num), rlnorm),\n \"gumbel\" = lapply(rep(n, gen_num), rgumbel),\n \"extII\" = lapply(rep(n, gen_num), rextII)\n )\n statistics <- lapply(r_samples, get_main_bp_statistic, distribution = distribution, alternative=alternative)\n p.value <- mean(unlist(statistics) > statistic_val)\n return(p.value)\n}\n\n\n#' data investigation for outliers\n#'\n#' The procedure to find outliers and then check the goodness-of-fit with\n#' given distribution.\n#'\n#' @param data A given sample\n#' @export\n#' @examples\n#' investigate_sample(example1)\n#'\ninvestigate_sample <- function(data, alpha = 0.05, verbose = FALSE) {\n #require(evd)\n\n dist_list <- c(\"norm\", \"gumbel\", \"logis\", \"laplace\", \"cauchy\")#\n\n fit_list <- rep(list(1), length(dist_list))\n found_list <- c()\n number_list <- c()\n valid_dist <- \"\"\n\n for(i in 1:length(dist_list)) {\n bp <- bp_test(data, distribution = dist_list[i])\n found_list <- bp$found_outliers\n number_list <- bp$number_of_outliers\n x <- data[!bp$outlier]\n #ks <- ks.test(x, paste(\"p\", dist_list[i], sep=\"\"))\n ks <- ks_check(x, distribution = dist_list[i], verbose = verbose)\n ad <- ad_check(x, distribution = dist_list[i], verbose = verbose)\n\n if(!ad$rejected) {\n valid_dist <- dist_list[i];\n\n dist_n <- switch(valid_dist,\n norm = \"normal\",\n logis = \"logistic\",\n cauchy = \"cauchy\",\n laplace = \"laplace\",\n gumbel = \"gumbel\")\n cat(paste(\"\\n After checking the hypothesis about absence of outliers in \", dist_n, \" distribution,\\n\",\n \"the alternative \"))\n if(found_list) {\n cat(\" were accepted and \", number_list, \" outliers was identified.\\n\")\n cat(\"\\n After outliers removal in data, the goodness-of-fit hypothesis was checked:\\n\n the null hypothesis that data is from \", dist_n, \" distribution was accepted.\\n Cleaned sample could be used for futher investigation. \\n\")\n\n } else {\n cat(\" were rejected so no outliers was found.\\n\")\n cat(\"\\n The goodness-of-fit hypothesis was checked:\\n\n the null hypothesis that data is from \", dist_n, \" distribution was accepted.\\n Cleaned sample could be used for futher investigation. \\n\")\n }\n\n\n print(paste(\"KS test statistics U: \", round(ks$U, 2), \" with critical value: \", round(ks$critical, 2)))\n print(paste(\"AD test statistics A^2: \", round(ad$A2, 2), \" with critical value: \", round(ad$critical, 2)))\n\n break\n }\n }\n\n if (valid_dist == \"\") {\n cat(\"no distributions out of normal, cauchy, logistic, laplace does not fit the goodness-of-fit for given distributions after outliers removal.\")\n }\n\n\n}\n\n\nks_test <- function(x, distribution = \"norm\") {\n\n n <- length(x);\n distr <- switch(distribution,\n norm = pnorm,\n logis = plogis,\n cauchy = pcauchy,\n gumbel = pgumbel,\n extII = pextII,\n laplace = plaplace\n )\n x <- sort(x)\n\n va <- var(x)\n be <- sqrt(6 * va / pi^2);\n mu <- switch (distribution,\n norm = mean(x),\n gumbel = mean(x) - be * 0.5772,\n extII = mean(x) + be * 0.5772,\n logis = mean(x),\n cauchy = mean(x),\n laplace = mean(x)\n )\n\n sds <- switch (distribution,\n norm = sd(x),\n gumbel = be,\n extII = be,\n logis = sqrt(va * 3 / (pi^2)),\n cauchy = get_robust_estimates(x, distribution = distribution)$scale,\n laplace = sqrt(va/2)\n )\n\n U <- distr(x, mu, sds);\n Dp <- max((1:n) / n - U);\n Dm <- max(U - (1:n - 1) / n);\n D <- max(Dm, Dp);\n\n return(D);\n}\n\n\nks_check <- function(x, distribution = \"norm\", alpha = 0.05, verbose = FALSE, gen_num = 10000) {\n n <- length(x);\n ks <- ks_test(x, distribution = distribution);\n critical <- NA;\n\n if (alpha == 0.05) {\n critical <- switch(distribution,\n norm = exp(-0.195445 - 0.485438 * log(n)),\n logis = exp(-0.107282 - 0.486688 * log(n)),\n cauchy = 0.8966121,\n gumbel = 1.0834,\n laplace = exp(-0.024938 - 0.476576 * log(n))\n )\n\n } else {\n distr <- switch(distribution,\n norm = rnorm,\n logis = rlogis,\n cauchy = rcauchy,\n gumbel = rgumbel,\n laplace = rlaplace\n )\n\n sam <- lapply(rep(n, gen_num), distr);\n ks <- lapply(sam, ks_test, distribution);\n critical <- quantile(unlist(ks), 1 - alpha);\n }\n\n rejected <- FALSE;\n if (ks > critical) {\n if(verbose) {\n print(paste(\"KS: The null hypothesis that data fit \", distribution, \" is rejected. Distribution is not \", distribution))\n }\n rejected <- TRUE;\n } else {\n if(verbose) {\n print(paste(\"KS: The null hypothesis that data fit \", distribution ,\" was accepted.\"))\n }\n rejected <- FALSE;\n }\n\n return(list(rejected = rejected, U = ks, critical = critical))\n\n}\n\n\nad_test <- function(x, distribution = 'norm') {\n n <- length(x);\n x <- sort(x);\n f <- switch (distribution,\n norm = pnorm,\n gumbel = pgumbel,\n logis = plogis,\n cauchy = pcauchy,\n laplace = plaplace\n )\n #mu <- mean(x)\n va <- var(x)\n be <- sqrt(6 * va / pi^2);\n mu <- switch (distribution,\n norm = mean(x),\n gumbel = mean(x) - be * 0.5772,\n logis = mean(x),\n cauchy = mean(x),\n laplace = mean(x)\n )\n\n sds <- switch (distribution,\n norm = sd(x),\n gumbel = be,\n logis = sqrt(va * 3 / (pi^2)),\n cauchy = get_robust_estimates(x, distribution = distribution)$scale,\n laplace = sqrt(va/2)\n )\n log1 <- f(x, mu, sds);\n log2 <- f(rev(x), mu, sds);\n id <- 1:n;\n h <- (2*id - 1)*(log(log1) + log(1-log2))\n A <- -n - mean(h)\n\n return(A);\n}\n\n\n\nad_check <- function(x, distribution = \"norm\", alpha = 0.05, verbose = FALSE, gen_num = 10000) {\n n <- length(x);\n ks <- ad_test(x, distribution = distribution);\n critical <- NA;\n\n if (alpha == 0.05) {\n critical <- switch(distribution,\n norm = 0.7388575,\n logis = 0.8962129,\n cauchy = exp(-1.351995 + 1.056177 * log(n)),\n gumbel = 1.071733,\n laplace = 1.323736\n )\n\n } else {\n distr <- switch(distribution,\n norm = rnorm,\n logis = rlogis,\n cauchy = rcauchy,\n gumbel = rgumbel,\n laplace = rlaplace\n )\n\n sam <- lapply(rep(n, gen_num), distr);\n ks <- lapply(sam, ad_test, distribution);\n critical <- quantile(unlist(ks), 1 - alpha);\n }\n\n rejected <- FALSE;\n if (ks > critical) {\n if(verbose) {\n print(paste(\"AD: The null hypothesis that data fit \", distribution, \" is rejected. Distribution is not \", distribution))\n }\n rejected <- TRUE;\n } else {\n if(verbose) {\n print(paste(\"AD: The null hypothesis that data fit \", distribution ,\" was accepted.\"))\n }\n rejected <- FALSE;\n }\n\n return(list(rejected = rejected, A2 = ks, critical = critical))\n\n}\n\ndextII <- function(q, mu = 0, sigma = 1) {\n p <- -exp((q - mu)/sigma - exp((q - mu)/sigma))/sigma\n return(p)\n}\n\n\npextII <- function(q, mu = 0, sigma = 1) {\n p <- 1-exp(-exp((q-mu)/sigma))\n return(p)\n}\n\nqextII <- function(p, mu = 0, sigma = 1) {\n q<- mu + sigma * log(-log(1-p))\n return(q)\n}\n\nrextII <- function(n, mu = 0, sigma = 1) {\n r <- runif(n)\n q <- mu + sigma * log(-log(1-r))\n return(q)\n}\n\n#' outliersTests: A package containing statistical tests of identification\n#' unknown number of outliers\n#'\n#' Statistical test for various location-scale family distributions\n#' normal, logistic, cauchy, laplace to test does sample contain outliers and\n#' identifying those outliers in sample.\n#'\n#' @section outliersTests functions:\n#'\n#'\n#' \\code{\\link{bp_test}}: The calculation of the test statistic U and the p-value of the BP test for\n#' outliers and finding of observations declared by the test as outliers.\n#'\n#' \\code{\\link{investigate_sample}}: The procedure to find outliers and then visualize sample after outliers removal\n#' and calculating goodness-of-fit with packages fitdistrplus and flexsurv\n#'\n#' \\code{\\link{get_robust_estimates}}: The robust estimates of the scale (Q_n) and location parameters for\n#' location-scale families of distributions.\n#' Implemented distributions: normal, gumbel, cauchy, laplace, logistic\n#'\n#' @section outliersTests package data:\n#'\n#' \\code{\\link{example1}}: - example data\n#'\n#' \\code{\\link{example2}}: - example data\n#'\n#' @docType package\n#' @name outliersTests\nNULL\n", "meta": {"hexsha": "4302bc70c622d4a8dd1235cf364598a9693f40a5", "size": 19864, "ext": "r", "lang": "R", "max_stars_repo_path": "R/outliersTests.r", "max_stars_repo_name": "linas-p/outliersTests", "max_stars_repo_head_hexsha": "2f806908066d90b688ba06a40f12455f314d8119", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-04-23T02:25:42.000Z", "max_stars_repo_stars_event_max_datetime": "2021-04-23T02:25:42.000Z", "max_issues_repo_path": "R/outliersTests.r", "max_issues_repo_name": "linas-p/outliersTests", "max_issues_repo_head_hexsha": "2f806908066d90b688ba06a40f12455f314d8119", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/outliersTests.r", "max_forks_repo_name": "linas-p/outliersTests", "max_forks_repo_head_hexsha": "2f806908066d90b688ba06a40f12455f314d8119", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 28.9562682216, "max_line_length": 149, "alphanum_fraction": 0.5961035038, "num_tokens": 5942, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9073122163480667, "lm_q2_score": 0.8397339656668286, "lm_q1q2_score": 0.7619008855319216}} {"text": "## 2. Brief Recap ##\n\np_2 <- 1/6\np_odd <- 3/6\np_2_or_4 <- 2/6\n\n## 3. Updating Probabilities With New Information ##\n\np_3 <- 1/4\np_6 <- 0/4\np_odd <- 2/4\np_even <- 2/4\n\n## 4. Conditional Probability ##\n\np_december <- 1/3\np_31 <- 2/3\np_summer <- 0/3\np_ends_r <- 1/3\n\n## 5. Conditional Probability Formula ##\n\ncard_b <- 21\ncard_a_and_b <- 9\np_a_given_b <- card_a_and_b / card_b\n\n## 6. Example Walkthough ##\n\np_negative_given_non_hiv <- 6/30\nprint(p_negative_given_non_hiv)\n\n## 7. Conditional Probability Formula Revisited ##\n\np_premium_given_chrome <- 158/2762\np_basic_given_safari <- 274/1288\np_free_given_firefox <- 2103/2285\nmore_likely_premium <- 'Safari'", "meta": {"hexsha": "47f3b4d6b53e4d1e2b846c98e34f45f016e71f2a", "size": 655, "ext": "r", "lang": "R", "max_stars_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/4. Conditional Probability in R/1. Conditional Probability.r", "max_stars_repo_name": "MyArist/Dataquest", "max_stars_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 8, "max_stars_repo_stars_event_min_datetime": "2020-07-27T12:04:54.000Z", "max_stars_repo_stars_event_max_datetime": "2021-03-01T04:39:33.000Z", "max_issues_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/4. Conditional Probability in R/1. Conditional Probability.r", "max_issues_repo_name": "myarist/Dataquest", "max_issues_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/4. Conditional Probability in R/1. Conditional Probability.r", "max_forks_repo_name": "myarist/Dataquest", "max_forks_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 15, "max_forks_repo_forks_event_min_datetime": "2021-03-30T06:45:19.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-17T03:55:02.000Z", "avg_line_length": 17.7027027027, "max_line_length": 52, "alphanum_fraction": 0.7038167939, "num_tokens": 251, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9637799482964023, "lm_q2_score": 0.7905303112671294, "lm_q1q2_score": 0.7618972625197727}} {"text": "library(nimble)\nlibrary(igraph)\n\n# note: ~ and <- have meanings same as JAGS/BUGS\npumpCode <- nimbleCode({\n \n for (i in 1:N) {\n theta[i] ~ dgamma(alpha,beta)\n lambda[i] <- theta[i]*t[i]\n x[i] ~ dpois(lambda[i])\n }\n \n alpha ~ dexp(1.0)\n beta ~ dgamma(0.1,1.0)\n})\n\n# we need to divide the data (something that appears in the likelihood function) and\n# constants - two separate lists (warnings are issued if constants are included in data)\npumpConsts <- list(N = 10, t = c(94.3, 15.7, 62.9, 126, 5.24, 31.4, 1.05, 1.05, 2.1, 10.5))\n\npumpData <- list(x = c(5, 1, 5, 14, 3, 19, 1, 1, 4, 22))\n\n\npumpInits <- list(alpha = 1, beta = 1, theta = rep(0.1, pumpConsts$N))\n\n# call to set up model - compiles and checks for correct syntax\npump <- nimbleModel(code = pumpCode, name = \"pump\", constants = pumpConsts, data = pumpData, inits = pumpInits)\n\npump$getNodeNames()\n\npump$logProb_x\npump$lifted_d1_over_beta\n\n\npump$modelDef\n\npump$modelDef$BUGScode\n\n# Plot the graphs\npump$plotGraph()\n\npump$getDependencies(c(\"alpha\"))\npump$getDependencies(c(\"beta\"))\n\n# Check the way the samplers are applied.\npump$checkConjugacy()\n\n# generate from the distribution for theta (can use nimble to simulate data)\nset.seed(0)\nsimulate(pump,\"theta\") # takes current alpha and betas to create new thetas\nprint(pump$theta)\n\n# calculate the log probabilities (log posterior distribution)\npump$calculate(pump$getDependencies(c(\"theta\")))\n# can use function like you would use a function in R\n\n\nmcmc.out <- nimbleMCMC(code = pumpCode, constants = pumpConsts,\n data = pumpData, inits = pumpInits, \n monitors = c(\"alpha\",\"beta\",\"theta\"),\n nchains = 2, niter = 10000,thin=1,nburnin=2000,\n samplesAsCodaMCMC = TRUE,\n summary = TRUE, WAIC = TRUE)\n\n# Compile the model\nCpump <- compileNimble(pump,showCompilerOutput = TRUE)\n\n# smart to compile model first if you plan to run the model multiple times\n# as opposed to the code above, where it is compiled & run in the same function call\nmcmc.out <- nimbleMCMC(model=Cpump,\n monitors = c(\"alpha\",\"beta\",\"theta\"),\n nchains = 2, niter = 10000, thin=1,nburnin=2000,\n samplesAsCodaMCMC = TRUE,\n summary = TRUE, WAIC = TRUE)\n\nprint(str(mcmc.out))\nmcmc.out$summary\n\n\npumpConf <- configureMCMC(pump, print = TRUE)\n\n", "meta": {"hexsha": "b40e966afe7c6c518b10d6809ed00686bd4d1d69", "size": 2427, "ext": "r", "lang": "R", "max_stars_repo_path": "classes/intro_to_nimble/Lecture4a.r", "max_stars_repo_name": "emilysellinger/fish558", "max_stars_repo_head_hexsha": "8fd811c222d20446b0d0e3f1aee45ec708d51494", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "classes/intro_to_nimble/Lecture4a.r", "max_issues_repo_name": "emilysellinger/fish558", "max_issues_repo_head_hexsha": "8fd811c222d20446b0d0e3f1aee45ec708d51494", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "classes/intro_to_nimble/Lecture4a.r", "max_forks_repo_name": "emilysellinger/fish558", "max_forks_repo_head_hexsha": "8fd811c222d20446b0d0e3f1aee45ec708d51494", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 29.5975609756, "max_line_length": 111, "alphanum_fraction": 0.6460651009, "num_tokens": 729, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9005297834483232, "lm_q2_score": 0.845942439250491, "lm_q1q2_score": 0.7617963616279909}} {"text": "#!/usr/bin/env Rscript\n\n# Author : Bhishan Poudel\n# Date : Feb 9, 2016\n# Program : \n\n# setting working directory\nthis.dir <- dirname(parent.frame(2)$ofile)\nsetwd(this.dir)\n\n# Start device driver to save output\n#postscript(file=\"Pareto_distribution.eps\", height=14, width=8)\n\n# Define Pareto distributions for Salpeter IMF\ndpareto <- function(x, alpha=1.35, b=1) (alpha>0)*(b>0)^alpha / x^(alpha+1)\nppareto <- function(x, alpha=1.35, b=1) (x>b)*(1-((b>0)/x)^(alpha>0))\nqpareto <- function(u, alpha=1.35, b=1) (b>0)/(1-u)^(1/(alpha>0)) # 0 0\n zp = ResidueClassRing(Integer, mod)\n pzp = Polynomial(zp, f.variable)\n f = f.convert_to(pzp)\n end\n fact = f.factorize\n printf \"mod %2d: %-15s => %s\\n\", mod, f, fact\n end\n \n Px = Polynomial(Integer, \"x\")\n x = Px.var\n f = x**4 + 10*x**2 + 1\n #f = x**4 - 10*x**2 + 1\n show(f)\n Primes.new.each do |mod|\n break if mod > 100\n show(f, mod)\n end\n \n #mod 0: x^4 + 10x^2 + 1 => x^4 + 10x^2 + 1\n #mod 2: x^4 + 1 => (x + 1)^4\n #mod 3: x^4 + x^2 + 1 => (x + 2)^2(x + 1)^2\n #mod 5: x^4 + 1 => (x^2 + 3)(x^2 + 2)\n #mod 7: x^4 + 3x^2 + 1 => (x^2 + 4x + 6)(x^2 + 3x + 6)\n #mod 11: x^4 - x^2 + 1 => (x^2 + 5x + 1)(x^2 + 6x + 1)\n #mod 13: x^4 + 10x^2 + 1 => (x^2 - x + 12)(x^2 + x + 12)\n #mod 17: x^4 + 10x^2 + 1 => (x^2 + 3x + 1)(x^2 + 14x + 1)\n #mod 19: x^4 + 10x^2 + 1 => (x + 17)(x + 10)(x + 9)(x + 2)\n #mod 23: x^4 + 10x^2 + 1 => (x^2 + 6)(x^2 + 4)\n #mod 29: x^4 + 10x^2 + 1 => (x^2 + 21)(x^2 + 18)\n #mod 31: x^4 + 10x^2 + 1 => (x^2 + 22x + 30)(x^2 + 9x + 30)\n #mod 37: x^4 + 10x^2 + 1 => (x^2 + 32x + 36)(x^2 + 5x + 36)\n #mod 41: x^4 + 10x^2 + 1 => (x^2 + 19x + 1)(x^2 + 22x + 1)\n #mod 43: x^4 + 10x^2 + 1 => (x + 40)(x + 29)(x + 14)(x + 3)\n #mod 47: x^4 + 10x^2 + 1 => (x^2 + 32)(x^2 + 25)\n #mod 53: x^4 + 10x^2 + 1 => (x^2 + 41)(x^2 + 22)\n #mod 59: x^4 + 10x^2 + 1 => (x^2 + 13x + 1)(x^2 + 46x + 1)\n #mod 61: x^4 + 10x^2 + 1 => (x^2 + 54x + 60)(x^2 + 7x + 60)\n #mod 67: x^4 + 10x^2 + 1 => (x + 55)(x + 39)(x + 28)(x + 12)\n #mod 71: x^4 + 10x^2 + 1 => (x^2 + 43)(x^2 + 38)\n #mod 73: x^4 + 10x^2 + 1 => (x + 68)(x + 44)(x + 29)(x + 5)\n #mod 79: x^4 + 10x^2 + 1 => (x^2 + 64x + 78)(x^2 + 15x + 78)\n #mod 83: x^4 + 10x^2 + 1 => (x^2 + 18x + 1)(x^2 + 65x + 1)\n #mod 89: x^4 + 10x^2 + 1 => (x^2 + 9x + 1)(x^2 + 80x + 1)\n #mod 97: x^4 + 10x^2 + 1 => (x + 88)(x + 54)(x + 43)(x + 9)\n((<_|CONTENTS>))\n=end\n", "meta": {"hexsha": "54ed43c8645785bd994a7bb999fb963c7e1dce37", "size": 2028, "ext": "rd", "lang": "R", "max_stars_repo_path": "doc-ja/sample-factorize05.rb.v.rd", "max_stars_repo_name": "kunishi/algebra-ruby2", "max_stars_repo_head_hexsha": "ab8e3dce503bf59477b18bfc93d7cdf103507037", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 6, "max_stars_repo_stars_event_min_datetime": "2015-04-25T17:00:02.000Z", "max_stars_repo_stars_event_max_datetime": "2021-07-08T02:59:44.000Z", "max_issues_repo_path": "work/consider/algebra-0.72/doc/sample-factorize05.rb.v.rd", "max_issues_repo_name": "rubyworks/stick", "max_issues_repo_head_hexsha": "7e89d1a1ade1db085ddfecf19f774f0ba9bc2b70", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2017-03-10T14:02:43.000Z", "max_issues_repo_issues_event_max_datetime": "2017-03-10T14:02:43.000Z", "max_forks_repo_path": "doc/sample-factorize05.rb.v.rd", "max_forks_repo_name": "kunishi/algebra-ruby2", "max_forks_repo_head_hexsha": "ab8e3dce503bf59477b18bfc93d7cdf103507037", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 37.5555555556, "max_line_length": 64, "alphanum_fraction": 0.4033530572, "num_tokens": 1228, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9314625069680097, "lm_q2_score": 0.817574478416099, "lm_q1q2_score": 0.7615399732985225}} {"text": " \r\n\r\nybar = 390 # sample mean \r\nmu0 = 380 # hypothesized value \r\nsigma = 35.2 # population standard deviation \r\nn = 50 # sample size \r\nz = (ybar- mu0)/(sigma/sqrt(n))\r\nprint(z) # test statistic\r\n\r\n# We then compute the critical value at .01 significance level.\r\n# For alpha= .01, reject the null hypothesis if lies more than 2.33 \r\nalpha = .01 \r\n# critical value\r\nz.alpha = qnorm(1-alpha) \r\nprint(z.alpha)\r\nprint(\"the observed value of z < critical value, so we might be tempted to accept the null hypothesis\") \r\n# but Beta is not computed so there is insufficient evidence to reject the null hypothesis.\r\n# To reach a conclusion about whether to accept or reject H0, beta should be calculated.\r\n", "meta": {"hexsha": "f5bdb33c56256fe442bc11d13aa63ab7ece7ce59", "size": 750, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH5/EX5.7/Ex5_7.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH5/EX5.7/Ex5_7.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH5/EX5.7/Ex5_7.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 39.4736842105, "max_line_length": 106, "alphanum_fraction": 0.6626666667, "num_tokens": 184, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9632305307578324, "lm_q2_score": 0.7905303186696747, "lm_q1q2_score": 0.7614629384323491}} {"text": "## Dale W.R. Rosenthal, 2018\n## You are free to distribute and use this code so long as you attribute\n## it to me or cite the text.\n## The legal disclaimer in _A Quantitative Primer on Investments with R_\n## applies to this code. Use or distribution without these comment lines\n## is forbidden.\nlibrary(xts)\nlibrary(Quandl)\n\n# Grab constant-maturity US Treasuries\nust.tickers <- c(\"FRED/DGS3MO\", \"FRED/DGS2\", \"FRED/DGS5\", \"FRED/DGS10\", \"FRED/DGS30\")\nust <- Quandl(ust.tickers, type=\"xts\")/100\nust.colnames <- c(\"T3M\", \"T2Y\", \"T5Y\", \"T10Y\", \"T30Y\")\ncolnames(ust) <- ust.colnames\n\n# Grab inflation-indexed US Treasuries\ntips.yields <- c(\"TIPSY02\", \"TIPSY05\", \"TIPSY10\")\ntips <- Quandl(\"FED/TIPSY\", type=\"xts\")[,tips.yields]/100\n\n# expected inflation and CPI are only available monthly...\n# For expected inflation and CPI, only get the first column of data... like so:\nexinfl <- Quandl(\"FRBC/EXIN\", type=\"xts\")[,1]\ncolnames(exinfl) <- c(\"EXINFL\")\ncpi <- Quandl(\"FRBC/USINFL\", type=\"xts\")[,1]\ncolnames(cpi) <- c(\"CPI\")\n\n# Calculate inflation and surprise by projecting CPI for one year ahead\n# The surprise is how much the CPI differed from what was\n# projected a year earlier\ninfl.yoy <- log(cpi) - log(lag(cpi, 12))\ncolnames(infl.yoy) <- c(\"INFL.YOY\")\ninfl.mom <- (log(cpi) - log(lag(cpi)))*12\ncolnames(infl.mom) <- c(\"INFL.MOM\")\nexcpi <- cpi*(1+exinfl) # expected CPI in twelve months\ncpi.surprise <- log(cpi) - log(lag(excpi, 12)) # % CPI surprise\ncolnames(cpi.surprise) <- c(\"INFLSURP\")\n\n# combine the data and carry monthly observations forward\ninflation.tmp <- cbind(ust, tips, infl.yoy, infl.mom, exinfl, cpi, excpi, cpi.surprise)[\"1999/\"]\ninflation.data <- na.locf(inflation.tmp)\n\n# backward Hodrick-Prescott filter function\nhpbackfilter <- function(y, lambda) {\n n <- length(y)\n I <- diag(1, nrow = n)\n # build the curvature matrix\n K <- matrix(0, nrow=n-2, ncol=n)\n for (i in 1:(n-2)) {\n K[i,i:(i+2)] = c(1,-2,1)\n }\n # now invert and multiply by the data\n hat.matrix <- solve(I+2*lambda*t(K)%*%K)\n hat.matrix %*% y\n}\nlambda.monthly <- 129600 # for monthly data\ntau <- hpbackfilter(cpi, lambda.monthly)\n", "meta": {"hexsha": "725fde2048c56aa2be2f464c7f3c554282d22dac", "size": 2146, "ext": "r", "lang": "R", "max_stars_repo_path": "Quantitative Primer/samples/ch6-exercises.r", "max_stars_repo_name": "bmoretz/Quantitative-Investments", "max_stars_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 7, "max_stars_repo_stars_event_min_datetime": "2020-03-26T05:47:30.000Z", "max_stars_repo_stars_event_max_datetime": "2022-02-18T21:50:54.000Z", "max_issues_repo_path": "Quantitative Primer/samples/ch6-exercises.r", "max_issues_repo_name": "bmoretz/Quantitative-Investments", "max_issues_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Quantitative Primer/samples/ch6-exercises.r", "max_forks_repo_name": "bmoretz/Quantitative-Investments", "max_forks_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2020-11-03T09:23:54.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-18T21:50:55.000Z", "avg_line_length": 37.649122807, "max_line_length": 96, "alphanum_fraction": 0.6780055918, "num_tokens": 722, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9161096090086367, "lm_q2_score": 0.8311430478583168, "lm_q1q2_score": 0.7614181326037293}} {"text": "# likelihood ratio statistics for testing the significanse of added model parameters\n# and Akaike's An Information Criterion\n\n# input\n\nn.par.1<-91 # number of parameter in model 1\nn.par.2<-87 # number of parameter in model 2\nneg.like.1<- -175.477 # negative log likelihood, model 1 (taken from file sms.rep \"objective function (negative log likelihood):\" or from sms.par file \nneg.like.2<- -167.324 # negative log likelihood, model 2\n\n#################\n\n# likelihood ratio statistics for testing the significanse of a change in model parameters\n\nn.free<-abs(n.par.1-n.par.2)\n\nP.value<-1-pchisq(2*abs(neg.like.1-neg.like.2),n.free)\nP.value\n# a P.value <0.05 shows significant effect of changing the number of parameters\n\n##############################################\n#Akaike's An Information Criterion\n# Generic function calculating the Akaike information criterion for\n# one or several fitted model objects for which a log-likelihood\n# value can be obtained, according to the formula -2*log-likelihood\n# + k*npar, where npar represents the number of parameters in the\n# fitted model, and k = 2 for the usual AIC, or k = log(n) (n the\n# number of observations) for the so-called BIC or SBC (Schwarz's\n# Bayesian criterion).\n\nk<-2\nAIC1<-2*neg.like.1+k*n.par.1\nAIC1\n\nAIC2<-2*neg.like.2+k*n.par.2\nAIC2\nAIC1\n\n", "meta": {"hexsha": "1b9179a3411e0aee1a29c5d9dbbbc0940f94ec0e", "size": 1374, "ext": "r", "lang": "R", "max_stars_repo_path": "SMS_R_prog/r_prog_less_frequently_used/chi_2_test.r", "max_stars_repo_name": "ices-eg/wg_WGSAM", "max_stars_repo_head_hexsha": "d5f93c431d1ec6c2fb1f3929f63cd9e636fc258a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 5, "max_stars_repo_stars_event_min_datetime": "2018-09-28T11:13:54.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-28T08:40:03.000Z", "max_issues_repo_path": "SMS_R_prog/r_prog_less_frequently_used/chi_2_test.r", "max_issues_repo_name": "ices-eg/wg_WGSAM", "max_issues_repo_head_hexsha": "d5f93c431d1ec6c2fb1f3929f63cd9e636fc258a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "SMS_R_prog/r_prog_less_frequently_used/chi_2_test.r", "max_forks_repo_name": "ices-eg/wg_WGSAM", "max_forks_repo_head_hexsha": "d5f93c431d1ec6c2fb1f3929f63cd9e636fc258a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 35.2307692308, "max_line_length": 156, "alphanum_fraction": 0.6775836972, "num_tokens": 373, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9449947101574299, "lm_q2_score": 0.805632181981183, "lm_q1q2_score": 0.7613181503048059}} {"text": "######################################################################\n###\n### Hierarchilca clustering\n### https://www.datacamp.com/community/tutorials/hierarchical-clustering-R\n#######################################################################\n# Data Set Information:\n# The examined group comprised kernels belonging to three different varieties of wheat: Kama, Rosa and Canadian, 70 elements each, randomly selected for 
the experiment. High quality visualization of the internal kernel structure was detected using a soft X-ray technique. It is non-destructive and considerably cheaper than other more sophisticated imaging techniques like scanning microscopy or laser technology. The images were recorded on 13x18 cm X-ray KODAK plates. Studies were conducted using combine harvested wheat grain originating from experimental fields, explored at the Institute of Agrophysics of the Polish Academy of Sciences in Lublin. 
\n\n# Attribute Information:\n# To construct the data, seven geometric parameters of wheat kernels were measured: 
# 1. area A, 
# 2. perimeter P, 
# 3. compactness C = 4*pi*A/P^2, 
# 4. length of kernel, 
# 5. width of kernel, 
# 6. asymmetry coefficient 
# 7. length of kernel groove. 
\n\nrm(list=ls())\n## Libraries\nlibrary(cluster)\nlibrary(dendextend)\nlibrary(dplyr)\nlibrary(ggplot2)\n\n##\nWD = \"/Users/gianlucamastrantonio/Desktop/statistico/lavori/lezioni/DataSpace/2018/Lez9/\"\nsetwd(WD)\n\n\n# carichiamo i dati\nseeds_df <- read.csv(paste(WD,\"seeds_dataset.txt\",sep=\"\"),sep = '\\t',header = FALSE)\n# cambiamo i nomi\nfeature_name <- c('area','perimeter','compactness','length.of.kernel','width.of.kernal','asymmetry.coefficient','length.of.kernel.groove','type.of.seed')\ncolnames(seeds_df) <- feature_name\nstr(seeds_df)\nsummary(seeds_df)\n\n# eliminiamo gli NA\nfor(i in 1:ncol(seeds_df))\n{\n\tW = which(!is.na(seeds_df[,i]))\n\tseeds_df = seeds_df[W,]\n}\n\n\n\n# \"standardizziamo\" le variabili e salviamo la clusterizzazione\nseeds_label <- seeds_df$type.of.seed\nseeds_df$type.of.seed <- NULL\nstr(seeds_df)\nseeds_df_sc <- as.data.frame(scale(seeds_df))\nsummary(seeds_df_sc)\n\n# plots\nggplot(seeds_df_sc, aes(x=area, y = perimeter, color = factor(seeds_label))) + geom_point()\nggplot(seeds_df_sc, aes(x=area, y = compactness, color = factor(seeds_label))) + geom_point()\nggplot(seeds_df_sc, aes(x=area, y = length.of.kernel, color = factor(seeds_label))) + geom_point()\n\nplot(density(seeds_df_sc$area))\nplot(density(seeds_df_sc$perimeter))\nplot(density(seeds_df_sc$compactness))\n#...\n\n# calcoliamo la matrice distanza\ndist_mat <- dist(seeds_df_sc, method = 'euclidean')\n# stimiamo il modello\nhclust_avg <- hclust(dist_mat, method = 'average')\nplot(hclust_avg)\n# tagliamo il dendogramma con 3 clusters\ncut_avg <- cutree(hclust_avg, k = 3)\ntable(cut_avg,seeds_label)\n\n# qualche plot\nggplot(seeds_df_sc, aes(x=area, y = perimeter, color = factor(cut_avg))) + geom_point()\nggplot(seeds_df_sc, aes(x=area, y = compactness, color = factor(cut_avg))) + geom_point()\nggplot(seeds_df_sc, aes(x=area, y = length.of.kernel, color = factor(cut_avg))) + geom_point()\n\n\n# calcoliamo le varianze dentro i gruppi con un funzione\nwss <- function(d) {\n sum(scale(d, scale = FALSE)^2)\n}\nwrap <- function(i, hc, x) {\n cl <- cutree(hc, i)\n spl <- split(x, cl)\n wss <- sum(sapply(spl, wss))\n wss\n}\nres <- sapply(seq.int(1, 10), wrap, h = hclust_avg, x = seeds_df_sc)\n\nplot(1:10,res,type=\"b\", main=\"Total Within SS by Various K\",\n ylab=\"Average Total Within Sum of Squares\",\n xlab=\"Value of K\")\n\n\n\n# possiamo vedere i cluster che stiamo creando\nplot(hclust_avg)\nrect.hclust(hclust_avg , k = 3, border = 2:6)\nabline(h = 3, col = 'red')\n\n# un'latro modo di rappresentare i clusters\navg_dend_obj <- as.dendrogram(hclust_avg)\navg_col_dend <- color_branches(avg_dend_obj, h = 3)\nplot(avg_col_dend)\n\n\n# vediamo il numero di osservazione nei cluster\ncut_avg <- cutree(hclust_avg, k = 3)\nseeds_df_cl <- mutate(seeds_df, cluster = cut_avg)\ncount(seeds_df_cl,cluster)\n\n\nggplot(seeds_df_cl, aes(x=area, y = perimeter, color = factor(cluster))) + geom_point()\n\n# vediamo la silhouette\nD <- daisy(seeds_df_sc)\nk =3\nplot(silhouette(cutree(hclust_avg, k = k), D), col=1:8, border=NA)\n\n## potremmo vedere i risultati che si\n# ottengono con il k-means\n\n", "meta": {"hexsha": "5b5c739983d0a9481594a7f539677e1bd735489f", "size": 4230, "ext": "r", "lang": "R", "max_stars_repo_path": "theory/R_script_plus_data/Hierarchical.r", "max_stars_repo_name": "franec94/R-Script-Analyses", "max_stars_repo_head_hexsha": "a9c875759f63b63ceeeb7d44b98092dce075a7e1", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2020-07-04T06:36:25.000Z", "max_stars_repo_stars_event_max_datetime": "2020-07-04T06:36:25.000Z", "max_issues_repo_path": "theory/R_script_plus_data/Hierarchical.r", "max_issues_repo_name": "franec94/R-Script-Analyses", "max_issues_repo_head_hexsha": "a9c875759f63b63ceeeb7d44b98092dce075a7e1", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "theory/R_script_plus_data/Hierarchical.r", "max_forks_repo_name": "franec94/R-Script-Analyses", "max_forks_repo_head_hexsha": "a9c875759f63b63ceeeb7d44b98092dce075a7e1", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 35.8474576271, "max_line_length": 656, "alphanum_fraction": 0.7146572104, "num_tokens": 1226, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9019206844384595, "lm_q2_score": 0.8438951084436077, "lm_q1q2_score": 0.7611264538017267}} {"text": "#'@title calcHMFormFactor\n#'\n#'@description Calculate form factor (1+k_1) from the Holtrop & Mennen method.\n#'\n#'@param maxDraft Maximum summer load line draft (vector of numericals, m)\n#'@param lwl Waterline length (vector of numericals, m) (see \\code{\\link{calclwl}})\n#'@param breadth Moulded breadth (vector of numericals, m)\n#'@param maxDisplacement Maximum ship displacement (vector of numericals, m^3)\n#'@param Cp Prismatic coefficient (vector of numericals, dimensionless) (see \n#' \\code{\\link{calcCp}})\n#'@param Cstern Afterbody form coefficient:\n#'\\itemize{\\item V-shaped Hull = -10\n#' \\item U-Shaped Hull = 10\n#' \\item Normal Hull = 0 (default) }\n#' Can supply either a vector of numericals, a single number, or rely on the default\n#'@param lcb Longitudinal position of center of buoyancy (vector of numericals,\n#' see \\code{\\link{calclcb}})\n#'\n#'@return \\code{formFactor} (vector of numericals)\n#'\n#'@references\n#'Holtrop, J. and Mennen, G. G. J. 1982. \"An approximate power prediction\n#'method.\" International Shipbuilding Progress 29.\n#'\n#'Holtrop, J. and Mennen, G. G. J. 1984. \"A Statistical Re-Analysis of Resistance\n#'and Propulsion Data'.\n#'\n#'@seealso \\itemize{\n#'\\item \\code{\\link{calclwl}}\n#'\\item \\code{\\link{calcCp}}\n#'\\item \\code{\\link{calclcb}} }\n#'\n#'@family Holtrop-Mennen Calculations\n#'\n#'@examples\n#' calcHMFormFactor(c(13.57,11.49),c(218.75, 209.25),c(32.25,32.20),c(80097,52382.04),c(0.81,0.67))\n#' calcHMFormFactor(13.57,218.75,32.25,80097,0.81)\n#'\n#'@export\n\ncalcHMFormFactor<-function(maxDraft,lwl,breadth,maxDisplacement,Cp,Cstern=0,lcb=0){\n\n formFactor<-\n 0.93+0.487118*\n #c14\n (1+0.011*Cstern)*\n ((breadth/lwl)^1.06806)*\n ((maxDraft/lwl)^0.46106)*\n ( #L/Lr\n (1/(1-Cp+(0.06*Cp*-lcb)/(4*Cp-1))\n )^0.121563)*\n ((lwl^3/maxDisplacement)^0.36486)*((1-Cp)^-0.604247)\n\nreturn(formFactor)\n\n}\n\n", "meta": {"hexsha": "eb3548a06a959d030aae19b0bdfb31ad92f4f7fa", "size": 1876, "ext": "r", "lang": "R", "max_stars_repo_path": "ShipPowerModel/R/calcHMFormFactor.r", "max_stars_repo_name": "USEPA/Marine_Emissions_Tools", "max_stars_repo_head_hexsha": "28e12dc51acb5baafc460b1a9de35d355f3cc64f", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 7, "max_stars_repo_stars_event_min_datetime": "2020-05-13T17:14:11.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-26T18:47:39.000Z", "max_issues_repo_path": "ShipPowerModel/R/calcHMFormFactor.r", "max_issues_repo_name": "USEPA/Marine_Emissions_Tools", "max_issues_repo_head_hexsha": "28e12dc51acb5baafc460b1a9de35d355f3cc64f", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "ShipPowerModel/R/calcHMFormFactor.r", "max_forks_repo_name": "USEPA/Marine_Emissions_Tools", "max_forks_repo_head_hexsha": "28e12dc51acb5baafc460b1a9de35d355f3cc64f", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-09-08T15:55:06.000Z", "max_forks_repo_forks_event_max_datetime": "2021-09-08T15:55:06.000Z", "avg_line_length": 32.3448275862, "max_line_length": 99, "alphanum_fraction": 0.6791044776, "num_tokens": 650, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9658995723244553, "lm_q2_score": 0.7879311906630568, "lm_q1q2_score": 0.7610624000825454}} {"text": "#' Harmonic mean\n#'\n#' @description Calculates harmonic mean\n#'\n#' @param x numeric vector\n#'\n#' @return Harmonic mean\n#' @export\n#'\n#' @examples\n#'\n#' x <- rexp(100,.5)\n#'\n#' harmonic_mean(x)\n#'\n\nharmonic_mean <- function(x){\n\n if(sum(x == 0, na.rm = TRUE) > 0 ){\n warning(\"There is at least one value = 0 and that cause the harmonic mean to be 0.\")\n }\n\n 1/mean(1/x, na.rm = TRUE)\n\n}\n", "meta": {"hexsha": "2c1f6d486aa800fe01880a7ef439967293b09755", "size": 391, "ext": "r", "lang": "R", "max_stars_repo_path": "R/harmonic_mean.r", "max_stars_repo_name": "vbfelix/relper", "max_stars_repo_head_hexsha": "edb2f21087857eb4a3f44cf2af9292db632fe210", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 7, "max_stars_repo_stars_event_min_datetime": "2020-05-09T23:13:37.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-31T00:45:50.000Z", "max_issues_repo_path": "R/harmonic_mean.r", "max_issues_repo_name": "vbfelix/relper", "max_issues_repo_head_hexsha": "edb2f21087857eb4a3f44cf2af9292db632fe210", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/harmonic_mean.r", "max_forks_repo_name": "vbfelix/relper", "max_forks_repo_head_hexsha": "edb2f21087857eb4a3f44cf2af9292db632fe210", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2021-12-17T12:27:58.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-19T12:50:55.000Z", "avg_line_length": 15.0384615385, "max_line_length": 88, "alphanum_fraction": 0.5984654731, "num_tokens": 127, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.8872045937171068, "lm_q2_score": 0.8577681031721325, "lm_q1q2_score": 0.7610158014783251}} {"text": "findLargestprime <- function(x) {\n n <- 2\n while (x %% n != 0) {\n n <- n+1\n } \n\n if (n == x) {\n return (x)\n }\n return (findLargestprime(x/n))\n}\n\nl <- findLargestprime(600851475143)\nprint(l)", "meta": {"hexsha": "005cd8ca6d133a60a6154655069a7cac71decae9", "size": 220, "ext": "r", "lang": "R", "max_stars_repo_path": "R/Problem3.r", "max_stars_repo_name": "nuhfurkan/projectEuler", "max_stars_repo_head_hexsha": "f29ca583154b15bdbe527152a2df3909ed0d3332", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/Problem3.r", "max_issues_repo_name": "nuhfurkan/projectEuler", "max_issues_repo_head_hexsha": "f29ca583154b15bdbe527152a2df3909ed0d3332", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/Problem3.r", "max_forks_repo_name": "nuhfurkan/projectEuler", "max_forks_repo_head_hexsha": "f29ca583154b15bdbe527152a2df3909ed0d3332", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 15.7142857143, "max_line_length": 35, "alphanum_fraction": 0.4909090909, "num_tokens": 77, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9230391727723468, "lm_q2_score": 0.8244619350028205, "lm_q1q2_score": 0.7610106624672918}} {"text": "#Sign test se usa para decidir si una\n#distribucion binomial tiene la misma posibilidad\n#de exito de gallo\n\n'''\nA soft drink company has invented a new drink,\nand would like to find out if it will be as\npopular as the existing favorite drink. \nFor this purpose, its research department \narranges 18 participants for taste testing. \nEach participant tries both drinks in random \norder before giving his or her opinion.\n\nIt turns out that 5 of the participants like the\nnew drink better, and the rest prefer \nthe old one. At .05 significance level,\ncan we reject the notion that the two drinks are equally popular?\n'''\n\nbinom.test(5,18)\n\n'''\n\tExact binomial test\n\ndata: 5 and 18\nnumber of successes = 5, number of trials =\n18, p-value = 0.09625\nalternative hypothesis: true probability of success is not equal to 0.5\n95 percent confidence interval:\n 0.09694921 0.53480197\nsample estimates:\nprobability of success \n 0.2777778 \n\nDebido a que p-value es mayor a la significancia\naceptamos la hipotesis nula\n'''", "meta": {"hexsha": "ec5a5151ac9e9ace586babdbcc8dacfaefdfea49", "size": 1018, "ext": "r", "lang": "R", "max_stars_repo_path": "Parcial/5. Metodos no parametricos/SignTest.r", "max_stars_repo_name": "jchudb93/Exp-Numerica", "max_stars_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Parcial/5. Metodos no parametricos/SignTest.r", "max_issues_repo_name": "jchudb93/Exp-Numerica", "max_issues_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Parcial/5. Metodos no parametricos/SignTest.r", "max_forks_repo_name": "jchudb93/Exp-Numerica", "max_forks_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 27.5135135135, "max_line_length": 71, "alphanum_fraction": 0.7642436149, "num_tokens": 261, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9334308073258009, "lm_q2_score": 0.815232489352, "lm_q1q2_score": 0.7609631206940597}} {"text": "\ninstall.packages(\"plotly\")\nlibrary(plotly)\n\n\n# experimento completamente al azar \n\nx <- seq(0, 1, length=100)\nfd <- dunif(x)\n\nplot_ly(x = x , y = fd, type = 'scatter', mode='lines', fill = 'tozeroy')\n\n\n\nfp <- punif(x)\nplot_ly(x = x , y = fp, type = 'scatter', mode='lines', fill = 'tozeroy')\n\n\n\n#-------------------------------------------------\n# uniform\n# params specific minimum and maximum\n\n# dunif for density plot\nlimits <- seq(0,10,by=0.01)\nz <-dunif(x=limits,min=0,max=5)\nnames(z) <- limits\nplot(x=limits, y=z,type=\"l\",xlim=c(0,10))\n\n#punif for cumulative density (= tail probabilities)\nlimits <- seq(0,10,by=0.01)\nz <-punif(q=limits,min=0,max=5)\nnames(z) <- limits\nplot(x=limits, y=z,type=\"l\",xlim=c(0,10))\n\n#qunif for quantiles\nqunif(p=c(0.025,0.975),min=0,max=5)\n\n#runif for random data\nhist(runif(n=100,min=0,max=5))\nhist(runif(n=1000,min=0,max=5))\n#------------------------------------", "meta": {"hexsha": "3e87353d8ed7619501d2d9279dff02dbb60b5a3c", "size": 899, "ext": "r", "lang": "R", "max_stars_repo_path": "Distributions/d_uniform_discret.r", "max_stars_repo_name": "gcvalderrama/sta_foundations", "max_stars_repo_head_hexsha": "98f48fad5463a7c1ec17aad37e580f207cdbf9cf", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Distributions/d_uniform_discret.r", "max_issues_repo_name": "gcvalderrama/sta_foundations", "max_issues_repo_head_hexsha": "98f48fad5463a7c1ec17aad37e580f207cdbf9cf", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Distributions/d_uniform_discret.r", "max_forks_repo_name": "gcvalderrama/sta_foundations", "max_forks_repo_head_hexsha": "98f48fad5463a7c1ec17aad37e580f207cdbf9cf", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 21.4047619048, "max_line_length": 73, "alphanum_fraction": 0.5928809789, "num_tokens": 298, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9416541610257062, "lm_q2_score": 0.8080672158638528, "lm_q1q2_score": 0.7609198562066545}} {"text": "# https://baseballwithr.wordpress.com/2017/02/20/bayesian-learning-about-a-hitting-probability/\n\nlibrary('TeachBayes')\n\n# Construct df of plausible hitting probabilities\n\nbayes_df <- data.frame(P = seq(0.2, 0.34, by=0.01),\n Prior=rep(1/15, 15))\n\n# Player hits 100 times, getting 30 hits\n# Add column with likelihood of this outcome,\n# as a function of the hitting P\n\nbayes_df$Likelihood <- dbinom(30, size=100, prob=bayes_df$P)\n\n# Use bayesian_crank() function to compute posteriors\nbayes_df <- bayesian_crank(bayes_df)\n\n# Plot priors and posteriors\nprior_post_plot(bayes_df)\n\n# Use discint to find prob interval for P\n\ndiscint(select(bayes_df, P, Posterior), 0.6)\n\n# Investigate Joey Votto's 2016 batting probability\n\nnormal_prior <- normal.select(list(p=.5, x=.320), list(p=.1, x=.280))\n\nnormal_prior\n\nnormal_draw(c(0.320, 0.031))\n\n# Votto hit .326 in 556 AB's\n# SE = sqrt(.326 * (1 - .326) / 556) = 0.0199\n\nnormal_update(normal_prior, c(0.326, 0.0199))\n\nmany_normal_plots(list(c(0.32, 0.0312), c(0.324, 0.0168)))\n\nqnorm(c(0.05, 0.95), mean=.324, sd=0.0168)", "meta": {"hexsha": "954d3faac9e17b9858896fd9cff56bfd6651c69a", "size": 1081, "ext": "r", "lang": "R", "max_stars_repo_path": "baseball_data_r/bayesian_hitting_prob.r", "max_stars_repo_name": "KT12/Training", "max_stars_repo_head_hexsha": "ac4de382a1387ccfe51404eb3302cc518762a781", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-08-17T04:44:53.000Z", "max_stars_repo_stars_event_max_datetime": "2017-08-17T04:44:53.000Z", "max_issues_repo_path": "baseball_data_r/bayesian_hitting_prob.r", "max_issues_repo_name": "KT12/training", "max_issues_repo_head_hexsha": "ac4de382a1387ccfe51404eb3302cc518762a781", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "baseball_data_r/bayesian_hitting_prob.r", "max_forks_repo_name": "KT12/training", "max_forks_repo_head_hexsha": "ac4de382a1387ccfe51404eb3302cc518762a781", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.3658536585, "max_line_length": 95, "alphanum_fraction": 0.7058279371, "num_tokens": 363, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.947381042195331, "lm_q2_score": 0.8031737892899222, "lm_q1q2_score": 0.7609116215614598}} {"text": "library(dslabs)\nlibrary(tidyverse)\nlibrary(haven)\n\ngalton_heights <- read_dta('galton-stata11.dta')\nstr(galton_heights)\n\n#Getting the average of sons with whose fathers' height is around 72 inches\nconditional_avg <- galton_heights %>% filter(gender == \"M\", round(father) == 72) %>% summarize(avg = mean(height)) %>% .$avg\nconditional_avg\n\n#plot(father, son)\ngalton_heights %>% mutate(father_strata = factor(round(father))) %>% filter(gender == \"M\") %>% ggplot(aes(father_strata, height)) + geom_boxplot() + geom_point()\n\n#plotting conditional sons' height due to fathers' height\ngalton_heights %>% mutate(father = round(father)) %>% group_by(father) %>% filter(gender == \"M\") %>% summarise(son_conditional_avg = mean(height)) %>% ggplot(aes(father, son_conditional_avg)) + geom_point()\n\n#correlation\nr <- galton_heights %>% filter(gender == \"M\") %>% summarise(r = cor(father, height)) %>% .$r\n\n#plottoing the relation between heights and the correlation regression\ngalton_heights %>% mutate(father = round(father)) %>% group_by(father) %>% filter(gender == \"M\") %>% summarise(son = mean(height)) %>% mutate(z_father = scale(father), z_son = scale(son)) %>%\n ggplot(aes(z_father, z_son)) + geom_point() + geom_abline(intercept = 0, slope = r)\n\n#parameters of linear regression y = b + m*x\nmale <- galton_heights %>% filter(gender == \"M\")\nmu_x <- mean(galton_heights$father)\nmu_y <- mean(male$height)\ns_x <- sd(galton_heights$father)\ns_y <- sd(male$height)\nr <- cor(galton_heights$father, male$height)\nm <- r*s_y / s_x\nb <- mu_y - m*mu_x\n\n#plot\ngalton_heights %>% filter(gender == \"M\") %>% ggplot(aes(father, height)) + geom_point(alpha = 0.5) + geom_abline(intercept = b, slope = m)\n\n\n#Stratifying sons' height by the standardized fathers' height\ngalton_heights %>% filter(gender == \"M\") %>% mutate(z_father = round((father - mean(father))/sd(father))) %>% filter(z_father %in% -2:2) %>%\n ggplot() + stat_qq(aes(sample = height)) + facet_wrap(~z_father)\n\n#Variance \n#When two variables follow a bivariate normal distribution, the variation \n#explained can be calculated as 𝜌2×100 \nvari <- r^2\nvari\n\n#linear regression\nlm(height ~ father, data = male)\n\n#least squares estimate\nrss <- function(beta0, beta1, data) {\n resid <- male$height - (beta0 + beta1 * male$father)\n return(sum(resid^2))\n}\nbeta1 = seq(0, 1, len=nrow(galton_heights))\nresults <- data.frame(beta1 = beta1, rss = sapply(beta1, rss, beta0 = 25))\nresults %>% ggplot(aes(beta1, rss)) + geom_line() + geom_line(aes(beta1, rss), col=2)\n\n#Monte Carlo simulation\nB <- 1000\nN <- 100\nlse <- replicate(B, {\n sample_n(male, N, replace = TRUE) %>% \n lm(height ~ father, data = .) %>% .$coef \n})\n\nsample_n(male, N, replace = TRUE) %>% \n lm(male ~ father, data = .) %>% summary\n\nlse <- data.frame(beta_0 = lse[1,], beta_1 = lse[2,]) \nlse %>% summarize(cor(beta_0, beta_1))\n\nlibrary(gridExtra)\np1 <- lse %>% ggplot(aes(beta_0)) + geom_histogram(bins = 20, binwidth = 1, color = \"black\")\np2 <- lse %>% ggplot(aes(beta_1)) + geom_histogram(bins = 20, binwidth = 0.01, color = \"black\") \ngrid.arrange(p1, p2, ncol = 2) \n\n#If we standardize the father heights\nB <- 1000\nN <- 50\nlse <- replicate(B, {\n sample_n(male, N, replace = TRUE) %>%\n mutate(father = father - mean(father)) %>%\n lm(height ~ father, data = .) %>% .$coef \n})\n\ncor(lse[1,], lse[2,])\n\n#Drawing graphs with confidence interval and different ways to get the predictions\nmale %>% ggplot(aes(father, height)) + geom_point() +\n geom_smooth(method = \"lm\")\n\nmale %>% mutate(Y_hat = predict(lm(height ~ father, data = .))) %>%\n ggplot(aes(father, Y_hat)) + geom_line()\n\nfit <- male %>% lm(height ~ father, data = .)\nY_hat = predict(fit, se.fit = TRUE)\nnames(Y_hat)\n\nmodel <- lm(height ~ father, data = male)\npredictions <- predict(model, interval = c(\"confidence\"), level = 0.95)\ndata <- as_tibble(predictions) %>% bind_cols(father = male$father)\n\nggplot(data, aes(x = father, y = fit)) +\n geom_line(color = \"blue\", size = 1) + \n geom_ribbon(aes(ymin=lwr, ymax=upr), alpha=0.2) + \n geom_point(data = male, aes(x = father, y = height))\n\n ", "meta": {"hexsha": "d27c3cfb963627abb1c1338ec0c7ec3dd4865f2b", "size": 4070, "ext": "r", "lang": "R", "max_stars_repo_path": "Galton_heigths.r", "max_stars_repo_name": "wagnernoise/galton-heights-data-analysis", "max_stars_repo_head_hexsha": "3782b94eae657b424bd1c202a2d25d83cc692cc6", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Galton_heigths.r", "max_issues_repo_name": "wagnernoise/galton-heights-data-analysis", "max_issues_repo_head_hexsha": "3782b94eae657b424bd1c202a2d25d83cc692cc6", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Galton_heigths.r", "max_forks_repo_name": "wagnernoise/galton-heights-data-analysis", "max_forks_repo_head_hexsha": "3782b94eae657b424bd1c202a2d25d83cc692cc6", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 36.6666666667, "max_line_length": 206, "alphanum_fraction": 0.6697788698, "num_tokens": 1293, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.944176863577751, "lm_q2_score": 0.8056321866478979, "lm_q1q2_score": 0.7606592711864976}} {"text": "# Black-Scholes model: value function and some greeks\n# Dale Roberts (c) 2010\n\n# S = Asset price\n# K = Strike price\n# r = Risk-free rate\n# tau = Time to maturity\n# sigma = Volatility of asset price\n\nEPS <- 1./365. \n\nbscall.value <- function(S, K, tau, r, sigma) {\n d1 <- (log(S/K) + (r + 0.5*sigma^2)*tau)/(sigma*sqrt(tau))\n d2 <- d1 - sigma*sqrt(tau)\n if (tau < EPS) { # Small time to expiry\n return(max(S-K,0))\n } else {\n return(S*pnorm(d1) - K*exp(-r*(tau))*pnorm(d2))\n }\n}\n\nbsput.value <- function(S, K, tau, r, sigma) {\n d1 <- (log(S/K) + (r + 0.5*sigma^2)*tau)/(sigma*sqrt(tau))\n d2 <- d1 - sigma*sqrt(tau)\n if (tau < EPS) { # Small time to expiry\n return(max(K-S,0))\n } else {\n return(K*exp(-r*(tau))*pnorm(-d2) - S*pnorm(-d1))\n }\n}\n\nbscall.delta <- function(S, K, tau, r, sigma) {\n d1 <- (log(S/K) + (r + 0.5*sigma^2)*tau)/(sigma*sqrt(tau))\n if (tau < EPS) { # by hand for small time to expiry\n if (K-S < 0) {\n return(1.0)\n } else {\n return(0.0)\n }\n } else {\n return(pnorm(d1))\n }\n}\n\nbsput.delta <- function(S, K, tau, r, sigma) {\n d1 <- (log(S/K) + (r + 0.5*sigma^2)*tau)/(sigma*sqrt(tau))\n if (tau < EPS) { # by hand for small time to expiry\n if (K-S > 0) {\n return(-1.0)\n } else {\n return(0.0)\n }\n } else {\n return(pnorm(d1)-1)\n }\n}\n\nbscall.gamma <- function(S, K, tau, r, sigma) {\n d1 <- (log(S/K) + (r + 0.5*sigma^2)*tau)/(sigma*sqrt(tau))\n return(dnorm(d1)/(S*sigma*sqrt(tau)))\n}\n\nbscall.theta <- function(S, K, tau, r, sigma) {\n d1 <- (log(S/K) + (r + 0.5*sigma^2)*tau)/(sigma*sqrt(tau))\n d2 <- d1 - sigma*sqrt(tau)\n return(-S*dnorm(d1)*sigma/(2*sqrt(tau)) - r*K*exp(-r*tau)*pnorm(d2))\n}\n\nbsput.theta <- function(S, K, tau, r, sigma) {\n d1 <- (log(S/K) + (r + 0.5*sigma^2)*tau)/(sigma*sqrt(tau))\n d2 <- d1 - sigma*sqrt(tau)\n return(-S*dnorm(d1)*sigma/(2*sqrt(tau)) + r*K*exp(-r*tau)*pnorm(-d2))\n}\n\nbscall.vega <- function(S, K, tau, r, sigma) {\n d1 <- (log(S/K) + (r + 0.5*sigma^2)*tau)/(sigma*sqrt(tau))\n return(S*sqrt(tau)*dnorm(d1))\n}\n\nbscall.rho <- function(S, K, tau, r, sigma) {\n d1 <- (log(S/K) + (r + 0.5*sigma^2)*tau)/(sigma*sqrt(tau))\n d2 <- d1 - sigma*sqrt(tau)\n return(K*tau*exp(-r*tau)*pnorm(d2))\n}\n\nbsput.rho <- function(S, K, tau, r, sigma) {\n d1 <- (log(S/K) + (r + 0.5*sigma^2)*tau)/(sigma*sqrt(tau))\n d2 <- d1 - sigma*sqrt(tau)\n return(-K*tau*exp(-r*tau)*pnorm(-d2))\n}\n", "meta": {"hexsha": "6394c148c0fa14e1610bb09a45173c3f7f333d0a", "size": 2393, "ext": "r", "lang": "R", "max_stars_repo_path": "black-scholes.r", "max_stars_repo_name": "Richard-L-Johnson/black-scholes-R", "max_stars_repo_head_hexsha": "654ed90aef632ec2717e60f19d426ec9e784bf44", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 35, "max_stars_repo_stars_event_min_datetime": "2015-03-12T00:46:19.000Z", "max_stars_repo_stars_event_max_datetime": "2021-07-07T02:44:51.000Z", "max_issues_repo_path": "black-scholes.r", "max_issues_repo_name": "Richard-L-Johnson/black-scholes-R", "max_issues_repo_head_hexsha": "654ed90aef632ec2717e60f19d426ec9e784bf44", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "black-scholes.r", "max_forks_repo_name": "Richard-L-Johnson/black-scholes-R", "max_forks_repo_head_hexsha": "654ed90aef632ec2717e60f19d426ec9e784bf44", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 20, "max_forks_repo_forks_event_min_datetime": "2015-01-17T15:19:22.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-22T07:39:25.000Z", "avg_line_length": 26.2967032967, "max_line_length": 71, "alphanum_fraction": 0.5503552027, "num_tokens": 977, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9496693688269985, "lm_q2_score": 0.8006920020959544, "lm_q1q2_score": 0.7603926682552907}} {"text": "library(deSolve)\nlibrary(ggplot2)\nlibrary(reshape2)\n\n\nm<-5 #Number of risk groups\nbeta<-0.0016*c(0,3,10,60,100)%*%t(c(0,3,10,60,100)) #Matrix of transmission rates between to risk group i (rows) from risk group j (columns)\ngamma<-rep(0.2,m) #Vector of recovery rate per risk group \nn<-c(0.06,0.31,0.52,0.08,0.03) #Vector of proportion of the population that are in each risk group\nx<-c(0.0,0.0,0.0,0.0,1e-5) #Vector of initial proportions of the population that are both infectious and in each risk group\nMaxTime<-30 #Number of years\n\nsis_ode <- function(times,x,parms){\n with(as.list(c(parms,x)),{\n # ODEs\n I<-matrix(x[1:m],nrow=m,ncol=1)\n dI<-+(beta%*%I)*(n-I)-gamma*I\n list(c(dI))\n })\n}\n\ntimes<-seq(0,MaxTime,1)\nparms<-list(beta=beta,gamma=gamma,n=n,m=m)\nsis_out <- as.data.frame(lsoda(x,times,sis_ode,parms))\n\nsis_out_long <- melt(sis_out,\"time\") #Collapse dataset from \"wide\" to \"long\" format for plotting\nggplot(sis_out_long,aes(x=time,y=value,colour=variable,group=variable)) +\n geom_line(lwd=2) + labs(x=\"Time (Years)\",y=\"Proportion of Population\",color=\"Risk Group\")\n", "meta": {"hexsha": "bd9160e59509406f78db6975217875e49e255cf6", "size": 1094, "ext": "r", "lang": "R", "max_stars_repo_path": "models/keeling_rohani_2008/program_3_2_sis.r", "max_stars_repo_name": "epimodels/epicookbook", "max_stars_repo_head_hexsha": "496088ddc8fc913505d92877e0a687c81976c8f2", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "models/keeling_rohani_2008/program_3_2_sis.r", "max_issues_repo_name": "epimodels/epicookbook", "max_issues_repo_head_hexsha": "496088ddc8fc913505d92877e0a687c81976c8f2", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "models/keeling_rohani_2008/program_3_2_sis.r", "max_forks_repo_name": "epimodels/epicookbook", "max_forks_repo_head_hexsha": "496088ddc8fc913505d92877e0a687c81976c8f2", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2020-10-10T12:46:31.000Z", "max_forks_repo_forks_event_max_datetime": "2020-10-10T12:46:31.000Z", "avg_line_length": 37.724137931, "max_line_length": 140, "alphanum_fraction": 0.7001828154, "num_tokens": 379, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.949669363129097, "lm_q2_score": 0.8006919997179627, "lm_q1q2_score": 0.7603926614347207}} {"text": "library(pomp)\n\n## Fake data\n\nN <- 500\nT <- 60\nsteps <- 7\nh <- 1 / steps\nsigma <- 10\n\npars_true <- c(R0 = 3.0, \t# new infected people per infected person\n \t\tr = 0.1, \t# recovery rate\n \t\tsigma = 5,\t# observation error intensity\n \t\tI0 = 5)\t\t# initial condition, number of infected people\n\nB <- pars_true['R0'] * pars_true['r'] / N\n \nodeout <- matrix(NA, nrow = (T+1), ncol = 3)\nodeout[1,] <- c(N - pars_true['I0'], pars_true['I0'],0)\ncolnames(odeout) <- c(\"S\", \"I\", \"R\")\n\nS <- odeout[1,1]\nI <- odeout[1,2]\nR <- odeout[1,3]\nR0 <- pars_true['R0']\nr <- pars_true['r']\n\nfor (i in 1:(T*steps)) {\n\n dS <- - B*S*I\n dI <- B*S*I - r*I\n dR <- r*I\n\n S <- S + h*dS;\n I <- I + h*dI;\n R <- R + h*dR; \n\n if (i %% 7 == 0)\n \todeout[(i/7) + 1,] = c(S, I, R)\n\n}\n\ninfec_counts_raw <- odeout[,'I'] + rnorm(T+1, 0, sigma)\ninfec_counts <- ifelse(infec_counts_raw < 0, 0, infec_counts_raw)\n\ndata <- data.frame(time = 0:T, y = infec_counts)\n\n\n\nsir_step <- Csnippet(\"\n\tdouble dS = - (R0*r/500.0)*S*I;\n\tdouble dI = (R0*r/500.0)*S*I - r*I;\n\tdouble dR = r*I;\n\tS += dt*dS;\n\tI += dt*dI;\n\tR += dt*dR;\n\")\n\nsir_init <- Csnippet(\"\n\tS = 500.0 - I0;\n\tI = I0;\n\tR = 0;\n\")\n\ndmeas <- Csnippet(\"\n \tlik = dnorm(y, I, sigma, give_log);\n\")\n\nrmeas <- Csnippet(\"\n y = rnorm(I, sigma);\n\")\n\nsir <- pomp(data = data,\n time = \"time\",\n t0 = 0,\n initializer = sir_init,\n rprocess = euler.sim(step.fun = sir_step,\n delta.t = 1.0/steps),\n dmeasure = dmeas,\n rmeasure = rmeas,\n statenames = c(\"S\",\"I\",\"R\"),\n paramnames = c(\"R0\",\"r\",\"I0\",\"sigma\"))\n\nsimStates <- simulate(sir,nsim=1,params=c(R0 = 3.0, r = 0.1, I0 = 5.0, sigma = 10.0),\n states = TRUE, obvs = TRUE, as = TRUE)\n\nm1 <- mif2(sir,\n\t Nmif = 50,\n\t start = c(R0 = 3.0, r = 0.1, I0 = 5.0, sigma = 10.0),\n\t rw.sd = rw.sd(R0 = 0.3, r = 0.01, I0 = 0.5, sigma = 1.0,\n\t cooling.fraction.50 = 0.95,\n\t Np = 1000\n\t )\n\nplot(m1)\n", "meta": {"hexsha": "23c93506dd6b72401d3d0a2f8f61623a0aeacd0d", "size": 2044, "ext": "r", "lang": "R", "max_stars_repo_path": "code/pomp/pompsir.r", "max_stars_repo_name": "dbarrows/epidemic-forecasting", "max_stars_repo_head_hexsha": "a0865fa20c992dc4159e79bb332500e3ff2357ae", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "code/pomp/pompsir.r", "max_issues_repo_name": "dbarrows/epidemic-forecasting", "max_issues_repo_head_hexsha": "a0865fa20c992dc4159e79bb332500e3ff2357ae", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "code/pomp/pompsir.r", "max_forks_repo_name": "dbarrows/epidemic-forecasting", "max_forks_repo_head_hexsha": "a0865fa20c992dc4159e79bb332500e3ff2357ae", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 21.2916666667, "max_line_length": 85, "alphanum_fraction": 0.4902152642, "num_tokens": 790, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9273632956467158, "lm_q2_score": 0.8198933337131076, "lm_q1q2_score": 0.76033898403096}} {"text": "#' @export\n#'\n#' @title Agresti-Coull adjustment to binomial proportion\n#'\n#' @description Applies the Agresti and Coull (1998) adjustment\n#' to an observed number of 'successes' out of a number of 'trials'.\n#'\n#' @param x The number of 'successes' (an integer vector)\n#'\n#' @param n The number of 'trials' (an integer vector)\n#'\n#' @param conf Confidence interval level (a scalar between 0.5 and 1)\n#'\n#' @details\n#' The Agresti-Coull adjusted point estimate of a binomial proportion\n#' is,\n#' \\deqn{phat = (x+(z^2)/2) / (n+z^2)}\n#' where \\code{z} is the \\code{(1-(1-conf)/2)} quantile of a standard\n#' normal distribution. This point estimator was actually proposed by\n#' Brown et al. (2001) but named for Agresti and Coull because the latter\n#' discussed performance of the confidence interval under the\n#' special case of \\code{conf = 0.95} (i.e., \\code{z = 1.96}).\n#'\n#' The estimated standard error of the Agresti-Coull adjusted proportion\n#' is,\n#' \\deqn{se = sqrt( phat*(1-phat) / (n+z^2)).}\n#'\n#' The Agresti-Coull confidence interval is,\n#' \\deqn{phat +- z*se.}\n#'\n#' The Agresti-Coull confidence interval has\n#' excellent coverage for ratios between\n#' approximately 2% and 98%. For ratios between 0% and 2% (and 98% and 100%)\n#' interval coverage\n#' is too high (i.e., coverage exceeds \\code{conf} substantially).\n#' The Agresti-Coull point estimator is biased high except when true p = 0.5.\n#' Simulations by the author of this routine suggest bias\n#' in the point estimate is <10% for true p's between approximately\n#' 0.15 and 0.85. For ratios between 0 and 0.02 (and 0.98 and 1), bias\n#' in the point estimate can exceed 100%, but these are small (and large)\n#' ratios so percent bias is sensitive to small changes. The author of\n#' this routine is not aware of any studies of the variance estimator.\n#'\n#'\n#'\n#'\n#' @return A data frame containing the Agresti-Coull adjusted proportion,\n#' standard error, and confidence limits. The data frame has the\n#' following columns:\n#' \\enumerate{\n#' \\item \\code{phat} : the Agresti-Coull adjusted point estimates.\n#' \\item \\code{se.phat} : the Agresti-Coull estimated standard\n#' error of the point estimates \\code{phat}.\n#' \\item \\code{ll.phat} : the lower limit of a \\code{100*(1-(1-conf)/2)}%\n#' confidence interval for \\code{phat}.\n#' \\item \\code{ul.phat} : the upper limit of a \\code{100*(1-(1-conf)/2)}%\n#' confidence interval for \\code{phat}.\n#' }\n#'\n#' @author Trent McDonald\n#'\n#' @references\n#' Agresti, A. and B. A. Coull. 1998. Approximate is Better than\n#' \"Exact\" for Interval Estimation of Binomial Proportions.\n#' The American Statistician 52: 119:126.\n#'\n#' Brown, L. D., T. T. Cai, and A. DasGupta. 2001. Interval Estimation\n#' for a Binomial Proportion. Statistical Science 16:101-133.\n#'\n#' @seealso \\code{\\link{bayesPhat}}\n#'\n#' @examples\n#' agrestiCoullPhat(0:5, 100)\n#'\n#' # Simulation: point est bias and ci coverage\n#' trueP <- 0.01\n#' n <- 1000\n#' x <- rbinom( 1000, n, trueP)\n#' agPhat <- agrestiCoullPhat( x, n )\n#' muAG <- mean(agPhat$phat)\n#' covAG <- mean(agPhat$ll.phat <= trueP & trueP <= agPhat$ul.phat)\n#' agStats <- c(mean=muAG,\n#' relBias = abs(muAG-trueP)/trueP),\n#' coverage = covAG)\n#'\nagrestiCoullPhat <- function(x,n,conf=.9){\n z <- qnorm(1-(1-conf)/2,0,1)\n x <- x + z^2/2\n n <- n + z^2\n phat <- x / n\n\n se <- sqrt(phat*(1-phat)/n)\n\n ll <- phat - z*se\n ul <- phat + z*se\n\n data.frame(phat=phat, se.phat=se , ll.phat=ll, ul.phat=ul)\n}\n", "meta": {"hexsha": "372f4142a29778179e43ceee7ccdf8e6bf3c9881", "size": 3483, "ext": "r", "lang": "R", "max_stars_repo_path": "R/agrestiCoullPhat.r", "max_stars_repo_name": "tmcd82070/EoAR", "max_stars_repo_head_hexsha": "30bdd48e88046332fdb1c97d55fb9a6a1a983e06", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/agrestiCoullPhat.r", "max_issues_repo_name": "tmcd82070/EoAR", "max_issues_repo_head_hexsha": "30bdd48e88046332fdb1c97d55fb9a6a1a983e06", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/agrestiCoullPhat.r", "max_forks_repo_name": "tmcd82070/EoAR", "max_forks_repo_head_hexsha": "30bdd48e88046332fdb1c97d55fb9a6a1a983e06", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 35.1818181818, "max_line_length": 77, "alphanum_fraction": 0.6686764284, "num_tokens": 1138, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9273632896242073, "lm_q2_score": 0.8198933271118221, "lm_q1q2_score": 0.7603389729713556}} {"text": "## Dale W.R. Rosenthal, 2018\n## You are free to distribute and use this code so long as you attribute\n## it to me or cite the text.\n## The legal disclaimer in _A Quantitative Primer on Investments with R_\n## applies to this code. Use or distribution without these comment lines\n## is forbidden.\n\n## example of gamma GLM fit\nlibrary(MASS)\ntypes <- rbinom(100, 1, 0.6) # create types (0 or 1)\ntimes <- rgamma(100, 3, 0.2+0.1*types) # gamma r.v.s w/rate 0.2 (0.3 for types==1)\nmodel.fit <- glm(times ~ types, family=Gamma())\nsummary(model.fit) # show linear model for 1/mu = rate/m = rate/3\n## moment estimator of m, preferred by McCullagh and Nelder\nm.hat1 <- 1/summary(model.fit)$dispersion\n## common estimator of m\nm.hat2 <- summary(model.fit)$df.residual/summary(model.fit)$deviance\n## MLE estimator of m, implemented in MASS\nm.hat3 <- gamma.shape(model.fit)\n\n## example of survival analysis\n## suppose bonds mature at 15 years so times > 15 are censored\nlibrary(survival)\nlibrary(flexsurv)\ndefaulted <- times < 15 # TRUE => data not censored\ntimes.censored <- pmin(times, 15)\n\n## Fit gamma parameters\n## Note that covariate coefficients are modeling rate\n## anc (ancillary) parameter allows modeling shape parameter\nmodel.fit <- flexsurvreg(Surv(times, defaulted) ~ types, dist=\"gamma\")\nmodel.fit # show parameter estimates\n", "meta": {"hexsha": "87a37be5959bb8ac16987886d717d4a3c039bc50", "size": 1332, "ext": "r", "lang": "R", "max_stars_repo_path": "Quantitative Primer/samples/ch22-default-intensity-models.r", "max_stars_repo_name": "bmoretz/Quantitative-Investments", "max_stars_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 7, "max_stars_repo_stars_event_min_datetime": "2020-03-26T05:47:30.000Z", "max_stars_repo_stars_event_max_datetime": "2022-02-18T21:50:54.000Z", "max_issues_repo_path": "Quantitative Primer/samples/ch22-default-intensity-models.r", "max_issues_repo_name": "bmoretz/Quantitative-Investments", "max_issues_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Quantitative Primer/samples/ch22-default-intensity-models.r", "max_forks_repo_name": "bmoretz/Quantitative-Investments", "max_forks_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2020-11-03T09:23:54.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-18T21:50:55.000Z", "avg_line_length": 40.3636363636, "max_line_length": 82, "alphanum_fraction": 0.7282282282, "num_tokens": 378, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.938124016006303, "lm_q2_score": 0.8104789063814616, "lm_q1q2_score": 0.7603297265429733}} {"text": "# Regression estimation.\n# This R script contains functions for the calculation of\n# the regression estimation known form survey sampling in\n# statistics.\n# Joshua Simon, 17.02.2020.\n\n\nreg_estimation <- function(N, n, xu_mean, xk_sum, yk_sum, \n xk_squared_sum, yk_squared_sum, xk_yk_sum) {\n #' Functions takes sample values as input arguments to\n #' calculate different estimators. All results are returned\n #' as terminal output. Mean estimates and variance estimates\n #' are also returned as a matrix.\n sx_squared <- 1/(n-1) * (xk_squared_sum - n * (xk_sum/n)^2)\n sy_squared <- 1/(n-1) * (yk_squared_sum - n * (yk_sum/n)^2)\n sxy <- 1/(n-1) * (xk_yk_sum - n * (xk_sum/n) * (yk_sum/n))\n r_squared <- sxy^2/(sx_squared * sy_squared)\n \n # Regression estimators.\n bx <- sxy/sx_squared\n y_reg <- yk_sum/n + bx * (xu_mean - (xk_sum/n))\n t_reg <- y_reg * N\n var_y_reg <- (1/n - 1/N) * sy_squared * (1 - r_squared)\n \n # Difference estimators.\n y_diff <- yk_sum/n - xk_sum/n + xu_mean\n t_diff <- N * y_diff\n var_y_diff <- (1/n - 1/N) * (sx_squared + sy_squared - 2 * sxy)\n \n # Ratio estimators.\n y_ra <- (yk_sum/n) / (xk_sum/n) * xu_mean\n t_ra <- N * y_ra\n r_head <- (yk_sum/n) / (xk_sum/n)\n approx_var_y_ra <- (1/n - 1/N) * \n (sy_squared + r_head^2 * sx_squared - 2 * r_head * sxy)\n \n # Output.\n print(paste(\"sx_squared:\", sx_squared))\n print(paste(\"sy_squared:\", sy_squared))\n print(paste(\"sxy:\", sxy))\n print(paste(\"r_squared:\", r_squared))\n print(\"\")\n print(\"----- Regression estimation -----\")\n print(paste(\"bx:\", bx))\n print(paste(\"y_reg:\", y_reg))\n print(paste(\"t_reg:\", t_reg))\n print(paste(\"var(y_reg):\", var_y_reg))\n print(\"\")\n print(\"----- Difference estimation -----\")\n print(paste(\"y_diff:\", y_diff))\n print(paste(\"t_diff:\", t_diff))\n print(paste(\"var_y_diff:\", var_y_diff))\n print(\"\")\n print(\"----- Ratio estimation -----\")\n print(paste(\"y_ra:\", y_ra))\n print(paste(\"t_ra:\", t_ra))\n print(paste(\"r_head:\", r_head))\n print(paste(\"approx_var(y_ra):\", approx_var_y_ra))\n \n return(matrix(c(y_reg, y_diff, y_ra, \n var_y_reg, var_y_diff, approx_var_y_ra),\n nrow = 3, ncol = 2))\n}\n\n\nci_estimation <- function(alpha, n, y_mean, var__) {\n #' Calculates the confidence interval (CI) of given estimations.\n ci_lower <- y_mean - qt(1 - alpha/2, n) * sqrt(var__)\n ci_upper <- y_mean + qt(1 - alpha/2, n) * sqrt(var__)\n \n print(paste0(\"CI: [\", ci_lower, \" ,\", ci_upper, \"]\"))\n}\n\n# ----- Main program. -----\n# Set values.\nN <- 5000\nn <- 500\nxu_mean <- 121.2\nxk_sum <- 60e3\nyk_sum <- 65e3\nxk_squared_sum <- 8.5e6\nyk_squared_sum <- 10.25e6\nxk_yk_sum <- 9.1e6\n\n# Call functions.\nestimators <- reg_estimation(N, n, xu_mean, xk_sum, yk_sum, \n xk_squared_sum, yk_squared_sum, xk_yk_sum)\n\nalpha <- 0.05\n# CI for regression estimation.\nci_estimation(alpha, n, estimators[1,1], estimators[1,2])\n\n# CI for difference estimation.\nci_estimation(alpha, n, estimators[2,1], estimators[2,2])\n\n# CI for ratio estimation.\nci_estimation(alpha, n, estimators[3,1], estimators[3,2])\n", "meta": {"hexsha": "b42ea0200dee59e3e273265a36ed4c1641fdfb56", "size": 3069, "ext": "r", "lang": "R", "max_stars_repo_path": "Regression Estimation/regression_estimation.r", "max_stars_repo_name": "JoshuaSimon/University-Projects", "max_stars_repo_head_hexsha": "9d2e9c7ace3725acea7242bd69826349ef97b63f", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Regression Estimation/regression_estimation.r", "max_issues_repo_name": "JoshuaSimon/University-Projects", "max_issues_repo_head_hexsha": "9d2e9c7ace3725acea7242bd69826349ef97b63f", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Regression Estimation/regression_estimation.r", "max_forks_repo_name": "JoshuaSimon/University-Projects", "max_forks_repo_head_hexsha": "9d2e9c7ace3725acea7242bd69826349ef97b63f", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 31.3163265306, "max_line_length": 66, "alphanum_fraction": 0.642228739, "num_tokens": 1008, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9353465098415278, "lm_q2_score": 0.8128673269042767, "lm_q1q2_score": 0.7603126171841273}} {"text": "# Example : 2 Chapter : 9.2 Page No: 475\n# Norm of diagonal matrix\nA<-matrix(c(2,0,0,3),ncol=2)\nprint(\"The norm of the diagonal matrix is its largest entry\")\nprint(A[2,2])\nprint(\"Largest eigen value and norm are equal for this matrix\")\nlambdamax<-eigen(A)$values[1]\nprint(lambdamax)\nprint(\"Eigen vectors of this matrix are\")\nev<-round(eigen(A)$vectors)\nprint(ev)\n", "meta": {"hexsha": "df06d5b6db326cbdddf3bbf0293a187ac3d88153", "size": 369, "ext": "r", "lang": "R", "max_stars_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH9/EX9.2.2/Ex9.2_2.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH9/EX9.2.2/Ex9.2_2.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH9/EX9.2.2/Ex9.2_2.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 30.75, "max_line_length": 63, "alphanum_fraction": 0.7154471545, "num_tokens": 118, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9196425267730007, "lm_q2_score": 0.8267117898012104, "lm_q1q2_score": 0.760279319285815}} {"text": "#ML in 180 Minutes group/self exercise...\n\n#Download training design matrix and labels \nA <- read.csv(url(\"https://raw.githubusercontent.com/yoninazarathy/MathematicalEngineeringDeepLearning/master/ML180Minutes/A_3vs8_matrix_train.csv\"))\ny <- read.csv(url(\"https://raw.githubusercontent.com/yoninazarathy/MathematicalEngineeringDeepLearning/master/ML180Minutes/y_3vs8_vector_train.csv\"))\n\n#Download testing design matrix (each row is an image) for the digit \"3\" (positive)\nA3test <- read.csv(url(\"https://raw.githubusercontent.com/yoninazarathy/MathematicalEngineeringDeepLearning/master/ML180Minutes/A_3_test.csv\"))\n\n#Download testing design matrix (each row is an image) for the digit \"8\" (negative)\nA8test <- read.csv(url(\"https://raw.githubusercontent.com/yoninazarathy/MathematicalEngineeringDeepLearning/master/ML180Minutes/A_8_test.csv\"))\n\n#Task 1: Finding the least squares beta based on A and y. \n #Taks 1a: Do this via the pseudoinverse, or GLM, or similar.\n #Task 1b: Do this via an iterative gradient descent implementation\n#Task 2: Evaluate the accuracy of the estimator(s) from task 1 on the accuracy", "meta": {"hexsha": "2ed3e133da6ef596f500f7a21c85cf65326c7394", "size": 1116, "ext": "r", "lang": "R", "max_stars_repo_path": "ML180Minutes/exercise.r", "max_stars_repo_name": "yoninazarathy/MathematicalEngineeringDeepLearning", "max_stars_repo_head_hexsha": "b551ad5720ffa96f5cecac0d34cce2d5cf680e9a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 39, "max_stars_repo_stars_event_min_datetime": "2020-09-27T19:13:45.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-26T19:50:46.000Z", "max_issues_repo_path": "ML180Minutes/exercise.r", "max_issues_repo_name": "yoninazarathy/MathematicalEngineeringDeepLearning", "max_issues_repo_head_hexsha": "b551ad5720ffa96f5cecac0d34cce2d5cf680e9a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "ML180Minutes/exercise.r", "max_forks_repo_name": "yoninazarathy/MathematicalEngineeringDeepLearning", "max_forks_repo_head_hexsha": "b551ad5720ffa96f5cecac0d34cce2d5cf680e9a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2021-01-12T05:04:11.000Z", "max_forks_repo_forks_event_max_datetime": "2021-12-04T04:28:23.000Z", "avg_line_length": 69.75, "max_line_length": 149, "alphanum_fraction": 0.8010752688, "num_tokens": 278, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9553191309994467, "lm_q2_score": 0.7956581000631542, "lm_q1q2_score": 0.7601074047250033}} {"text": "## Author: Sergio García Prado\n## Title: Statistical Inference - Non parametric Tests - Exercise 02\n\nrm(list = ls())\n\nx <- c(5.2, 8.5, 9.8, 12.3, 17.1, 17.9, 23.7, 29.8)\n\n(n.x <- length(x))\n# 8\n\ny <- c(1.1, 2.3, 3.2, 6.3, 7.0, 7.2, 9.1, 15.2, 18.3, 21.1)\n\n(n.y <- length(y))\n# 1.1, 2.3, 3.2, 6.3, 7.0, 7.2, 9.1, 15.2, 18.3, 21.1\n\n(n <- n.x + n.y)\n# 18\n\nsum(duplicated(c(y, x))) > 0\n# FALSE\n\n\n(W <- sum(rank(c(y, x))[1:length(y)]))\n# 76\n\n(W.mean <- n.y * (n + 1) / 2)\n# 95\n\n(W.var <- n.y * n.x * (n + 1) / 12)\n# 126.67\n\n(W.yx <- W - n.y * (n.y + 1) / 2)\n# 21\n\n(W.yx.mean <- n.x * n.y / 2)\n# 40\n\n(W.yx.var <- n.x * n.y * (n + 1) / 12)\n# 126.67\n\n### H0: X >= Y\n\n## Asymptotic pvalue (with continuity correction)\npnorm((W.yx + 0.5 - W.yx.mean) / sqrt(W.yx.var))\n# 0.050112052808869\n\n## Exact\npwilcox(W.yx, n.y, n.x)\n# 0.0505507564331094\n\n### Shift Parameter Estimation\n\na <- matrix(rep(0, n.x * n.y), n.x, n.y)\nfor(i in 1:n.x) {\n for(j in 1:n.y) {\n a[i, j] <- y[j] - x[i]\n }\n}\nmedian(a)\n# -6.1\n\n\nwilcox.test(y, x, alternative = \"less\", conf.int = TRUE)\n# Wilcoxon rank sum test\n#\n# data: y and x\n# W = 21, p-value = 0.05055\n# alternative hypothesis: true location shift is less than 0\n# 95 percent confidence interval:\n# -Inf 0.4\n# sample estimates:\n# difference in location\n# -6.1\n", "meta": {"hexsha": "aaf0193cdc79f6f333eba2aa064d6905571f724c", "size": 1305, "ext": "r", "lang": "R", "max_stars_repo_path": "statistical-inference/non-parametric/exercise-02.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "statistical-inference/non-parametric/exercise-02.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "statistical-inference/non-parametric/exercise-02.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 17.6351351351, "max_line_length": 68, "alphanum_fraction": 0.5340996169, "num_tokens": 598, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9005297887874624, "lm_q2_score": 0.8438951025545426, "lm_q1q2_score": 0.7599526784622161}} {"text": "\r\n#Data\r\nrevenue <- c(14574.49, 7606.46, 8611.41, 9175.41, 8058.65, 8105.44, 11496.28, 9766.09, 10305.32, 14379.96, 10713.97, 15433.50)\r\n\r\nexpenses <- c(12051.82, 5695.07, 12319.20, 12089.72, 8658.57, 840.20, 3285.73, 5821.12, 6976.93, 16618.61, 10054.37, 3803.96)\r\n\r\n#Solution\r\n\r\n#PROFIT PER MONTH\r\nprofit <- revenue - expenses\r\nprofit\r\n\r\n#30% TAX VALUE\r\n\r\n#Alternative function for round is signif()\r\n#The signif function rounds a numeric input to a specified number of digits.\r\n\r\ntax <- round(0.30 * profit, 2)\r\ntax \r\n\r\n#PROFIT AFTER TAX\r\nprofit.after.tax <- profit - tax\r\nprofit.after.tax\r\n\r\n#PROFIT MARGIN IN %\r\n\r\n#Round To 2 Decimal Points, Then Multiply By 100 To Get %\r\n\r\n#Round function in R, rounds off the values in its first argument to the specified number of decimal places. \r\n#Round() function in R rounds off the list of values in vector and also rounds off the column of a dataframe.\r\n#It can also accomplished by using signif() function\r\n\r\nprofit.margin <- round(profit.after.tax / revenue, 2) * 100\r\nprofit.margin\r\n\r\n#MEAN PROFIT AFTER TAX\r\n#The function mean() is used to calculate mean by taking the sum of the values and dividing with the number of \r\n#values in a data series. \r\n\r\nmean_profit_after_tax <- mean(profit.after.tax)\r\nmean_profit_after_tax\r\n\r\n#GOOD MONTHS\r\ngood.months <- profit.after.tax > mean_profit_after_tax\r\ngood.months\r\n\r\n#BAD MONTHS\r\n\r\n#Bad month is not equall to good month\r\nbad.months <- !good.months\r\nbad.months\r\n\r\n#BEST MONTH\r\n\r\n#max() function in R Language is used to find the maximum element present in an object. \r\n#This object can be a Vector, a list, a matrix, a data frame, etc..\r\n\r\nbest.month <- profit.after.tax == max(profit.after.tax)\r\nbest.month\r\n\r\n#WORST MONTH\r\n\r\n#min function in R min(), is used to calculate the minimum of vector elements or minimum of a particular\r\n# column of a dataframe.\r\n\r\nworst.month <- profit.after.tax == min(profit.after.tax)\r\nworst.month\r\n\r\n#RESULTS FOR $ VALUES NEED TO BE CALCULATED WITH $0.01 PRECISION, BUT UNITS OF $1,000 WITH NO DECIMAL POINTS.\r\n#It can also accomplished by using signif() function\r\n\r\nrevenue.1000 <- round(revenue / 1000, 0)\r\nexpenses.1000 <- round(expenses / 1000, 0)\r\nprofit.1000 <- round(profit / 1000, 0)\r\nprofit.after.tax.1000 <- round(profit.after.tax / 1000, 0)\r\n\r\n#cbind() and rbind() both create matrices by combining several vectors of the same \r\n#length. cbind() combines vectors as columns, while rbind() combines them as rows.\r\n#cbind() stands for column binding.\r\n\r\nmtrxc <- cbind(revenue.1000,expenses.1000,profit.1000,profit.after.tax.1000,profit.margin,good.months,bad.months,best.month,worst.month)\r\nmtrxc\r\n\r\n#rbind() function in R Language is used to combine specified Vector, Matrix or\r\n#Data Frame by rows. deparse. \r\n#rbind() stands for row binding.\r\n\r\nmtrxr <- rbind(revenue.1000,expenses.1000,profit.1000,profit.after.tax.1000,profit.margin,good.months,bad.months,best.month,worst.month)\r\nmtrxr\r\n\r\n#By using matrices TRUE/FALSE are changed to 1's and 0'S. therefore True = 1, False = 0.\r\n", "meta": {"hexsha": "53d71319e72432755bf77a1f53eeb2221bf358d0", "size": 3025, "ext": "r", "lang": "R", "max_stars_repo_path": "Financial_Statement_analysis/FINANCIAL_STATEMENT_ANALYSIS.r", "max_stars_repo_name": "doddanikhil/Data-Analytics", "max_stars_repo_head_hexsha": "15cd81c20ca4f592871561abe6717a19df6b18fb", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Financial_Statement_analysis/FINANCIAL_STATEMENT_ANALYSIS.r", "max_issues_repo_name": "doddanikhil/Data-Analytics", "max_issues_repo_head_hexsha": "15cd81c20ca4f592871561abe6717a19df6b18fb", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Financial_Statement_analysis/FINANCIAL_STATEMENT_ANALYSIS.r", "max_forks_repo_name": "doddanikhil/Data-Analytics", "max_forks_repo_head_hexsha": "15cd81c20ca4f592871561abe6717a19df6b18fb", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 32.8804347826, "max_line_length": 137, "alphanum_fraction": 0.7229752066, "num_tokens": 889, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9294404057671712, "lm_q2_score": 0.8175744739711883, "lm_q1q2_score": 0.7598867508326629}} {"text": " \r\n\r\nybar = 31.2 # sample mean \r\nmu0 = 33 # hypothesized value \r\nsigma = 8.4 # population standard deviation \r\nn = 35 # sample size \r\nz = (ybar- mu0)/(sigma/sqrt(n))\r\nprint(z) # test statistic\r\n\r\n# We then compute the critical value at .05 significance level.\r\n# For alpha = .05, we will reject the null hypothesis if z <= -1.645\r\nalpha = .05 \r\nz.alpha = qnorm(1-alpha) \r\n# the observed value of z is not less than -z.alpha, the test statistic does not fall in the rejection region. \r\n\r\n\r\n", "meta": {"hexsha": "44173f70695b28e8458886b69224734fdd265061", "size": 535, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH5/EX5.9/Ex5_9.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH5/EX5.9/Ex5_9.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH5/EX5.9/Ex5_9.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 31.4705882353, "max_line_length": 115, "alphanum_fraction": 0.6130841121, "num_tokens": 144, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9609517106286379, "lm_q2_score": 0.7905303137346446, "lm_q1q2_score": 0.7596614572871005}} {"text": "weather <- read.table(text=\"\n outlook temperature humidity wind play\n 1 sunny hot high normal no\n 2 sunny hot high high no\n 3 overcast hot high normal yes\n 4 rainy mild high normal yes\n 5 rainy cold normal normal yes\n 6 rainy cold normal high no\n 7 overcast cold normal high yes\n 8 sunny mild high normal no\n 9 sunny cold normal normal yes\n 10 rainy mild normal normal yes\n 11 sunny mild normal high yes\n 12 overcast mild high high yes\n 13 overcast hot normal normal yes\n 14 rainy mild high high no\")\n \nweatherc <- read.table(text=\"\n outlook temperature humidity wind play\n 1 sunny 27 80 normal no\n 2 sunny 28 65 high no\n 3 overcast 29 90 normal yes\n 4 rainy 21 75 normal yes\n 5 rainy 17 40 normal yes\n 6 rainy 15 25 high no\n 7 overcast 19 50 high yes\n 8 sunny 22 95 normal no\n 9 sunny 18 45 normal yes\n 10 rainy 23 30 normal yes\n 11 sunny 24 55 high yes\n 12 overcast 25 70 high yes\n 13 overcast 30 35 normal yes\n 14 rainy 26 85 high no\")\nsummary(weatherc)\n\n\nweatherr <- read.table(text=\"\n outlook temperature humidity wind playability\n 1 sunny 27 80 normal 0.48\n 2 sunny 28 65 high 0.46\n 3 overcast 29 90 normal 0.68\n 4 rainy 21 75 normal 0.52\n 5 rainy 17 40 normal 0.54\n 6 rainy 15 25 high 0.47\n 7 overcast 19 50 high 0.74\n 8 sunny 22 95 normal 0.49\n 9 sunny 18 45 normal 0.64\n 10 rainy 23 30 normal 0.55\n 11 sunny 24 55 high 0.57\n 12 overcast 25 70 high 0.68\n 13 overcast 30 35 normal 0.79\n 14 rainy 26 85 high 0.33\")\nsummary(weatherr)\nweathercl <- weatherc[,-5]\n\ninstall.packages(\"/home/users/chojnar1/Desktop/STUD/MOW/Book/Packages/dmr.data_1.0.tar.gz\")\n\n\ndata(weather, package=\"dmr.data\")\ndata(weatherc, package=\"dmr.data\")\ndata(weatherr, package=\"dmr.data\")\n\n# mean calculation\nbs.mean <- function(v) {sum(v)/length(v)}\n\n# my variant\nbs.mean(weatherc$temperature)\n# typical approach\nmean(weatherc$temperature)\n\n\nbs.weighted.mean <- function(v, w=rep(1, length(v))) { sum(w*v)/sum(w) }\n# demonstration\nbs.weighted.mean(weatherc$temperature, ifelse(weatherc$play==\"yes\",5,1))\nweighted.mean(weatherc$temperature, ifelse(weatherc$play==\"yes\",5,1))\n\n\n# Median - notice that k1 and k2 are equal if m (the dataset size) is odd.\nbs.median <- function(v)\n{\n k1 <- (m <- length(v))%/%2+1\n k2 <- (m+1)%/%2\n ((v <- sort(v))[k1]+v[k2])/2\n}\n\n# demonstration\nbs.median(weatherc$temperature)\nbs.median(weatherc$temperature[weatherc$play==\"yes\"])\nmedian(weatherc$temperature)\nmedian(weatherc$temperature[weatherc$play==\"yes\"])\n\n\n#The rank of instance x with respect \n#to attribute a on dataset S,\n#is the ordinal number of x\n#after sorting S nondecreasingly by a\n\n#The R code presented below implements and demonstrates weighted median calculation. \n#Since there is no equivalent standard R function, the results are verified by applying \n#the median function to appropriately resampled data, simulating the effect of weighting. \n#The shift.right utility function is used to shift the cumulative weight sum to the right.\n\nweighted.median <- function(v, w=rep(1, length(v)))\n{\n v <- v[ord <- order(v)]\n w <- w[ord]\n tw <- (sw <- cumsum(w))[length(sw)]\n mean(v[which(sw>=0.5*tw & tw-shift.right(sw, 0)>=0.5*tw)])\n}\n\n # demonstration\nweighted.median(weatherc$temperature, ifelse(weatherc$play==\"yes\", 5, 1))\nmedian(c(weatherc$temperature[weatherc$play==\"no\"],\n rep(weatherc$temperature[weatherc$play==\"yes\"], 5)))\nweighted.median(weatherc$temperature, ifelse(weatherc$play==\"yes\", 0.2, 1))\nmedian(c(weatherc$temperature[weatherc$play==\"yes\"],\n rep(weatherc$temperature[weatherc$play==\"no\"], 5)))\n\n\n#Rank calculation is implemented and demonstrated by the following R code\nbs.rank <- function(v)\n{\n r.min <- match(v, sort(v))\n r.max <- length(v)+1-match(v, rev(sort(v)))\n (r.min+r.max)/2\n}\n\n#demonstration\nprint(weatherr$playability)\nbs.rank(weatherr$playability)\nrank(weatherr$playability)\n\n#Order statistics can be though of as an inverse of ranks\n#The order statistic of attribute a is the attribute's value\n#for the instance that has rank k with respect to a under \n#ordinal ranking\n\n#The R code presented below implements and demonstrates order statistic calculation\nord <- function(v, k=1:length(v))\n{\n sort(v)[k]\n}\n\n# demonstration\nord(weatherr$playability, 11)\nweatherr$playability[rank(weatherr$playability, ties.method=\"first\")==11]\nord(weatherr$playability, 10:13)\nweatherr$playability[rank(weatherr$playability, ties.method=\"first\") %in% 10:13]\n\n\n#Simplified reimplementation of the standard quantile \n#function and demonstrates its usage\n\nbs.quantile <- function(v, p=c(0, 0.25, 0.5, 0.75, 1))\n{\n b <- 1-p\n k <- floor((ps <- p*length(v))+b)\n beta <- ps+b-k\n `names<-`((1-beta)*(v <- sort(v))[k]+beta*(ifelse(k 1) {\n stop(\"`predicted` cannot contain values greater than 1.\", call. = FALSE)\n }\n\n if (min(predicted) < 0) {\n stop(\"`predicted` cannot contain values less than 0.\", call. = FALSE)\n }\n\n n <- length(predicted)\n brier_score <- sum((actual - predicted)^2) / n\n\n brier_score\n}\n", "meta": {"hexsha": "e9fbc6c123363b2209e92d64ba784c2f9d35fbd0", "size": 2119, "ext": "r", "lang": "R", "max_stars_repo_path": "R/brier-score.r", "max_stars_repo_name": "maiing/metrics", "max_stars_repo_head_hexsha": "ae4e4cbe5b025c53f2fbf552a46f335aa34f687f", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/brier-score.r", "max_issues_repo_name": "maiing/metrics", "max_issues_repo_head_hexsha": "ae4e4cbe5b025c53f2fbf552a46f335aa34f687f", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/brier-score.r", "max_forks_repo_name": "maiing/metrics", "max_forks_repo_head_hexsha": "ae4e4cbe5b025c53f2fbf552a46f335aa34f687f", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 29.4305555556, "max_line_length": 81, "alphanum_fraction": 0.6436998584, "num_tokens": 654, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8991213826762113, "lm_q2_score": 0.8438951064805861, "lm_q1q2_score": 0.7587641349725132}} {"text": "qqplot_dlh <- function(x, dist, suppress='yes') {\r\n\r\n ## grab name of variable passed in as x\r\n xlabel <- deparse(substitute(x))\r\n\r\n ## first sort x so it increases\r\n## x <- sort(x)\r\n good <- !is.na(x)\r\n ord <- order(x[good])\r\n x <- x[good][ord]\r\n\r\n ## determine quantiles for data\r\n num <- length(x)\r\n P <- ppoints(num)\r\n if (dist == 'normal') {\r\n quantiles <- qnorm(P, mean = mean(x), sd = sd(x))\r\n \r\n } else if (dist == 'weibull') {\r\n ## mass::fitdistr\r\n ## Distributions \"beta\", \"cauchy\", \"chi-squared\", \"exponential\", \"gamma\", \"geometric\",\r\n ## \"log-normal\", \"lognormal\", \"logistic\", \"negative binomial\", \"normal\",\r\n ## \"Poisson\", \"t\" and \"weibull\" are recognised, case being ignored.\r\n out <- MASS::fitdistr(x, densfun = 'weibull')\r\n shape <- out$estimate[[1]]\r\n scale <- out$estimate[[2]]\r\n quantiles <- qweibull(P, shape = shape, scale = scale)\r\n\r\n } else if (dist == 'johnson') {\r\n library(SuppDists) # need for Johnson distribution\r\n jparms <- SuppDists::JohnsonFit(x)\r\n quantiles <- SuppDists::qJohnson(P, jparms)\r\n\r\n }\r\n\r\n ylabel <- paste('Quantiles for', dist, 'distribution', sep=' ')\r\n ## plot data vs. quantiles\r\n ## df <- data.frame(x, quantiles)\r\n ## plotfit(df, x, quantiles,\r\n ## main = paste('QQ Plot for', xlabel, sep=' '),\r\n ## xlabel = xlabel,\r\n ## ylabel = ylabel,\r\n ## interval='conf', alpha=0.05, sided=2, # confidence intervals are wrong\r\n ## suppress=suppress)\r\n plot(x, quantiles,\r\n main = paste('QQ Plot for', xlabel, sep=' '),\r\n xlab = xlabel,\r\n ylab = ylabel)\r\n abline(a=0, b=1, col='red') # theoretical line fit\r\n\r\n ## ## students-t for dataset\r\n ## num <- length(x)\r\n ## conf <- 0.05\r\n ## t <- qt(1-conf/2, num-1)\r\n ## uncert <- t * sd(x) / sqrt(num)\r\n\r\n ## ## confidence limits for plot\r\n ## ## following makes confidence limits but they do not match standard R and following is only for normal\r\n ## ## https://stats.stackexchange.com/questions/111288/confidence-bands-for-qq-line\r\n ## z <- qnorm(P)\r\n ## plot(z, x, type=\"p\")\r\n ## coef <- coef(rlm(x ~ z))\r\n ## b <- coef[1]\r\n ## m <- coef[2]\r\n ## fit.value <- b + m*z\r\n ## ## abline(b, m, col=\"red\", lwd=1)\r\n ## lines(z, fit.value, lty=1, lwd=1, col='red')\r\n ## conf <- 0.95\r\n ## zz <- qnorm(1-(1-conf)/2)\r\n ## SE <- (m/dnorm(z))*sqrt(P*(1-P)/num) #[WHY?]\r\n ## upper <- fit.value+zz*SE\r\n ## lower <- fit.value-zz*SE\r\n ## lines(z,upper, lty=2, lwd=1, col=\"red\")\r\n ## lines(z,lower, lty=2, lwd=1, col=\"red\")\r\n\r\n ## lines(x, lquant, col='black', lty='dashed') # lower confidence line\r\n ## lines(x, uquant, col='black', lty='dashed') # upper confidence line\r\n\r\n}\r\n\r\n\r\n\r\nqqplot_dlh_test <- function() {\r\n ## test qqplot_dlh against qualityTools::qqplot\r\n\r\n plotspace(2,2)\r\n\r\n ## normal distribution plots\r\n set.seed(1)\r\n x <- rnorm(n=1E2, mean=10, sd=1)\r\n qualityTools::qqPlot(x, \"normal\", col='black')\r\n qqplot_dlh(x, 'normal')\r\n\r\n ## Weibull distribution plots\r\n set.seed(1)\r\n x <- rweibull(1E2, shape=10, scale=2)\r\n qualityTools::qqPlot(x, \"Weibull\", col='black')\r\n qqplot_dlh(x, 'weibull')\r\n \r\n}\r\n", "meta": {"hexsha": "f01d7da96a0a948e4bf36184afffbc2130d3de06", "size": 3468, "ext": "r", "lang": "R", "max_stars_repo_path": "modules/qqplot_dlh.r", "max_stars_repo_name": "TECComputing/R-setup", "max_stars_repo_head_hexsha": "f4b5e45c6e2e55fcc6f58f804bb50cea3a697fe0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "modules/qqplot_dlh.r", "max_issues_repo_name": "TECComputing/R-setup", "max_issues_repo_head_hexsha": "f4b5e45c6e2e55fcc6f58f804bb50cea3a697fe0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "modules/qqplot_dlh.r", "max_forks_repo_name": "TECComputing/R-setup", "max_forks_repo_head_hexsha": "f4b5e45c6e2e55fcc6f58f804bb50cea3a697fe0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 34.68, "max_line_length": 113, "alphanum_fraction": 0.5173010381, "num_tokens": 1048, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9252299570920386, "lm_q2_score": 0.8198933293122506, "lm_q1q2_score": 0.7585898698996223}} {"text": "#install.packages(\"GA\")\nlibrary(GA)\n\n# Funkcja Eggholder function\nfunc3d <- function(x, y)\n{\n -(x+47)*sin(sqrt(abs(x/2+(y+47))))-x*sin(sqrt(abs(x-(y+47))))\n}\nlbound <- -512\nrbound <- 512\n\nx <- y <- seq(lbound, rbound, by=2) # generowanie wektorów od lbound to rbound co 0.1\nf <- outer(x, y, func3d)\npersp3D(x, y, f, theta = 50, phi = 20, col.palette = bl2gr.colors) # Perspektywa 3D funkcji\n\nfilled.contour(x, y, f, color.palette = bl2gr.colors) # Rzut z góry wykresu funkcji\n\nfA <- function(x) -func3d(x[1], x[2])\n\nGA <- ga(\n type = \"real-valued\",\n fitness = function(x) -func3d(x[1], x[2]), # (minus) - minimalizacja funkcji 3D\n lower = c(lbound, lbound), upper = c(rbound, rbound),\n popSize = 50, maxiter = 1000, run = 100\n)\nsummary (GA)\nplot(GA)\n\nfilled.contour(\n x, y, f,\n color.palette = bl2gr.colors,\n plot.axes = {\n axis(1); axis(2);\n points(\n GA@solution[,1], GA@solution[,2],\n pch = 3, cex = 2, col = \"white\", lwd = 2\n )\n }\n)\n", "meta": {"hexsha": "32201b3b6a137e017dbdce60a3ac9ab7ee69440a", "size": 964, "ext": "r", "lang": "R", "max_stars_repo_path": "R/ga/func/3d/ga_minimum_of_eggholder_func.r", "max_stars_repo_name": "reyzeer/algorytmy-genetyczne", "max_stars_repo_head_hexsha": "c8803dd19dd5105d35b287fa13efdc130531403f", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/ga/func/3d/ga_minimum_of_eggholder_func.r", "max_issues_repo_name": "reyzeer/algorytmy-genetyczne", "max_issues_repo_head_hexsha": "c8803dd19dd5105d35b287fa13efdc130531403f", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/ga/func/3d/ga_minimum_of_eggholder_func.r", "max_forks_repo_name": "reyzeer/algorytmy-genetyczne", "max_forks_repo_head_hexsha": "c8803dd19dd5105d35b287fa13efdc130531403f", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 24.1, "max_line_length": 91, "alphanum_fraction": 0.6109958506, "num_tokens": 374, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9473810466522863, "lm_q2_score": 0.8006920068519376, "lm_q1q2_score": 0.7585604314975083}} {"text": "# wahpenayo at gmail dot com\n# 2018-04-16\n#-----------------------------------------------------------------\nif (file.exists('e:/porta/projects/taiga')) {\n setwd('e:/porta/projects/taiga')\n} else {\n setwd('c:/porta/projects/taiga')\n}\n#source('src/scripts/r/functions.r')\n#-----------------------------------------------------------------\nlibrary(quantreg)\n#example(rq)\n#-----------------------------------------------------------------\nfit.summary <- function(y,yhat,p=0.75) {\n n <- length(yhat)\n r <- y -yhat\n rmean <- mean(r)\n rmse <- sqrt(sum(r*r/n))\n rmad <- sum(abs(r))/n\n rqr <- 2.0*sum(ifelse(r>=0,p*r,(p-1)*r))/n\n qrq <- 0.5*sum(ifelse(r>=0,r/(1-p),-r/p))/n\n list(rmean=rmean,rmse=rmse,rmad=rmad,rqr=rqr,qrq=qrq)\n}\n#-----------------------------------------------------------------\ndata(engel)\ny <- engel$foodexp\nx <- data.frame(income=engel$income)\n\naffine.l2 <- lm(foodexp~income,data=engel)\nyhat <- predict(affine.l2,newdata=x)\nprint(\"l2 affine\")\nprint(affine.l2,digits=16)\nprint(fit.summary(y,yhat),digits=16)\n\naffine.q50 <- rq(foodexp~income,data=engel,tau=0.5) \nyhat <- predict(affine.q50,newdata=x)\nprint(\"q50 affine\")\nprint(affine.q50,digits=16)\nprint(fit.summary(y=y,yhat=yhat),digits=16)\n\naffine.q75 <- rq(foodexp~income,data=engel,tau=0.75) \nyhat <- predict(affine.q75,newdata=x)\nprint(\"q75 affine\")\nprint(affine.q75,digits=16)\nprint(fit.summary(y=y,yhat=yhat),digits=16)\n\nlinear.l2 <- lm(foodexp~income - 1,data=engel) \nyhat <- predict(linear.l2,newdata=x)\nprint(\"l2 linear\")\nprint(linear.l2,digits=16)\nprint(fit.summary(y,yhat),digits=16)\n\nlinear.q50 <- rq(foodexp~income - 1,data=engel,tau=0.5) \nyhat <- predict(linear.q50,newdata=x)\nprint(\"q50 linear\")\nprint(linear.q50,digits=16)\nprint(fit.summary(y,yhat),digits=16)\n\nlinear.q75 <- rq(foodexp~income - 1,data=engel,tau=0.75) \nyhat <- predict(linear.q75,newdata=x)\nprint(\"q75 linear\")\nprint(linear.q75,digits=16)\nprint(fit.summary(y,yhat),digits=16)\n\nyhat <- rep_len(median(y),length(y))\nprint(\"q50 constant\")\nprint(yhat[1],digits=16)\nprint(fit.summary(y,yhat),digits=16)\n\nyhat <- rep_len(quantile(x=y,probs=0.75),length(y))\nprint(\"q75 constant\")\nprint(yhat[1],digits=16)\nprint(fit.summary(y,yhat),digits=16)\n\nyhat <- rep_len(mean(y),length(y))\nprint(\"l2 constant\")\nprint(yhat[1],digits=16)\nprint(fit.summary(y,yhat),digits=16)\n#-----------------------------------------------------------------\ndata(stackloss)\nyx <- data.frame(\n stackloss=stackloss$stack.loss,\n acidconc=stackloss$Acid.Conc.,\n airflow=stackloss$Air.Flow,\n watertemp=stackloss$Water.Temp)\ny <- yx$stackloss\nx <- data.frame(\n acidconc=yx$acidconc,\n airflow=yx$airflow,\n watertemp=yx$watertemp)\n\naffine.l2 <- lm(stackloss~acidconc+airflow+watertemp,data=yx)\nyhat <- predict(affine.l2,newdata=x)\nprint(\"l2 affine\")\nprint(affine.l2,digits=16)\nprint(fit.summary(y,yhat),digits=16)\n\naffine.q50 <- rq(stackloss~acidconc+airflow+watertemp,data=yx,tau=0.5) \nyhat <- predict(affine.q50,newdata=x)\nprint(\"q50 affine\")\nprint(affine.q50,digits=16)\nprint(fit.summary(y=y,yhat=yhat),digits=16)\n\naffine.q75 <- rq(stackloss~acidconc+airflow+watertemp,data=yx,tau=0.75) \nyhat <- predict(affine.q75,newdata=x)\nprint(\"q75 affine\")\nprint(affine.q75,digits=16)\nprint(fit.summary(y=y,yhat=yhat),digits=16)\n\nlinear.l2 <- lm(stackloss~acidconc+airflow+watertemp - 1,data=yx) \nyhat <- predict(linear.l2,newdata=x)\nprint(\"l2 linear\")\nprint(linear.l2,digits=16)\nprint(fit.summary(y,yhat),digits=16)\n\nlinear.q50 <- rq(stackloss~acidconc+airflow+watertemp - 1,data=yx,tau=0.5) \nyhat <- predict(linear.q50,newdata=x)\nprint(\"q50 linear\")\nprint(linear.q50,digits=16)\nprint(fit.summary(y,yhat),digits=16)\n\nlinear.q75 <- rq(stackloss~acidconc+airflow+watertemp - 1,data=yx,tau=0.75) \nyhat <- predict(linear.q75,newdata=x)\nprint(\"q75 linear\")\nprint(linear.q75,digits=16)\nprint(fit.summary(y,yhat),digits=16)\n\nyhat <- rep_len(mean(y),length(y))\nprint(\"l2 constant\")\nprint(yhat[1],digits=16)\nprint(fit.summary(y,yhat),digits=16)\n\nyhat <- rep_len(median(y),length(y))\nprint(\"q50 constant\")\nprint(yhat[1],digits=16)\nprint(fit.summary(y,yhat),digits=16)\n\nyhat <- rep_len(quantile(x=y,probs=0.75),length(y))\nprint(\"q75 constant\")\nprint(yhat[1],digits=16)\nprint(fit.summary(y,yhat),digits=16)\n#-----------------------------------------------------------------\n", "meta": {"hexsha": "d16dc87a3f92685e9c4d87e79f085cb682378887", "size": 4274, "ext": "r", "lang": "R", "max_stars_repo_path": "src/scripts/r/quantreg.r", "max_stars_repo_name": "wahpenayo/taiga", "max_stars_repo_head_hexsha": "9d142149240f3f5db5dd8fbfbc0ce0552b81d490", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 4, "max_stars_repo_stars_event_min_datetime": "2017-09-02T01:14:37.000Z", "max_stars_repo_stars_event_max_datetime": "2018-04-30T14:29:40.000Z", "max_issues_repo_path": "src/scripts/r/quantreg.r", "max_issues_repo_name": "wahpenayo/taiga", "max_issues_repo_head_hexsha": "9d142149240f3f5db5dd8fbfbc0ce0552b81d490", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2017-10-24T18:35:41.000Z", "max_issues_repo_issues_event_max_datetime": "2017-10-24T18:35:41.000Z", "max_forks_repo_path": "src/scripts/r/quantreg.r", "max_forks_repo_name": "wahpenayo/taiga", "max_forks_repo_head_hexsha": "9d142149240f3f5db5dd8fbfbc0ce0552b81d490", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 29.8881118881, "max_line_length": 76, "alphanum_fraction": 0.6492746841, "num_tokens": 1401, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9196425245706048, "lm_q2_score": 0.8244619350028204, "lm_q1q2_score": 0.7582102553183596}} {"text": "# Example : 2 Chapter : 7.3 Page No: 401\r\n# Similar Projection Matrices\r\nA<-matrix(c(0.5,-0.5,-0.5,0.5),ncol=2)\r\nAev<-eigen(A)$values\r\nW<-matrix(c(2,0,1,1),ncol=2)\r\nW1<-solve(W)\r\nB<-W1%*%A%*%W\r\nprint(\"Matrix B = W-1 * A * W\")\r\nprint(B)\r\nBev<-eigen(B)$values\r\nprint(\"A and B are similar matrices\")\r\nprint(Aev)\r\nprint(Bev)", "meta": {"hexsha": "5d9120da4e3c7ef51e17378ab4d9eb45421a6286", "size": 326, "ext": "r", "lang": "R", "max_stars_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH7/EX7.3.2/Ex7.3_2.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH7/EX7.3.2/Ex7.3_2.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH7/EX7.3.2/Ex7.3_2.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 25.0769230769, "max_line_length": 47, "alphanum_fraction": 0.6073619632, "num_tokens": 139, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9273632976542185, "lm_q2_score": 0.8175744739711883, "lm_q1q2_score": 0.7581885602598343}} {"text": "sieve <- function(n) {\n if (n < 2) return(NULL)\n a <- rep(T, n)\n a[1] <- F\n for(i in seq(n)) {\n if (a[i]) {\n j <- i * i\n if (j > n) return(which(a))\n a[seq(j, n, by=i)] <- F\n }\n }\n}\n\nsieve(1000)\n", "meta": {"hexsha": "3a680a6d35ebe225b026653cb5a238ad3ad7b173", "size": 221, "ext": "r", "lang": "R", "max_stars_repo_path": "Task/Sieve-of-Eratosthenes/R/sieve-of-eratosthenes.r", "max_stars_repo_name": "LaudateCorpus1/RosettaCodeData", "max_stars_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Sieve-of-Eratosthenes/R/sieve-of-eratosthenes.r", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Sieve-of-Eratosthenes/R/sieve-of-eratosthenes.r", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 14.7333333333, "max_line_length": 33, "alphanum_fraction": 0.4027149321, "num_tokens": 92, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9621075744568837, "lm_q2_score": 0.7879312031126512, "lm_q1q2_score": 0.758074578665607}} {"text": "#' Calculate root-mean-square error metric\n#'\n#' @param true the true response values\n#' @param pred the predicted response values\n#' @export\n\nrmse <- function (true, pred) {\n return(sqrt(mean((true - pred)^2)));\n}\n\n#' Calculate log-loss error metric\n#'\n#' @param true the true response values\n#' @param pred the predicted response values\n#' @param eps a lower bound on predicted probabilities\n#' @export\n\nlogloss <- function (true, pred, eps=1e-15) {\n pred <- pmin(pmax(pred, eps), 1-eps);\n return(-mean(true * log(pred)) - mean((1 - true) * log(1 - pred)));\n}\n\n#' Calculate mean absolute error metric\n#'\n#' @param true the true response values\n#' @param pred the predicted response values\n#' @export\n\nmae <- function (true, pred) {\n return(mean(abs(true - pred)));\n}", "meta": {"hexsha": "50710908aabb36ad606215a5772c07539b0ed437", "size": 772, "ext": "r", "lang": "R", "max_stars_repo_path": "R/errfuncs.r", "max_stars_repo_name": "valexandersaulys/medley", "max_stars_repo_head_hexsha": "e2c07b6780c4a57d8a29142cda6b11c7c1d4f88f", "max_stars_repo_licenses": ["BSD-2-Clause"], "max_stars_count": 26, "max_stars_repo_stars_event_min_datetime": "2015-03-18T19:20:05.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-09T20:45:40.000Z", "max_issues_repo_path": "R/errfuncs.r", "max_issues_repo_name": "valexandersaulys/medley", "max_issues_repo_head_hexsha": "e2c07b6780c4a57d8a29142cda6b11c7c1d4f88f", "max_issues_repo_licenses": ["BSD-2-Clause"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/errfuncs.r", "max_forks_repo_name": "valexandersaulys/medley", "max_forks_repo_head_hexsha": "e2c07b6780c4a57d8a29142cda6b11c7c1d4f88f", "max_forks_repo_licenses": ["BSD-2-Clause"], "max_forks_count": 8, "max_forks_repo_forks_event_min_datetime": "2015-02-17T03:56:14.000Z", "max_forks_repo_forks_event_max_datetime": "2018-06-14T10:56:34.000Z", "avg_line_length": 24.9032258065, "max_line_length": 69, "alphanum_fraction": 0.6774611399, "num_tokens": 203, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9073122188543453, "lm_q2_score": 0.8354835371034368, "lm_q1q2_score": 0.758044421865596}} {"text": "# Eilers and Marx (1996)\r\n# code borrowed from http://bragqut.github.io/2016/05/24/samclifford-splines/index.html#disqus_thread\r\n\r\ncreate.bspline <- function(x, K = nbasis, bdeg=degree, cyclic=FALSE, xl=min(x), xr=max(x)){\r\n x <- as.matrix(x,ncol=1)\r\n ndx <- K - bdeg\r\n \r\n # as outlined in Eilers and Marx (1996)\r\n dx <- (xr - xl) / ndx\r\n t <- xl + dx * (-bdeg:(ndx+bdeg))\r\n T <- (0 * x + 1) %*% t\r\n X <- x %*% (0 * t + 1)\r\n P <- (X - T) / dx\r\n B <- (T <= X) & (X < (T + dx))\r\n r <- c(2:length(t), 1)\r\n \r\n for (k in 1:bdeg){\r\n B <- (P * B + (k + 1 - P) * B[ ,r]) / k; \r\n }\r\n \r\n B <- B[,1:(ndx+bdeg)]\r\n \r\n if (cyclic == 1){\r\n for (i in 1:bdeg){\r\n B[ ,i] <- B[ ,i] + B[ ,K-bdeg+i] \r\n }\r\n B <- B[ , 1:(K-bdeg)]\r\n }\r\n \r\n return(B)\r\n}\r\n", "meta": {"hexsha": "8f72c87b2d6fd6a42794bef619932453f7482d0f", "size": 772, "ext": "r", "lang": "R", "max_stars_repo_path": "functions/create_bspline.r", "max_stars_repo_name": "heblab/pronghornsurvival", "max_stars_repo_head_hexsha": "03c5e109bcb1d328632584bd56c416af5eceaf09", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "functions/create_bspline.r", "max_issues_repo_name": "heblab/pronghornsurvival", "max_issues_repo_head_hexsha": "03c5e109bcb1d328632584bd56c416af5eceaf09", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "functions/create_bspline.r", "max_forks_repo_name": "heblab/pronghornsurvival", "max_forks_repo_head_hexsha": "03c5e109bcb1d328632584bd56c416af5eceaf09", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 24.125, "max_line_length": 102, "alphanum_fraction": 0.4507772021, "num_tokens": 321, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9219218327098193, "lm_q2_score": 0.8221891392358014, "lm_q1q2_score": 0.7579941180783788}} {"text": "#X = X1,..Xn - експериментално получени случайни величини\n#математическо очакване Е(X) = mean(X) (mu)\n#дисперсия D(X) = var(x) (sigma^2)\n#стандартно отклонение s = sd(x) (sigma)\nx = c(74, 122, 235, 111, 292, 111, 211, 133, 156, 79)\nmean(x) #очакване\nvar(x) #дисперсия\nsd(x) #стандартно отклонение\n\n#централна гранична теорема - когато имаме много независими еднакво разпределенислучайни величини X1,..Xn, то сумата им след нориране е стандартна нормално разпределена велинина\n#Y = ( sum(Xi) - E(sum(Xi)) ) / sqrt( D(sum(xi)) ) e стандартно нормално разпределена случайна величина\n#E(sum(Xi)) = sum(EXi) -> очакването на сума е сума от очакванията\n#D(sum(Xi)) = sum(DXi) -> дисперсия на сума е сума от дисперсиите\n\n#твърдение: Xi = N(mu, sigma^2) - Xi случайни нормално разпределени величини с очакване mu и дисперсия sigma^2\n#Xn.cherta = N(mu, (sigma^2)/n ) -> Xn.cherta = sum(Xi)/n -> статистическо средно e нормално разпределено с очакване mu и дисперсия (sigma^2)/n\n\n#хи-квадрат разпределение\n#Y1,..,Yn стандартно нормално разпределени случайни величини N(0,1)\n#X^2(r) = sum(Yi^2) e хи-квадрат разпределение с r степени на свобода\n#функцията chisq() с префикси d,p,q,r за съответно плътност, разпределние, квантил и случайно разпределение(симулиране)\n\n#t-разпределение\n#X = X1,...,Xn n независими измервания Xi, очакване mu, извадково средно mean(x), oценка за стандартно отклонение sd(x) и неизвестно sigma \n#най-добрата оценка за неизвестното sigma се дава с t-разпределение с n-1 степени на свобода\n#функцията t() с префикси d,p,q,r за съответно плътност, разпределние, квантил и случайно разпределение(симулиране)\n\n#f-разпределение - непрекъснато статистическо разпределение, получено от отношението на две хи-квадрат разпределения\n#Fn,m = (X^2(n)/n) / (X^2(m)/m)\n#тества дали две извадки имат еднаква дисперсия\n#функцията f() с префикси d,p,q,r за съответно плътност, разпределние, квантил и случайно разпределение(симулиране)\n\n#доверителен интервал\n#имаме случайна величина X, която е с някакво разпределение, но не знаем някой параметър tita. Искаме да оценим този параметър tita с някаква вероятност на достоверност (gama = 1 - alpha). Тогава gama = 1 - alpha = P(-z* < tita < z*) -> от -z* до z* е доверителния интервал \n#нормално разпределение -> z*=qnorm(1-alpha / 2) (защото е симетрично)\n#биномно разпределение, когато tita = p (не знаем каква е вероятността за успех) -> интервала е [p.shapka - z* SE, p.shapka + z* SE], където p.shapka е експериментално получената вероятност, SE = sqrt((1/n) * p.shapka * (1-p.shapka))\n#биномно разпределение, когато tita = p1 - p2 (искаме да оценим разликата във вероятностите за две случайно разпределни величини с големина n и m) -> интервала е [tita - z* SE, tita + z* SE], където SE = sqrt( (p1*(1-p1)/n + (p2*(1-p2)/m ) )\n#нормално разпределение, когато tita = mu (не знаем очакването, но знаем дисперсията) -> интервала е [x.cherta - z* sigma/sqrt(n), x.cherta + z* sigma/sqrt(n)], където x.cherta = sum(Xi)/n = mean(xi) (средно аритметично - експериментално очакване)\n#нормално разпределение, когато tita = mu, sigma (не знаем нито очакването, нито дисперсията) -> интервала е [x.cherta - t* s/sqrt(n), x.cherta + t* s/sqrt(n)], където x.cherta = sum(Xi)/n = mean(xi), s = sd(Xi) (експериментално стандартно отклонение), t* = qt(1-alpha, df = n -1)квантил на t-разпределение с n-1 степени на свобода\n\n\n#-----------------------------------------------------\n\n#01\n#x1=Bi(100,1/2), x2=Bi(100,1/3)\ncgt.binom = function(n,p) {\n xi = rbinom(n = 100, size = n, prob = p)\n EXi = n * p #EXi = n*p -> очакване за биномно разпределени величини\n DXi = n * p * (1-p) #DXi = n*p*q = n*p*(1-p) -> дисперсия за биномно разпределени велчини\n x1.norm = (xi - EXi) / sqrt(DXi) #нормираме всички величини\n hist(x = x1.norm, probability = TRUE)\n x = rnorm(100) #симулираме нормално разпределени величини за да сравним \n curve(dnorm(x), add = T) #приличат си доста, значи и графично можем да кажем че е изпълнена централната гранична теорема\n}\ncgt.binom(100,1/2)\ncgt.binom(100,1/3)\n\n#02\ntemp = c(102.5, 101.7, 103.1, 100.9, 100.5, 102.2)\nsd = 1.2\nx=mean(temp)\nalpha=1-0.95\nz=qnorm(1-alpha/2) \nlower=x-z*sd\nupper=x+z*sd\n\n#03\n#1000 случайни нормално разпределени величини\ntest.mu = function(mu, sigma.sq) {\n x = rnorm(n = 1000, mean = mu, sd = sqrt(sigma.sq))\n alpha=1-0.95\n z=qnorm(1-alpha/2)\n x.cherta=mean(x)\n #N(mu,1) -> formula 11\n x.lower=x.cherta-z*1\n x.upper=x.cherta+z*1\n plot(x)\n lines(x=0:1000,y=rep(x.upper,1001), col='red')\n lines(x=0:1000,y=rep(x.lower,1001), col='blue')\n \n x.length=length(x[x>=x.lower&x<=x.upper]) #броят на стойностите влизащи в доверителния интервал\n print(x.length)\n print(mean(x[x>=x.lower&x<=x.upper])) #средното на броят стойностите, влизащи в интервала\n x.length/1000 #вероятността някоя от случайните величини да е вътре в доверителния интервал\n}\n\n#N(2,2)\ntest.mu(2,2)\n#N(2,1)\ntest.mu(2,1)\n\n#04\n#1000 случайни нормално разпределени величини\ntest.mu.sigma = function(mu, sigma.sq) {\n x = rnorm(n = 1000, mean = mu, sd = sqrt(sigma.sq))\n x.cherta = mean(x)\n s = sd(x)\n gama = 0.95\n t = qt(gama, df = 1000 - 1) #квантил на t-разпределение с n-1 степени на свобода\n #N(mu,sigma^2) -> формула 12\n x.lower = x.cherta - t*s\n x.upper = x.cherta + t*s\n plot(x)\n lines(x=0:1000,y=rep(x.upper,1001), col='red')\n lines(x=0:1000,y=rep(x.lower,1001), col='blue')\n \n x.length=length(x[x>=x.lower&x<=x.upper]) #броят на стойностите влизащи в доверителния интервал\n print(x.length)\n print(mean(x[x>=x.lower&x<=x.upper])) #средното на броят стойностите, влизащи в интервала\n x.length/1000 #вероятността някоя от случайните величини да е вътре в доверителния интервал\n}\n\n\n", "meta": {"hexsha": "f483c2744578e6454c3fb3161ee1ffd7ab1b961e", "size": 5690, "ext": "r", "lang": "R", "max_stars_repo_path": "week8.r", "max_stars_repo_name": "StelaN/Statistics-R", "max_stars_repo_head_hexsha": "c8f49614bfdb6a294287fb06fac99dfcd558c3d6", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-06-17T10:22:32.000Z", "max_stars_repo_stars_event_max_datetime": "2018-06-17T10:22:32.000Z", "max_issues_repo_path": "week8.r", "max_issues_repo_name": "StelaN/Statistics-R", "max_issues_repo_head_hexsha": "c8f49614bfdb6a294287fb06fac99dfcd558c3d6", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "week8.r", "max_forks_repo_name": "StelaN/Statistics-R", "max_forks_repo_head_hexsha": "c8f49614bfdb6a294287fb06fac99dfcd558c3d6", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-04-06T13:38:34.000Z", "max_forks_repo_forks_event_max_datetime": "2018-04-06T13:38:34.000Z", "avg_line_length": 49.9122807018, "max_line_length": 331, "alphanum_fraction": 0.6973637961, "num_tokens": 2676, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9407897426182322, "lm_q2_score": 0.8056321866478978, "lm_q1q2_score": 0.7579304975214394}} {"text": "## 3. Using Bayes' Theorem ##\n\np_spam <- 0.5\np_non_spam <- 0.5\np_new_message <- 0.5417\np_new_message_given_spam <- 0.75\np_new_message_given_non_spam <- 0.3334\np_spam_given_new_message <- (p_spam * p_new_message_given_spam) / p_new_message\np_non_spam_given_new_message <- (p_non_spam * p_new_message_given_non_spam) / p_new_message\n\nclassification <- \"spam\"\n\n## 4. Using Proportionality ##\n\np_spam <- 0.5\np_non_spam <- 0.5\np_new_message_given_spam <- 0.75\np_new_message_given_non_spam <- 0.3334\np_spam_given_new_message <- p_spam * p_new_message_given_spam\np_non_spam_given_new_message <- p_non_spam * p_new_message_given_non_spam\n\nclassification <- 'spam'\n\n## 5. Classifying One Word Messages ##\n\np_spam_given_secret <- 8/21\np_non_spam <- 1/3\np_secret_given_non_spam <- 1/4\np_non_spam_given_secret <- p_non_spam * p_secret_given_non_spam\nclassification <- 'spam'\n\n## 6. Classifying Multiple Word Messages ##\n\np_spam_given_w1_w2_w3_w4 <- 64/4802\np_non_spam <- 2/4\np_w1_given_non_spam <- 2/9\np_w2_given_non_spam <- 1/9\np_w3_given_non_spam <- 2/9\np_w4_given_non_spam <- 2/9\n\np_non_spam_given_w1_w2_w3_w4 <- (p_non_spam *\n p_w1_given_non_spam * p_w2_given_non_spam *\n p_w3_given_non_spam * p_w4_given_non_spam\n )\n\nclassification <- 'spam'\n\n## 9. Edge Case: Words Not In Vocabulary ##\n\np_spam <- 2/4\np_secret_given_spam <- 4/7\np_the_given_spam <- 0/7\np_money_given_spam <- 2/7\np_spam_given_message <- (p_spam * p_secret_given_spam *\n p_the_given_spam * p_money_given_spam)\np_non_spam <- 2/4\np_secret_given_non_spam <- 2/9\np_the_given_non_spam <- 1/9\np_money_given_non_spam <- 0/9\np_non_spam_given_message <- (p_non_spam * p_secret_given_non_spam *\n p_the_given_non_spam * p_money_given_non_spam)\n\n\nprint(p_spam_given_message)\nprint(p_non_spam_given_message)\n\n## 10. Additive Smoothing ##\n\np_spam <- 2/4\np_secret_given_spam <- (4 + 1) / (7 + 9)\np_the_given_spam <- (0 + 1) / (7 + 9)\np_money_given_spam <- (2 + 1) / (7 + 9)\np_spam_given_message <- (p_spam * p_secret_given_spam *\n p_the_given_spam * p_money_given_spam)\np_non_spam <- 2/4\np_secret_given_non_spam <- (2 + 1) / (9 + 9)\np_the_given_non_spam <- (1 + 1) / (9 + 9)\np_money_given_non_spam <- (0 + 1) / (9 + 9)\np_non_spam_given_message <- (p_non_spam * p_secret_given_non_spam *\n p_the_given_non_spam * p_money_given_non_spam)\n\nclassification <- 'spam'", "meta": {"hexsha": "27cf921137dfed651c7d0a7370fa50e6cf0b2d6e", "size": 2495, "ext": "r", "lang": "R", "max_stars_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/4. Conditional Probability in R/4. The Naive Bayes Algorithm.r", "max_stars_repo_name": "MyArist/Dataquest", "max_stars_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 8, "max_stars_repo_stars_event_min_datetime": "2020-07-27T12:04:54.000Z", "max_stars_repo_stars_event_max_datetime": "2021-03-01T04:39:33.000Z", "max_issues_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/4. Conditional Probability in R/4. The Naive Bayes Algorithm.r", "max_issues_repo_name": "myarist/Dataquest", "max_issues_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/4. Conditional Probability in R/4. The Naive Bayes Algorithm.r", "max_forks_repo_name": "myarist/Dataquest", "max_forks_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 15, "max_forks_repo_forks_event_min_datetime": "2021-03-30T06:45:19.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-17T03:55:02.000Z", "avg_line_length": 30.4268292683, "max_line_length": 91, "alphanum_fraction": 0.7042084168, "num_tokens": 840, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9525741322079105, "lm_q2_score": 0.7956581049086031, "lm_q1q2_score": 0.7579233288175032}} {"text": "## 2. What is a probability? ##\n\np_5 <- 1 / 6\np_lottery <- 1 / 350000\n\n## 3. Outcomes vs Events ##\n\np_heart <- 13 / 52\np_2_or_3 <- 8 / 52\n\n## 4. Empirical Probability ##\n\np_three <- 18 / 100\n\n## 5. Repeating Experiments ##\n\nset.seed(1)\n\ncoin_toss <- function() {\n toss <- runif(1)\n if (toss <= 0.5) {\n return(\"HEADS\")\n } else {\n return(\"TAILS\")\n }\n}\nheads <- 0\nn_experiments <- 10\nfor (i in 1:n_experiments) {\n toss <- coin_toss()\n if (toss == \"HEADS\") {\n heads <- heads + 1\n }\n}\n\nexperiment_one <- heads / n_experiments\n\nn_experiments <- 100\nheads_2 <- 0\nfor (i in 1:n_experiments) {\n toss <- coin_toss()\n if (toss == \"HEADS\") {\n heads_2 <- heads_2 + 1\n }\n}\n\nexperiment_two <- heads_2 / n_experiments\n\n## 6. The Law of Large Numbers ##\n\nset.seed(1)\n\ncoin_toss <- function() {\n toss <- runif(1)\n if (toss <= 0.5) {\n return(\"HEADS\")\n } else {\n return(\"TAILS\")\n }\n}\nheads <- 0\nn_experiments <- 10\nfor (i in 1:n_experiments) {\n toss <- coin_toss()\n if (toss == \"HEADS\") {\n heads <- heads + 1\n }\n}\n\nexperiment_diff_one <- 0.5 - (heads / n_experiments)\n\nn_experiments <- 100\nheads_2 <- 0\nfor (i in 1:n_experiments) {\n toss <- coin_toss()\n if (toss == \"HEADS\") {\n heads_2 <- heads_2 + 1\n }\n}\n\nexperiment_diff_two <- 0.5 - (heads_2 / n_experiments)\n\nn_experiments <- 1000\nheads_3 <- 0\nfor (i in 1:n_experiments) {\n toss <- coin_toss()\n if (toss == \"HEADS\") {\n heads_3 <- heads_3 + 1\n }\n}\n\nexperiment_diff_three <- 0.5 - (heads_3 / n_experiments)", "meta": {"hexsha": "c1376bb38d50a902a46c63a09517401c16bb2af9", "size": 1570, "ext": "r", "lang": "R", "max_stars_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/3. Probability Fundamentals in R/1. Estimating Probabilities.r", "max_stars_repo_name": "MyArist/Dataquest", "max_stars_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 8, "max_stars_repo_stars_event_min_datetime": "2020-07-27T12:04:54.000Z", "max_stars_repo_stars_event_max_datetime": "2021-03-01T04:39:33.000Z", "max_issues_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/3. Probability Fundamentals in R/1. Estimating Probabilities.r", "max_issues_repo_name": "myarist/Dataquest", "max_issues_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Data Analyst in R/Step 5 - Probability and Statistics/3. Probability Fundamentals in R/1. Estimating Probabilities.r", "max_forks_repo_name": "myarist/Dataquest", "max_forks_repo_head_hexsha": "d0ee0a2a5e9d1f69f09bf0f6c32f382b6fa46b18", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 15, "max_forks_repo_forks_event_min_datetime": "2021-03-30T06:45:19.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-17T03:55:02.000Z", "avg_line_length": 17.0652173913, "max_line_length": 56, "alphanum_fraction": 0.5624203822, "num_tokens": 557, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9019206870747658, "lm_q2_score": 0.8397339736884712, "lm_q1q2_score": 0.7573734425091293}} {"text": "# 210518_PCA_Principal_component_analysis\n# vector가 갖고있는 기초통계 분산 값이 클 수록 해당 데이터 설명을 잘하는 성분으로 간주\n# 위 경우 w 가중치 값을 크게 만든다.\n# ex) 위 자동차 변량(핸들모양, 차의 무게) 중 차의 무게 분산 값이 가장 크다면\n# 차 무게의 가중치 값을 크게 하여\n# 차종에 대한(차종,차의 무게) 2차원 정보를 -> 1차원 직선으로 표기한다?\n\n# [05_주성분분석.pdf] p3\n# 행렬식 표기 Xw = T\n# Var(X)가 최대가 되는 w 찾기\n# x11w1 + x12w2+ .... + x1pwp = t1\n\n# 연습\nx <- data.frame(c(1,2),c(3,4))\nx\nw <- c(2,2)\nx*w\n\n\n# [05_주성분분석.pdf] p11\nx1<-c(26,46,57,36,57,26,58,37,36,56,78,95,88,90,52,56)\nx2<-c(35,74,73,73,62,22,67,34,22,42,65,88,90,85,46,66)\nx3<-c(35,76,38,69,25,25,87,79,36,26,22,36,58,36,25,44)\nx4<-c(45,89,54,55,33,45,67,89,47,36,40,56,68,45,37,56)\n\n\nscore <- cbind(x1,x2,x3,x4)\nscore\n# x1 x2 x3 x4\n# [1,] 26 35 35 45\n# [2,] 46 74 76 89\n# [3,] 57 73 38 54\n# [4,] 36 73 69 55\n# [5,] 57 62 25 33\n# [6,] 26 22 25 45\n# [7,] 58 67 87 67\n# [8,] 37 34 79 89\n# [9,] 36 22 36 47\n# [10,] 56 42 26 36\n# [11,] 78 65 22 40\n# [12,] 95 88 36 56\n# [13,] 88 90 58 68\n# [14,] 90 85 36 45\n# [15,] 52 46 25 37\n# [16,] 56 66 44 56\n\ncolnames(score) <-c(\"국어\",\"영어\",\"수학\",\"과학\")\nrownames(score)<-1:16\nhead(score)\n\n\nresult <- prcomp(score)\nresult\n\n# Standard deviations (1, .., p=4):\n# [1] 30.122748 27.052808 9.076140 6.152386\n# \n# Rotation (n x k) = (4 x 4): 가중치 w1, w2, w3, w4\n# PC1 PC2 PC3\n# 국어 0.6093268 -0.39286407 -0.6126773\n# 영어 0.7185749 -0.09337973 0.6200124\n# 수학 0.2624323 0.73573272 0.1052861\n# 과학 0.2085672 0.54372366 -0.4786711\n# PC4\n# 국어 -0.3146508\n# 영어 0.3008572\n# 수학 -0.6154198\n# 과학 0.6570680\n\n?prcomp\n# Principal Components Analysis\n# Performs a principal components analysis on the given data matrix and returns the results as an object of class prcomp.\n\nsummary(result)\n# Importance of components:\n# PC1 \n# Standard deviation 30.1227 # 표준편차 \n# Proportion of Variance 0.5157 # 분산 비율\n# Cumulative Proportion 0.5157 # 설명력, 기여도, 약 52% 설명\n# PC2\n# Standard deviation 27.0528\n# Proportion of Variance 0.4159\n# Cumulative Proportion 0.9317 # 누적된 결과이므로 PC1과 PC2의 설명력\n# PC3\n# Standard deviation 9.07614\n# Proportion of Variance 0.04682\n# Cumulative Proportion 0.97849\n# PC4\n# Standard deviation 6.15239\n# Proportion of Variance 0.02151\n# Cumulative Proportion 1.00000\n\n\n\nbiplot(result)\n?biplot\nscreeplot(result, npcs=4, type=\"lines\", main=\"score\")\n", "meta": {"hexsha": "5d5c6500d2152ca4d047afe6534d2ae0ef03fff5", "size": 2268, "ext": "r", "lang": "R", "max_stars_repo_path": "week04/210518_principal_component_analysis.r", "max_stars_repo_name": "sohui96/r-study", "max_stars_repo_head_hexsha": "3d545b958f358a05e4b5973e2843d2744f16551b", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "week04/210518_principal_component_analysis.r", "max_issues_repo_name": "sohui96/r-study", "max_issues_repo_head_hexsha": "3d545b958f358a05e4b5973e2843d2744f16551b", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "week04/210518_principal_component_analysis.r", "max_forks_repo_name": "sohui96/r-study", "max_forks_repo_head_hexsha": "3d545b958f358a05e4b5973e2843d2744f16551b", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 23.1428571429, "max_line_length": 121, "alphanum_fraction": 0.6397707231, "num_tokens": 1241, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9019206844384594, "lm_q2_score": 0.839733963661418, "lm_q1q2_score": 0.7573734312517265}} {"text": "### Copyright (c) 2013 Kendrick Boyd. This is free software. See\n### LICENSE for details.\n\n### Precision-Recall Analysis Stuff for R\n### \n\n\n### Precision-Recall curves\n###\n### positive (cases) scores (outputs, probabilities, etc.) are random\n### variable Y negative (controls) scores are random variable X\n###\n### pi (prevalence) = # positives / (# positives + # negatives)\n\n\n######################################################################\n### Binormal\n### Assume scores are normally distributed.\n\n### parameters:\n### X ~ Normal(0,1)\n### Y ~ Normal(pos.mean,pos.sd)\n\n\n## Calculate true precision for a threshold under binormal distribution.\nbinormal.precision <- function(c,pi=0.5,pos.mean=1.0,pos.sd=1.0)\n{\n r = (pi*pnorm(c,pos.mean,pos.sd,lower.tail=FALSE))/(pi*pnorm(c,pos.mean,pos.sd,lower.tail=FALSE) + (1-pi)*pnorm(c,mean=0,sd=1,lower.tail=FALSE))\n r[is.nan(r)] = 1 ## nan from a denominator of 0 should be precision 1\n return(r)\n}\n\n\n## Calculate true recall for a threshold under binormal distribution.\nbinormal.recall <- function(c,pi=0.5,pos.mean=1.0,pos.sd=1.0)\n{\n pnorm(c,pos.mean,pos.sd,lower.tail=FALSE)\n}\n\n## Calculate true precision for a particular recall under binormal distribution.\nbinormal.precision.at.recall <- function(recall, pi=0.5,pos.mean=1.0,pos.sd=1.0) {\n return(binormal.precision(qnorm(recall,pos.mean,pos.sd,lower.tail=FALSE),pi=pi,pos.mean=pos.mean,pos.sd=pos.sd))\n}\n\n# Plot the true binormal PR curve.\nbinormal.plot <- function(pi=0.5,pos.mean=1.0,pos.sd=1.0)\n{\n plot(function(x) {binormal.precision(qnorm(x,pos.mean,pos.sd,lower.tail=FALSE),pi=pi,pos.mean=pos.mean,pos.sd=pos.sd)},xlim=c(0,1),ylim=c(0,1),xlab=\"Recall\",ylab=\"Precision\",sub=paste(\"pi=\",pi,\", pos.mean=\",pos.mean,\", pos.sd=\",pos.sd))\n}\n\n\n# Calculate true area under binormal PR curve using numeric integration.\nbinormal.area <- function(pi=0.5,pos.mean=1.0,pos.sd=1.0)\n{\n f <- function(q) { binormal.precision(qnorm(q,pos.mean,pos.sd,lower.tail=FALSE),pi=pi,pos.mean=pos.mean,pos.sd=pos.sd) }\n ## monte carlo integration \n #mean(f(runif(samples)))\n\n ## integrate method of R, much faster (although might have problems with x=0)\n r = integrate(f,0,1)\n return(r$value)\n}\n\n\n## Generate sample from binormal distribution. When pi.exact is false,\n## the number of positive examples is distributed according to\n## Binomial(n,pi). If pi.exact is false, the number of positive\n## examples is always pi*n.\nbinormal.sample <- function(n=1, pi=0.5, pos.mean=1.0, pos.sd=1.0, pi.exact = TRUE) {\n if (pi.exact) {\n num.pos = as.integer(pi*n)\n }\n else {\n num.pos = rbinom(n=1,prob=pi,size=n) \n }\n num.neg = n-num.pos\n\n pos.values = rnorm(num.pos,mean=pos.mean,sd=pos.sd)\n neg.values = rnorm(num.neg,mean=0,sd=1)\n return(list(pos.values=pos.values,neg.values=neg.values))\n}\n\n\n\n\n######################################################################\n### Bibeta\n### Assumes scores are from two Beta distributions.\n### Y ~ Beta(pos.a,pos.b)\n### X ~ Beta(neg.a,neg.b)\n\n\n## Calculates true precision for a threshold under bibeta distribution.\nbibeta.precision <- function(c,pi=0.5,pos.a=2,pos.b=1,neg.a=1,neg.b=1) {\n ## X ~ Beta(neg.a,neg.b), Y ~ Beta(pos.a,pos.b)\n r = (pi*pbeta(c,pos.a,pos.b,lower.tail=FALSE))/(pi*pbeta(c,pos.a,pos.b,lower.tail=FALSE) + (1-pi)*pbeta(c,neg.a,neg.b,lower.tail=FALSE))\n r[is.nan(r)] = 1 ## nan from a denominator of 0 should have precision of 1\n return(r)\n}\n\n## Calculates true recall for a threshold under bibeta distribution.\nbibeta.recall <- function(c,pi=0.5,pos.a=2,pos.b=1,neg.a=1,neg.b=1) {\n pbeta(c,pos.a,pos.b,lower.tail=FALSE)\n}\n\n## Calculate true precision for a particular recall under bibeta distribution.\nbibeta.precision.at.recall <- function(recall,pi=0.5,pos.a=2,pos.b=1,neg.a=1,neg.b=1) {\n return(bibeta.precision(qbeta(recall,pos.a,pos.b,lower.tail=FALSE),pi=pi,pos.a=pos.a,pos.b=pos.b,neg.a=neg.a,neg.b=neg.b))\n}\n\n## Plot the true bibeta PR curve.\nbibeta.plot <- function(pi=0.5,pos.a=2,pos.b=1,neg.a=1,neg.b=1) {\n plot(function(x) {bibeta.precision(qbeta(x,pos.a,pos.b,lower.tail=FALSE),pi=pi,pos.a=pos.a,pos.b=pos.b,neg.a=neg.a,neg.b=neg.b)},\n xlim=c(0,1),\n ylim=c(0,1),\n xlab=\"Recall\",\n ylab=\"Precision\",\n sub=paste(\"pi=\",pi,\",X (neg) ~ Beta(\",neg.a,\",\",neg.b,\"), Y (pos) ~ Beta(\",pos.a,\",\",pos.b,\")\")\n )\n \n}\n\n## Calculate the true area under the bibeta PR curve using numeric integration.\nbibeta.area <- function(pi=0.5,pos.a=2,pos.b=1,neg.a=1,neg.b=1) {\n f <- function(q) { bibeta.precision(qbeta(q,pos.a,pos.b,lower.tail=FALSE),pi=pi,pos.a=pos.a,pos.b=pos.b,neg.a=neg.a,neg.b=neg.b) }\n\n ## use R's integrate method\n res = integrate(f,0,1)\n return(res$value)\n}\n\n## Generate sample from bibeta distribution. When pi.exact is false,\n## the number of positive examples is distributed according to\n## Binomial(n,pi). If pi.exact is false, the number of positive\n## examples is always pi*n.\nbibeta.sample <- function(n=1,pi=0.5,pos.a=2,pos.b=1,neg.a=1,neg.b=1,pi.exact = TRUE) {\n if (pi.exact) {\n num.pos = as.integer(pi*n)\n }\n else {\n num.pos = rbinom(n=1,prob=pi,size=n)\n }\n \n num.neg = n-num.pos\n\n ## Generates a sample of observed values for neg.values (X) ~\n ## Beta(neg.a,neg.b) and pos.values (Y) ~ Beta(pos.a,pos.b).\n\n pos.values = rbeta(num.pos,pos.a,pos.b)\n neg.values = rbeta(num.neg,neg.a,neg.b)\n\n return(list(pos.values=pos.values,neg.values=neg.values))\n}\n\n\n######################################################################\n### Offset Uniform\n### Assumes the scores are drawn from two uniform distributions\n### spanning different ranges\n\n### X ~ Uniform(0,1)\n### Y ~ Uniform(a,a+b)\n\n\n## Calculate true precision for a threshold under offset uniform distributions.\noffsetuniform.precision <- function(c,pi=0.5,a=0.5,b=1) {\n r = (pi*punif(c,min=a,max=a+b,lower.tail=FALSE))/(pi*punif(c,min=a,max=a+b,lower.tail=FALSE) + (1-pi)*punif(c,min=0,max=1,lower.tail=FALSE))\n r[is.nan(r)] = 1 ## nan from denominator of 0 should have precision of 1\n return(r)\n}\n\n## Calculate true recall for a threshold under offset uniform distributions.\noffsetuniform.recall <- function(c,pi=0.5,a=0.5,b=1) {\n punif(c,min=a,max=a+b,lower.tail=FALSE)\n}\n\n## Calculate true precision for a particular recall under offset uniform distribution.\noffsetuniform.precision.at.recall <- function(recall, pi=0.5,a=0.5,b=1) {\n return(offsetuniform.precision(qunif(recall,a,a+b,lower.tail=FALSE),pi=pi,a=a,b=b))\n}\n\n## Plot the true offset uniform PR curve.\noffsetuniform.plot <- function(pi=0.5,a=0.5,b=1) {\n plot(function(x) {offsetuniform.precision(qunif(x,min=a,max=a+b,lower.tail=FALSE),\n pi=pi,\n a=a,\n b=b)},\n xlim=c(0,1),\n ylim=c(0,1),\n xlab=\"Recall\",\n ylab=\"Precision\",\n sub=paste(\"pi=\",pi,\" a=\",a,\"b=\",b)) \n}\n\n## Calculate true area under offset uniform PR curve using numeric integration.\noffsetuniform.area <- function(pi=0.5,a=0.5,b=1) {\n f <- function(q) { offsetuniform.precision(qunif(q,min=a,max=a+b,lower.tail=FALSE),\n pi=pi,\n a=a,\n b=b)}\n r = integrate(f,0,1)\n return (r$value)\n}\n\n## Generate sample from offset uniform distribution. When pi.exact is false,\n## the number of positive examples is distributed according to\n## Binomial(n,pi). If pi.exact is false, the number of positive\n## examples is always pi*n.\noffsetuniform.sample <- function(n=1,pi=0.5,a=0.5,b=1,pi.exact = TRUE) {\n if (pi.exact) {\n num.pos = as.integer(pi*n)\n }\n else {\n num.pos = rbinom(n=1,prob=pi,size=n)\n }\n num.neg = n-num.pos\n\n ## X (neg) ~ Uniform(0,1)\n ## Y (pos) ~ Uniform(a,a+b)\n\n pos.values = runif(n=num.pos,min=a,max=a+b)\n neg.values = runif(n=num.neg,min=0,max=1)\n\n return(list(pos.values=pos.values,neg.values=neg.values)) \n}\n\n\n\n\naucpr.conf.int <- function(estimate,pos.values,neg.values,prcurve.estimator,conf.level=0.95,method=\"binomial\",bootstrap.replicates=1000) {\n ## Calculates confidence interval for an AUCPR estimate.\n ## method=c(\"binomial\",\"expit\")\n m = match.arg(method,c(\"binomial\",\"expit\",\"bootstrap\"))\n \n if (m==\"binomial\") {\n return(aucpr.conf.int.binomial(estimate,num.pos=length(pos.values),num.neg=length(neg.values),conf.level=conf.level))\n }\n else if (m==\"expit\") {\n return(aucpr.conf.int.expit(estimate,num.pos=length(pos.values),num.neg=length(neg.values),conf.level=conf.level))\n }\n else if (m==\"bootstrap\") {\n return(aucpr.conf.int.bootstrap(estimate,pos.values,neg.values,prcurve.estimator,conf.level,bootstrap.replicates))\n }\n}\n\naucpr.conf.int.binomial <- function(estimate,num.pos,num.neg,conf.level=0.95) {\n ## Calculates confidence interval for an AUCPR estimate under\n ## binomial assumptions. Uses num.pos as the sample size (might not\n ## be best?).\n \n ci = estimate+qnorm(c((1-conf.level)/2,(1+conf.level)/2))*sqrt(estimate*(1-estimate)/num.pos)\n attr(ci,\"conf.level\") = conf.level\n attr(ci,\"method\") = \"binomial\"\n return(ci)\n}\n\naucpr.conf.int.expit <- function(estimate,num.pos,num.neg,conf.level=0.95) {\n ## Calculates confidence interval for an AUCPR estimate using expit.\n \n ## convert to logit scale\n est.logit = log(estimate/(1-estimate))\n ## standard error (from Kevin Eng)\n se.logit = sqrt(estimate*(1-estimate)/num.pos)*(1/estimate + 1/(1-estimate))\n ## confidence interval in logit\n ci.logit = est.logit+qnorm(c((1-conf.level)/2,(1+conf.level)/2))*se.logit\n\n ## back to original scale\n ci = exp(ci.logit)/(1+exp(ci.logit))\n attr(ci,\"conf.level\") = conf.level\n attr(ci,\"method\") = \"expit\"\n return(ci)\n}\n\naucpr.conf.int.bootstrap <- function(estimate,pos.values,neg.values,prcurve.estimator,conf.level=0.95,replicates=1000) {\n areas = rep(0,replicates)\n\n for (i in 1:replicates) {\n p.v = sample(pos.values,replace=TRUE)\n n.v = sample(neg.values,replace=TRUE)\n\n res = prcurve.estimator(p.v,n.v)\n areas[i] = res$area\n }\n\n q = quantile(areas,c((1-conf.level)/2,(1+conf.level)/2))\n \n ci = c(q[1],q[2])\n attr(ci,\"conf.level\") = conf.level\n attr(ci,\"method\") = \"bootstrap\"\n attr(ci,\"median\") = median(areas)\n attr(ci,\"mean\") = mean(areas)\n \n return (ci)\n}\n\naucpr.conf.int.crossvalidation <- function(estimate,pos.values,neg.values,prcurve.estimator,conf.level=0.95,folds=10) {\n areas = rep(0,folds)\n\n pos = sample(pos.values)\n neg = sample(neg.values)\n\n pos.counts = rep(c(as.integer(length(pos.values)/folds)+1,as.integer(length(pos.values)/folds)),c(length(pos.values)%%folds,10-length(pos.values)%%folds))\n neg.counts = rep(c(as.integer(length(neg.values)/folds)+1,as.integer(length(neg.values)/folds)),c(length(neg.values)%%folds,10-length(neg.values)%%folds))\n \n pos.index = 1\n neg.index = 1\n for (k in 1:folds) {\n p = pos[pos.index:(pos.index+pos.counts[k]-1)]\n n = neg[neg.index:(neg.index+neg.counts[k]-1)]\n\n areas[k] = prcurve.estimator(p,n)$area\n \n pos.index = pos.index + pos.counts[k]\n neg.index = neg.index + neg.counts[k]\n }\n \n\n ## normal approximation\n ##ci = mean(areas) + qnorm(c((1-conf.level)/2,(1+conf.level)/2))*sd(areas)/sqrt(length(areas))\n ## use t-distribution\n ci = mean(areas) + qt(c((1-conf.level)/2,(1+conf.level)/2),df=length(areas)-1)*sd(areas)/sqrt(length(areas))\n \n attr(ci,\"conf.level\") = conf.level\n attr(ci,\"method\") = \"crossvalidation, t-dist\"\n attr(ci,\"values\") = areas\n attr(ci,\"mean\") = mean(areas)\n \n return(ci)\n}\n\n\n\n\n\n# return confusion matrix info for >= threshold\n# assume labels are 0 and 1\nconfusion.matrix <- function(values,labels,threshold)\n{\n counts=table(factor(values>=threshold,c(FALSE,TRUE)),labels)\n ## print(counts)\n \n TP = counts[2,2]\n TN = counts[1,1]\n FP = counts[2,1]\n FN = counts[1,2]\n \n if (TP+FP == 0)\n return(list(tp=TP,tn=TN,fp=FP,fn=FN,precision=NaN,sensitivity=TP/(TP+FN),specificity=TN/(TN+FP),accuracy=(TP+TN)/(TP+TN+FP+TN)))\n else\t\n return(c(tp=TP,tn=TN,fp=FP,fn=FP,precision=TP/(TP+FP),sensitivity=TP/(TP+FN),specificity=TN/(TN+FP),accuracy=(TP+TN)/(TP+TN+FP+TN)))\n}\n\n\n## Create all confusion matrices from set of pos.values and neg.values\nmake.confusion.matrices <- function(pos.values,neg.values) {\n ## thresholds, sorting to have increasing recall\n thresholds = sort(c(-Inf,unique(c(pos.values,neg.values)),Inf),decreasing=TRUE)\n \n ## 0 - negative (control)\n ## 1 - positive (case)\n labels = c(rep(1,length(pos.values)),rep(0,length(neg.values)))\n values = c(pos.values,neg.values)\n \n # create set of confusion matrices\n d=sapply(thresholds,function(t) { confusion.matrix(values,labels,t) })\n\n return(d)\n}\n\nprecisions.recalls.fast <- function(pos.values,neg.values) {\n ## 0 for negative, 1 for positive\n l = rep(c(0,1),c(length(neg.values),length(pos.values)))\n v = c(neg.values,pos.values)\n\n ## sort by descending value\n indices = order(v,decreasing=TRUE)\n labels = l[indices]\n values = v[indices]\n\n tp = 0\n fp = 0\n\n z = 1\n precisions = rep(0,length(indices)+1)\n recalls = rep(0,length(indices)+1)\n\n tp = 0\n fp = 0\n\n for (i in 1:length(indices)) {\n if (labels[i]==1) {\n tp = tp + 1 \n }\n else {\n fp = fp + 1\n }\n\n ## make sure not between tied values\n if (i==length(indices) || values[i]>values[i+1]) {\n ## can put a threshold\n\n ## if first, insert (r=0,p=1) point\n if (z==1) {\n recalls[z] = 0\n precisions[z] = 1\n z = z + 1\n }\n recalls[z] = tp/(length(pos.values))\n precisions[z] = tp/(tp+fp)\n z = z + 1\n }\n }\n\n ## truncate recals and precisions\n recalls = recalls[1:(z-1)]\n precisions = precisions[1:(z-1)]\n \n return (list(recalls=recalls,precisions=precisions))\n}\n\n\n# return c(v1[1],v2[1],v1[2],v2[2],...) works with uneven vectors,\n# appending the extra elements from the longer vector so return always\n# has length of length(v1)+length(v2) from\n# http://tolstoy.newcastle.edu.au/R/help/06/03/22717.html\ninterleave <- function(v1,v2) {\n ord1 <- 2*(1:length(v1))-1\n ord2 <- 2*(1:length(v2))\n c(v1,v2)[order(c(ord1,ord2))]\n}\n\n\n#################################################################\n## Estimators\n#################################################################\n# Under, connects lowest precision on left side to highest precision\n# on the right\nprcurve.lowertrap <- function(pos.values,neg.values,conf.level=0.95,conf.int.method=\"binomial\") {\n t = precisions.recalls.fast(pos.values,neg.values)\n\n recalls = t$recalls\n precisions = t$precisions\n \n\n # get max and min precision for each unique recall\n r.unique = unique(recalls)\n p.min = sapply(r.unique,function(r) { min(precisions[recalls==r])})\n p.max = sapply(r.unique,function(r) { max(precisions[recalls==r])})\n\n # use min on left side and max on right side of each area between known recalls\n ids=2:length(r.unique)\n area = as.double((r.unique[ids]-r.unique[ids-1]) %*% (p.max[ids] + p.min[ids-1]) / 2)\n\n rs = rep(r.unique,each=2)\n ps = interleave(p.max,p.min)\n\n ci = aucpr.conf.int(area,\n pos.values=pos.values,\n neg.values=neg.values,\n prcurve.estimator=prcurve.lowertrap,\n conf.level=conf.level,\n method=conf.int.method)\n\n return(list(area=area,\n x=rs,\n y=ps,\n conf.int=ci)) \n}\n\n# connects highest precisions at each recall, definitely an\n# over-estimate\nprcurve.uppertrap <- function(pos.values,neg.values,conf.level=0.95,conf.int.method=\"binomial\") {\n t = precisions.recalls.fast(pos.values,neg.values)\n\n recalls = t$recalls\n precisions = t$precisions\n\n # get max and min precision for each unique recall\n r.unique = unique(recalls)\n p.min = sapply(r.unique,function(r) { min(precisions[recalls==r])})\n p.max = sapply(r.unique,function(r) { max(precisions[recalls==r])})\n\n # use max precision for all recalls (NOT LEGITIMATE!)\n \n ids=2:length(r.unique)\n area = as.double((r.unique[ids]-r.unique[ids-1]) %*% (p.max[ids] + p.max[ids-1]) / 2)\n\n\n ci = aucpr.conf.int(area,\n pos.values=pos.values,\n neg.values=neg.values,\n prcurve.estimator=prcurve.uppertrap,\n conf.level=conf.level,\n method=conf.int.method)\n \n\n return(list(area=area,\n x=r.unique,\n y=p.max,\n conf.int=ci))\n}\n\n\n## estimate PR curve and area under PR curve using average precision\n## method, mean precision at each positive example\nprcurve.ap.slow <- function(pos.values, neg.values, conf.level=0.95, conf.int.method=\"binomial\") {\n ## thresholds, sorting to have increasing recall\n ## only use thresholds for positives\n thresholds = sort(pos.values,decreasing=TRUE)\n \n labels = c(rep(1,length(pos.values)),rep(0,length(neg.values)))\n values = c(pos.values,neg.values)\n \n ## create set of confusion matrices\n d=sapply(thresholds,function(t) { confusion.matrix(values,labels,t) })\n recalls = unlist(d[6,])\n precisions = unlist(d[5,])\n \n area = mean(precisions)\n \n \n y = rep(precisions,each=2)\n x = c(0,rep(recalls[1:(length(recalls)-1)],each=2),recalls[length(recalls)])\n\n ci = aucpr.conf.int(area,\n pos.values=pos.values,\n neg.values=neg.values,\n prcurve.estimator=prcurve.ap.slow,\n conf.level=conf.level,\n method=conf.int.method)\n \n return (list(area=area,\n x=x,\n y=y,\n conf.int=ci)) \n}\n\nprcurve.ap <- function(pos.values, neg.values, conf.level=0.95, conf.int.method=\"binomial\") {\n ## 0 for negative, 1 for positive\n l = rep(c(0,1),c(length(neg.values),length(pos.values)))\n v = c(neg.values,pos.values)\n\n ## sort by descending value\n indices = order(v,decreasing=TRUE)\n labels = l[indices]\n values = v[indices]\n\n \n tp = 0\n fp = 0\n\n rs = rep(0,length(pos.values))\n ps = rep(0,length(pos.values))\n z = 1\n cur.tp = 0\n cur.fp = 0\n for (i in 1:length(indices)) {\n if (labels[i]==1) {\n cur.tp = cur.tp + 1 \n }\n else {\n cur.fp = cur.fp + 1\n }\n ## make sure not between tied values\n if (i==length(indices) || values[i]>values[i+1]) {\n ## can put a threshold here\n tp = tp + cur.tp\n fp = fp + cur.fp\n\n if (cur.tp > 0) {\n for (j in 1:cur.tp) {\n rs[z] = tp/length(pos.values)\n ps[z] = tp/(tp+fp)\n z = z + 1 \n }\n }\n cur.tp = 0\n cur.fp = 0\n }\n \n }\n\n \n if (z != length(pos.values)+1) {\n cat(\"WARNING: did not fill recall and precision arrays correctly (z: received=\",z,\", expected=\",length(pos.values)+1,\")\\n\",sep=\"\")\n }\n area = mean(ps)\n\n y = rep(ps,each=2)\n x = c(0,rep((rs[1:(length(rs)-1)]),each=2),rs[length(rs)])\n\n \n ci = aucpr.conf.int(area,\n pos.values=pos.values,\n neg.values=neg.values,\n prcurve.estimator=prcurve.ap,\n conf.level=conf.level,\n method=conf.int.method)\n \n return (list(area=area,\n x=x,\n y=y,\n conf.int=ci)) \n}\n\n## estimate PR curve and area under PR curve with MLE parameters for\n## positive and negative normal distributions\nprcurve.binormal <- function(pos.values,neg.values,conf.level=0.95,conf.int.method=\"binomial\") {\n ## Assume X ~ N(0,1), i.e. negatives have standard normal distribution.\n ## So only have 2 df to calculate.\n\n if (length(pos.values)<=1) {\n cat(\"ERROR: cannot use binormal estimate with fewer than 2 positive samples\\n\")\n }\n if (length(neg.values)<=1) {\n cat(\"ERROR: cannot use binormal estimate with fewer than 2 negative samples\\n\")\n }\n mean.hat = (mean(pos.values)-mean(neg.values))/sd(neg.values)\n sd.hat = sd(pos.values)/sd(neg.values)\n\n pi = length(pos.values)/(length(pos.values)+length(neg.values))\n \n area = binormal.area(pi=pi,pos.mean=mean.hat,pos.sd=sd.hat)\n\n ci = aucpr.conf.int(area,\n pos.values=pos.values,\n neg.values=neg.values,\n prcurve.estimator=prcurve.binormal,\n conf.level=conf.level,\n method=conf.int.method)\n \n return(list(area=area,pi.hat=pi,pos.mean.hat=mean.hat,pos.sd.hat=sd.hat, conf.int=ci))\n}\n\n\n## Use linear interpolation in ROC space, translate to PR space and\n## find the precision for the specified recall (r) for interpolating\n## between PR points (r1,p1) and (r2,p2)\ninterpolate.point <- function(r1,p1,r2,p2,r) {\n res = r / (r*(1 + (1-p2)*r2/(p2*(r2-r1)) - (1-p1)*r1/(p1*(r2-r1))) + (1-p1)*r1/p1 - r1*(1-p2)*r2/(p2*(r2-r1)) + r1*(1-p1)*r1/(p1*(r2-r1)))\n res[r==0] = p2\n return(res)\n## if (r==0) {\n## ## hmm, use limit which is just p2\n## return(p2)\n## }\n## else {\n## return(r / (r*(1 + (1-p2)*r2/(p2*(r2-r1)) - (1-p1)*r1/(p1*(r2-r1))) + (1-p1)*r1/p1 - r1*(1-p2)*r2/(p2*(r2-r1)) + r1*(1-p1)*r1/(p1*(r2-r1))))\n## }\n}\n\ninterpolate.curve <- function(recalls,precisions,num.samples=1000) {\n\n ## sort by increasing recall\n indices = order(recalls,decreasing=FALSE)\n rs = recalls[indices]\n ps = precisions[indices]\n\n xs = rep(0,num.samples)\n ys = rep(0,num.samples)\n ## point lies between rs[index-1] and rs[index]\n index = 1\n for (i in 1:num.samples) {\n ## evenly spaced in [0,1], including end-points\n recall = (i-1)/(num.samples-1)\n xs[i] = recall\n \n while (rs[index] r2) {\n cat(\"WARNING: recalls passed to interpolate.area are not sorted ascending\\n\")\n cat(\"recalls: \",recalls,\"\\n\")\n cat(\"precisions: \",precisions,\"\\n\")\n }\n \n if (r1==0) {\n ## definite integral is undefined\n ## use rectangle with height p2 (as interpolate.curve creates)\n area = area + p2*(r2-r1)\n \n }\n else {\n ## formula between these is p' = r' / (a + b*r')\n a = (1-p1)*r1/p1 - r1*(1-p2)*r2/(p2*(r2-r1)) + r1*(1-p1)*r1/(p1*(r2-r1))\n b = 1 + (1-p2)*r2/(p2*(r2-r1)) - (1-p1)*r1/(p1*(r2-r1))\n \n ## indefinite integral is (bx - a log (a + bx))/b^2\n ## area contribution is definite integral from r1 to r2\n area = area + (b*r2 - a*log(a+b*r2))/(b*b) - (b*r1 - a*log(a+b*r1))/(b*b)\n }\n \n }\n return(area)\n}\n\n## estimate PR curve and AUCPR by interpolating between the max\n## precisions for each recall\nprcurve.interpolate <- function(pos.values,neg.values,conf.level=0.95,conf.int.method=\"binomial\",aggregator = max) {\n t = precisions.recalls.fast(pos.values,neg.values)\n\n recalls = t$recalls\n precisions = t$precisions\n\n r.unique = unique(recalls)\n p.max = sapply(r.unique,function(r) { aggregator(precisions[recalls==r])})\n\n ## sort\n indices = order(r.unique,decreasing=FALSE)\n rs = r.unique[indices]\n ps = p.max[indices]\n\n area = interpolate.area(rs,ps)\n\n ci = aucpr.conf.int(area,\n pos.values=pos.values,\n neg.values=neg.values,\n prcurve.estimator= function(p.v,n.v,c.l,c.i.m) { prcurve.interpolate(pos.values=p.v,neg.values=n.v,conf.level=c.l,conf.int.method=c.i.m,aggregator) },\n conf.level=conf.level,\n method=conf.int.method)\n\n curve = interpolate.curve(rs,ps)\n \n return(list(area=area,x=curve$x,y=curve$y,conf.int=ci))\n \n}\n\n\nroccurve.points <- function(pos.values,neg.values) {\n ## 0 for negative, 1 for positive\n l = rep(c(0,1),c(length(neg.values),length(pos.values)))\n v = c(neg.values,pos.values)\n\n ## sort by descending value\n indices = order(v,decreasing=TRUE)\n labels = l[indices]\n values = v[indices]\n\n tp = 0\n fp = 0\n\n z = 1\n tprs = rep(0,length(indices)+1)\n fprs = rep(0,length(indices)+1)\n\n for (i in 1:length(indices)) {\n if (labels[i]==1) { tp = tp + 1 }\n else { fp = fp + 1 }\n\n ## make sure not between tied values\n if (i==length(indices) || values[i]>values[i+1]) {\n ## can place threshold\n\n ## if first, insert the all negative point (tpr=0,fpr=0)\n if (z==1) {\n tprs[z] = 0\n fprs[z] = 0\n z = z + 1\n }\n tprs[z] = tp/length(pos.values)\n fprs[z] = fp/length(neg.values)\n z = z + 1\n } \n }\n\n ## truncate to used indices\n tprs = tprs[1:(z-1)]\n fprs = fprs[1:(z-1)]\n\n return (list(tprs=tprs,fprs=fprs))\n}\n\n## Estimate PR curve by taking convex hull in ROC space, convert only\n## points on convex hull in ROC to PR, then use interpolation to go\n## between.\nprcurve.interpolate.convex <- function(pos.values, neg.values, conf.level=0.95,conf.int.method=\"binomial\") {\n pi = length(pos.values)/(length(pos.values)+length(neg.values))\n \n t = roccurve.points(pos.values,neg.values)\n\n ## add the point (1,0) to make convex hull calculation clean (won't\n ## pick up any worse than random points)\n points = matrix(c(t$fprs,1,t$tprs,0),ncol=2)\n\n hull.indices = chull(points)\n\n ## remove the dummy point (0,1) we added, it's always the last element\n ## with index length(points)/2\n indices = hull.indices[!hull.indices==length(points)/2]\n points = points[indices,]\n\n ## due to bugs in chull and just to be safe sort points ascending by\n ## recall (second column)\n points = points[order(points[,2],decreasing=FALSE),]\n \n ## convert to PR space\n precisions = rep(0,length(indices))\n recalls = rep(0,length(indices))\n for (i in 1:length(indices)) {\n if (points[i,1]==0 & points[i,2]==0) {\n ## all negative\n precisions[i] = 1.0\n recalls[i] = 0.0\n }\n else {\n recalls[i] = points[i,2]\n precisions[i] = pi*points[i,2]/(pi*points[i,2] + (1-pi)*points[i,1])\n }\n }\n\n ## remove duplicate recalls, most likely having multiple recall=1.0\n ## points coming from the y=1 horizontal line in ROC space\n recalls.unique = unique(recalls)\n precisions.unique = sapply(recalls.unique,function(r) { max(precisions[recalls==r])})\n\n ## check that recalls are sorted ascending, having problems with non-sorted recalls\n if (is.unsorted(recalls.unique)) {\n cat(\"pos.values = \",pos.values,\"\\n\")\n cat(\"neg.values = \",neg.values,\"\\n\")\n cat(\"recalls = \",recalls,\"\\n\")\n cat(\"precisions = \",precisions,\"\\n\")\n cat(\"recalls.unique = \",recalls.unique,\"\\n\")\n cat(\"precisions.unique = \",precisions.unique,\"\\n\")\n \n }\n \n area = interpolate.area(recalls.unique,precisions.unique)\n \n ci = aucpr.conf.int(area,\n pos.values=pos.values,\n neg.values=neg.values,\n prcurve.estimator=prcurve.interpolate.convex,\n conf.level=conf.level,\n method=conf.int.method)\n\n curve = interpolate.curve(recalls.unique,precisions.unique)\n\n return(list(area=area,x=curve$x,y=curve$y,conf.int=ci))\n \n}\n\n## stratified bootstrap\n## resample positive and negative separately\nbootstrap <- function(pos.values,neg.values,prcurve.function,replicates=1000) {\n areas = rep(0,replicates)\n \n for (i in 1:replicates) {\n p.v = sample(pos.values,replace=TRUE)\n n.v = sample(neg.values,replace=TRUE)\n\n res = prcurve.function(p.v,n.v)\n areas[i] = res$area\n }\n\n return(areas)\n}\n\n\n\n\n", "meta": {"hexsha": "533f73b289ae58e030d0c72dd84369ecc6646c12", "size": 27430, "ext": "r", "lang": "R", "max_stars_repo_path": "precision_recall.r", "max_stars_repo_name": "kboyd/raucpr", "max_stars_repo_head_hexsha": "a18099e5a32f619ce2377744ec1f3b59a1358cf3", "max_stars_repo_licenses": ["BSD-2-Clause"], "max_stars_count": 3, "max_stars_repo_stars_event_min_datetime": "2018-06-15T04:39:10.000Z", "max_stars_repo_stars_event_max_datetime": "2021-03-14T10:47:37.000Z", "max_issues_repo_path": "precision_recall.r", "max_issues_repo_name": "kboyd/raucpr", "max_issues_repo_head_hexsha": "a18099e5a32f619ce2377744ec1f3b59a1358cf3", "max_issues_repo_licenses": ["BSD-2-Clause"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "precision_recall.r", "max_forks_repo_name": "kboyd/raucpr", "max_forks_repo_head_hexsha": "a18099e5a32f619ce2377744ec1f3b59a1358cf3", "max_forks_repo_licenses": ["BSD-2-Clause"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 30.785634119, "max_line_length": 238, "alphanum_fraction": 0.6322639446, "num_tokens": 8268, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9161096204605946, "lm_q2_score": 0.8267117983401363, "lm_q1q2_score": 0.7573586318076779}} {"text": "\"\nПроверить работу арифметических операторов и приоритет выполнения операций в сложных выражениях\nВыполнить серию из 10 вычислений по различным самостоятельно придуманным\nформулам.Использовать все операторы из таблицы 1.\n\nВыяснить правило, по которому выполняется расчет, если в формуле используется целочисленное деление\nи остаток от деления. Убедиться, что значения выражений дают предсказуемый вами результа\nт.\"\n\nn <- 6\nk <- 4\nresult <- factorial(n)/factorial(n-k)\nprint(result)\n\nfor (n in 1:16) {\n print(paste(n, \"! = \", prod(1:n), sep = \"\"))\n}\n\nresult <- 1+3\nprint(result)\nresult <- 1-3\nprint(result)\nresult <- 1*3\nprint(result)\nresult <- 1/3\nprint(result)\nresult <- 2^3\nprint(result)\nresult <- 2%/%3\nprint(result)\nresult <- 2%%3\nprint(result)\n\n", "meta": {"hexsha": "d942c6e9522ead33e20abe7c8279c89751521a3f", "size": 755, "ext": "r", "lang": "R", "max_stars_repo_path": "Course II/R/pract/pract2/task3.r", "max_stars_repo_name": "GeorgiyDemo/FA", "max_stars_repo_head_hexsha": "641a29d088904302f5f2164c9b3e1f1c813849ec", "max_stars_repo_licenses": ["WTFPL"], "max_stars_count": 27, "max_stars_repo_stars_event_min_datetime": "2019-08-18T20:54:27.000Z", "max_stars_repo_stars_event_max_datetime": "2022-02-22T02:39:45.000Z", "max_issues_repo_path": "Course II/R/pract/pract2/task3.r", "max_issues_repo_name": "GeorgiyDemo/FA", "max_issues_repo_head_hexsha": "641a29d088904302f5f2164c9b3e1f1c813849ec", "max_issues_repo_licenses": ["WTFPL"], "max_issues_count": 217, "max_issues_repo_issues_event_min_datetime": "2019-09-22T14:43:25.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T13:49:18.000Z", "max_forks_repo_path": "Course II/R/pract/pract2/task3.r", "max_forks_repo_name": "GeorgiyDemo/FA", "max_forks_repo_head_hexsha": "641a29d088904302f5f2164c9b3e1f1c813849ec", "max_forks_repo_licenses": ["WTFPL"], "max_forks_count": 42, "max_forks_repo_forks_event_min_datetime": "2019-09-18T11:36:28.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-19T18:43:00.000Z", "avg_line_length": 22.2058823529, "max_line_length": 99, "alphanum_fraction": 0.7377483444, "num_tokens": 294, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9086179043564153, "lm_q2_score": 0.8333245911726382, "lm_q1q2_score": 0.7571736436799491}} {"text": "#!/usr/bin/env Rscript\n\n##########################################\n### 系数矩阵 (coeffcient matrix)\n##########################################\nr1 = c(1, -2, 1)\nr2 = c(0, 2, -8)\nr3 = c(-4, 5, 9)\ncoe = rbind(r1, r2, r3)\n\nrownames(coe) = paste(\"r\", seq(1, dim(coe)[1]), sep = \"\")\ncolnames(coe) = paste(\"x\", seq(1, dim(coe)[2]), sep = \"\")\n\n##########################################\n### 增广矩阵 (augmented matrix)\n##########################################\nb = c(0, 8, -9)\naug = cbind(coe, b)\n\ncolnames(aug)[4] <- \"y\"\n\n\n##########################################\n### 高斯消去(Gauss-Jordan elimination)\n##########################################\nlibrary(\"pracma\")\nhelp(\"rref\") # reduced row echelon form\nrref(aug)\n\nA = rbind(c(0,-3,-6,4,9),\n c(-1,-2,-1,3,1),\n c(-2,-3,0,3,-1),\n c(1,4,5,-9,-7))\nrref(A)\n\nB = rbind(c(0,3,-6,6,4,-5),\n c(3,-7,8,-5,8,9),\n c(3,-9,12,-9,6,15))\nrref(B)\n\n\n##########################################\n### 基本变量和自由变量\n### 主元列--> 基本变量 (化简后列上有非0值)\n### 存在自由变量 --> 有通解\n### R3 坐标系中, 有通解表示解再两个平面的交线上\n##########################################\n\n##########################################\n### 线性组合 (理解几何意义) ---> 很重要的一课\n### 向量加法的平行四边型法则 v, u, 0, (v+u) \n### 线性代数的主要思想: \n### TODO: 为某一已知的向量{v1, v2, v3, ... vp}线性组合出的所有向量 \n### span{v1, v2, ..., vp} = all c1v1 + c2v2 + ... + cpvp 向量集合\n### 组合的意义\n### 组合的几何意义\n### 某一向量的b --> [a1, a2, ..., an]线性组合--> 这个b应该就是span中的一个\n##########################################\n\n\n############################################################\n### 矩阵方程Ax = b\n### 向量的线性组合看作[矩阵]与[向量]的积\n### 矩阵 ---> 用来线性组合的列向量的组成\n### 向量 ---> 线性组合时用到的常数组成\n### >>>>> 矩阵方程, 向量方程, 线性方程组 <<<<<<\n############################################################\n\n############################################################\n### Test\n############################################################\nA = cbind(c(1,-4,-3),\n c(3,2,-2),\n c(4,-6,-7),\n c(-5, -5, 0))\nrref(A)\n\n############################################################\n### 齐次方程 Ax = 0\n### 非齐次 Ax = b\n### 通解的几何意义\n############################################################\n\n############################################################\n### 矩阵变换 一个空间--> 另一个空间 (映射像)\n### Ax = b --> T(x)\n### A的n列 --> T的定义域R(n) , A每列m个元素--> T的余定义域\n### m > n --> 原像\n### m < n --> 投影\n### m = n --> 剪切,拉伸等变换\n############################################################\n", "meta": {"hexsha": "101b77a005835ed081e5ef5cdba062b5fa345863", "size": 2372, "ext": "r", "lang": "R", "max_stars_repo_path": "R/learn/LAIA/ch01.r", "max_stars_repo_name": "qrsforever/workspace", "max_stars_repo_head_hexsha": "53c7ce7ca7da62c9fbb3d991ae9e4e34d07ece5f", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2017-06-07T03:20:42.000Z", "max_stars_repo_stars_event_max_datetime": "2020-01-07T09:14:26.000Z", "max_issues_repo_path": "R/learn/LAIA/ch01.r", "max_issues_repo_name": "qrsforever/workspace", "max_issues_repo_head_hexsha": "53c7ce7ca7da62c9fbb3d991ae9e4e34d07ece5f", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/learn/LAIA/ch01.r", "max_forks_repo_name": "qrsforever/workspace", "max_forks_repo_head_hexsha": "53c7ce7ca7da62c9fbb3d991ae9e4e34d07ece5f", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 25.7826086957, "max_line_length": 62, "alphanum_fraction": 0.2951096121, "num_tokens": 916, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9314625107731764, "lm_q2_score": 0.8128673155708975, "lm_q1q2_score": 0.7571554306871201}} {"text": "## Author: Sergio García Prado\n## Title: Statistical Inference - Goodness of Fit - Exercise 11\n\n\nrm(list = ls())\n\nobserved <- c(23, 18, 12, 7)\n\n(k <- length(observed))\n# 4\n\n(n <- sum(observed))\n# 60\n\nLogLikelihood <- function(p, y) {\n (sum(y[1:(k - 1)] * dgeom(0:(k - 2), prob = p, log = TRUE)) +\n y[k] * pgeom(k - 2, prob = p, lower.tail = TRUE))\n}\n\nNegativeLogLikelihood <- function(...) {\n - LogLikelihood(...)\n}\n\nopt <- optim(0.5, NegativeLogLikelihood, y = observed,\n lower = 10e-4, upper = 1 - 10e-4, method = \"L-BFGS-B\")\n\n(p.hat <- opt$par)\n# 0.568016367320236\n\n## a)\n\n(expected <- n * c(dgeom(0:(k - 2), prob = p.hat), 1 - pgeom(k - 2, prob = p.hat)))\n# 34.0809820392142 14.7224264265935 6.35984724962043 4.83674428457189\n\n(Q <- sum((observed - expected) ^ 2 / expected))\n# 10.3019299508017\n\n(pvalue <- 1 - pchisq(Q, df = (k - 1) - 1))\n# 0.00579381114321054\n\n## b)\n\nalpha <- 0.05\n\n(criticvalue <- qchisq(1 - alpha, df = k - 1))\n# 7.81472790325118\n\n(alternative <- n * c(dnbinom(0:(k - 2), size = 2, prob = 0.6), 1 - pnbinom(k - 2, size = 2, prob = 0.4)))\n# 21.6 17.28 10.368 28.512\n\n(null <- n * c(dgeom(0:(k - 2), prob = 0.4), 1 - pgeom(k - 2, prob = 0.4)))\n# 24 14.4 8.64 12.96\n\n(Q <- sum((alternative - null) ^ 2 / null ))\n# 19.824\n\n(power <- 1 - pchisq(criticvalue, df = k - 1, ncp = Q))\n# 0.973940021807995\n\n\n## c)\n\nfn <- function(n) {\n alternative <- n * c(dnbinom(0:(k - 2), size = 2, prob = 0.6), 1 - pnbinom(k - 2, size = 2, prob = 0.4))\n null <- n * c(dgeom(0:(k - 2), prob = 0.4), 1 - pgeom(k - 2, prob = 0.4))\n\n Q <- sum((alternative - null) ^ 2 / null )\n power <- 1 - pchisq(qchisq(1 - alpha, df = k - 1), df = k - 1, ncp = Q)\n\n return(power)\n}\n\n(n.exact <- uniroot(function(n){ fn(n) - 0.7 }, c(1, 100))$root)\n# 26.6113581747679\n\nceiling(n.exact)\n# 27\n", "meta": {"hexsha": "0c24232ec70082f6edf03d6d812a91f684f72c24", "size": 1797, "ext": "r", "lang": "R", "max_stars_repo_path": "statistical-inference/goodness-of-fit/exercise-11.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "statistical-inference/goodness-of-fit/exercise-11.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "statistical-inference/goodness-of-fit/exercise-11.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 23.0384615385, "max_line_length": 106, "alphanum_fraction": 0.5609348915, "num_tokens": 773, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9314625031628428, "lm_q2_score": 0.8128673201042493, "lm_q1q2_score": 0.7571554287235759}} {"text": "library(\"plyr\")\nlibrary(\"MASS\")\n\n################################################################################\n# a\n################################################################################\ncolours <- terrain.colors(5)\n\ndrawDataPoints <- function (inputs) {\n classA <- inputs[inputs$class == 1, ]\n classB <- inputs[inputs$class == 0, ]\n\n points(classA$x, classA$y, col = colours[1], lwd = 3)\n points(classB$x, classB$y, col = colours[2], lwd = 3)\n}\n\n\ndrawDecisionBoundaryL <- function (weights, i = 1) {\n a <- weights[1]\n b <- weights[2]\n c <- weights[3]\n plot(NA, NA, xlim=c(-2,2), ylim=c(-2,2), xlab=\"x\", ylab=\"y\", col = colours[i])\n abline(-(c/b), -(a/b))\n}\n\ndrawDecisionBoundaryQ <- function (weights, xlim = c(-2,2), ylim = c(-2,2), length = 10) {\n f <- Vectorize(function(x,y) sum(featureQ(c(x, y)) * weights))\n x <- seq(xlim[1], xlim[2], length = length)\n y <- seq(ylim[1], ylim[2], length = length)\n z <- outer(x,y,f)\n contour(\n x = x, y = x, z = z,\n levels = 0, las = 1, drawlabels = FALSE, lwd = 3,\n xlim=xlim, ylim=ylim, xlab=\"x\", ylab=\"y\", add = TRUE\n )\n}\ndrawErrors <- function (errors) {\n plot(errors, xlab=\"iteration\", ylab=\"error\", type=\"s\")\n}\n\n\nfeatureL <- function (input) {\n x <- unlist(input[1])\n y <- unlist(input[2])\n return(unlist(c(x, y, 1)))\n}\n\nfeatureQ <- function (input) {\n x <- unlist(input[1])\n y <- unlist(input[2])\n return(unlist(c(x * x, x * y, y * y, x, y, 1)))\n}\n\n# activation function\nhardlimiter <- function (n) {\n if (n > 0) {\n return(1)\n } else {\n return(0)\n }\n}\n\nsigmoid <- function (n) 1/(1 + exp(-n))\n\nid <- function (n) n\n\nperceptron <- function (input, weights, feature, activate) {\n return(activate(sum(feature(input) * weights)))\n}\n\nclassifyA <- function (feature, activation, learningRate, iteration, inputs, weights) {\n errors <- c()\n for (j in 1:iteration) {\n numberOfErrors <- 0\n for (i in 1:nrow(inputs)) {\n input <- inputs[i, ]\n output <- perceptron(input, weights, feature, activation)\n error <- input$class - output\n correction <- error * learningRate\n weights <- weights + feature(input) * correction\n if (error != 0)\n numberOfErrors <- numberOfErrors + 1\n }\n errors <- c(errors, numberOfErrors)\n }\n return(list(\n weights = weights,\n errors = errors\n ))\n}\n\n\ninputs <- data.frame(\n x = c(-1, -1, 1, 1),\n y = c(-1, 1, -1, 1),\n class = c(1, 0, 0, 1))\n\n\nresult <- classifyA(featureQ, hardlimiter, 0.1, 100, inputs, rep(0, 6))\nplot(NA, NA, xlim=c(-2,2), ylim=c(-2,2), xlab=\"x\", ylab=\"y\")\ndrawDecisionBoundaryQ(result$weights)\ndrawDataPoints(inputs)\ntitle(\"(a) dividing XOR with quadratic perceptrons\")\n\ndrawErrors(result$errors)\ntitle(\"error / iteration\")\n\n################################################################################\n# b\n################################################################################\n\nplotBoundary3 <- function(weights) {\n # vectors\n l01 <- weights[, 1] - weights[, 2]\n l12 <- weights[, 2] - weights[, 3]\n l20 <- weights[, 3] - weights[, 1]\n\n # cross point\n x <- ((l01[2]*l12[3])/l12[2] - l01[3]) / (l01[1] - (l12[1]*l01[2])/l12[2])\n y <- ((l01[1]*l12[3])/l12[1] - l01[3]) / (l01[2] - (l12[2]*l01[1])/l12[1])\n\n slope01 = l01[1]/(-l01[2])\n slope12 = l12[1]/(-l12[2])\n slope20 = l20[1]/(-l20[2])\n segments(x, y, x - 100, y - slope01 * 100)\n segments(x, y, x + 100, y + slope12 * 100)\n segments(x, y, x - 100, y - slope20 * 100)\n}\n\n\ntagClass <- function (inputs, class) {\n return(data.frame(x = inputs[, 1], y = inputs[, 2], class = class))\n}\n\nclass0 = list(\n mean = c(0, 0),\n sigma = matrix(c(1, 0, 0, 1), 2, 2))\n\nclass1 = list(\n mean = c(10, 0),\n sigma = matrix(c(1, 0, 0, 4), 2, 2))\n\nclass2 = list(\n mean = c(5, 10),\n sigma = matrix(c(4, 0, 0, 1), 2, 2))\n\nclass0raw = mvrnorm(n = 100, class0$mean, class0$sigma)\nclass1raw = mvrnorm(n = 100, class1$mean, class1$sigma)\nclass2raw = mvrnorm(n = 100, class2$mean, class2$sigma)\n\n\nclass0 = tagClass(class0raw, 0)\nclass1 = tagClass(class1raw, 1)\nclass2 = tagClass(class2raw, 2)\n\n\nweights = matrix(0, 3, 3)\nlearningRate <- 0.5\niteration <- 100\nerrors <- c()\nfor (j in 1:iteration) { # interation\n size <- nrow(class0)\n numberOfErrors <- 0\n for (i in 1:size) { # number of data\n inputs <- matrix(c(class0[i, ], class1[i, ], class2[i, ]), 3, 3)\n numberOfClasses <- 3\n for (k in 1:numberOfClasses) { # each classes\n input <- inputs[, k]\n outputs <- c(perceptron(input, weights[, 1], featureL, hardlimiter),\n perceptron(input, weights[, 2], featureL, hardlimiter),\n perceptron(input, weights[, 3], featureL, hardlimiter))\n\n correction <- featureL(input) * learningRate\n for (m in 1:numberOfClasses) {\n if (m == k && outputs[m] == 0) { # reinforce\n weights[, m] <- weights[, m] + correction\n numberOfErrors <- numberOfErrors + 1\n }\n\n if (m != k && outputs[m] == 1) { # punish\n weights[, m] <- weights[, m] - correction\n numberOfErrors <- numberOfErrors + 1\n }\n }\n }\n }\n errors <- c(errors, numberOfErrors)\n}\nplot(NA, NA, xlim=c(-20,20), ylim=c(-20,20), xlab=\"x\", ylab=\"y\")\npoints(class0, col = colours[1])\npoints(class1, col = colours[2])\npoints(class2, col = colours[3])\n\nplotBoundary3(weights)\ntitle(\"(b) linear multiclass perceptron with hardlimiter activation function\")\ndrawErrors(errors)\ntitle(\"error / iteration\")\n\nweights = matrix(0, 3, 3)\nlearningRate <- 0.5\niteration <- 100\nerrors <- c()\nfor (j in 1:iteration) { # interation\n size <- nrow(class0)\n numberOfErrors <- 0\n for (i in 1:size) { # number of data\n inputs <- matrix(c(class0[i, ], class1[i, ], class2[i, ]), 3, 3)\n numberOfClasses <- 3\n for (k in 1:numberOfClasses) { # each classes\n input <- inputs[, k]\n outputs <- c(perceptron(input, weights[, 1], featureL, sigmoid),\n perceptron(input, weights[, 2], featureL, sigmoid),\n perceptron(input, weights[, 3], featureL, sigmoid))\n\n # wrong prediction, adjust all weights\n if (max(outputs) != outputs[k] || min(outputs) == outputs[k]) {\n correction <- featureL(input) * learningRate\n for (m in 1:numberOfClasses) {\n if (m == k) { # reinforce\n weights[, m] <- weights[, m] + correction\n } else {\n weights[, m] <- weights[, m] - correction\n }\n }\n numberOfErrors <- numberOfErrors + 1\n }\n }\n }\n errors <- c(errors, numberOfErrors)\n}\n\n\nplot(NA, NA, xlim=c(-20,20), ylim=c(-20,20), xlab=\"x\", ylab=\"y\")\npoints(class0, col = colours[1])\npoints(class1, col = colours[2])\npoints(class2, col = colours[3])\n\nplotBoundary3(weights)\ntitle(\"(b) linear multiclass perceptron with sigmoid activation function\")\n\ndrawErrors(errors)\ntitle(\"error / iteration\")\n\n################################################################################\n# c\n################################################################################\n\nclass3 = list(\n mean = c(5, 5),\n sigma = matrix(c(1, 0, 0, 1), 2, 2))\nclass3 = tagClass(mvrnorm(n = 100, class3$mean, class3$sigma), 3)\n\nweights = matrix(0, 6, 4)\nlearningRate <- 1\niteration <- 500\nerrors <- c()\nfor (j in 1:iteration) { # interation\n size <- nrow(class0)\n numberOfErrors <- 0\n for (i in 1:size) { # number of data\n inputs <- matrix(c(class0[i, ], class1[i, ], class2[i, ], class3[i, ]), 3, 4)\n numberOfClasses <- 4\n for (k in 1:numberOfClasses) { # each classes\n input <- inputs[, k]\n outputs <- c(perceptron(input, weights[, 1], featureQ, hardlimiter),\n perceptron(input, weights[, 2], featureQ, hardlimiter),\n perceptron(input, weights[, 3], featureQ, hardlimiter),\n perceptron(input, weights[, 4], featureQ, hardlimiter))\n correction <- featureQ(input) * learningRate\n for (m in 1:numberOfClasses) {\n if (m == k && outputs[m] == 0) { # reinforce\n weights[, m] <- weights[, m] + correction\n numberOfErrors <- numberOfErrors + 1\n }\n\n if (m != k && outputs[m] == 1) { # punish\n weights[, m] <- weights[, m] - correction\n numberOfErrors <- numberOfErrors + 1\n }\n }\n }\n }\n errors <- c(errors, numberOfErrors)\n}\n\nplot(NA, NA, xlim=c(-20,20), ylim=c(-20,20), xlab=\"x\", ylab=\"y\")\npoints(class0, col = colours[1])\npoints(class1, col = colours[2])\npoints(class2, col = colours[3])\npoints(class3, col = colours[4])\ndrawDecisionBoundaryQ(weights[, 1], xlim = c(-20, 20), ylim = c(-20, 20), length = 100)\ndrawDecisionBoundaryQ(weights[, 2], xlim = c(-20, 20), ylim = c(-20, 20), length = 100)\ndrawDecisionBoundaryQ(weights[, 3], xlim = c(-20, 20), ylim = c(-20, 20), length = 100)\ndrawDecisionBoundaryQ(weights[, 4], xlim = c(-20, 20), ylim = c(-20, 20), length = 100)\ntitle(\"(b) quadratic multiclass perceptron with hardlimiter activation function\")\n\ndrawErrors(errors)\ntitle(\"error / iteration\")\n\n\nweights = matrix(0.5, 6, 4)\nlearningRate <- 0.1\niteration <- 500\nerrors <- c()\nfor (j in 1:iteration) { # interation\n size <- nrow(class0)\n numberOfErrors <- 0\n for (i in 1:size) { # number of data\n inputs <- matrix(c(class0[i, ], class1[i, ], class2[i, ], class3[i, ]), 3, 4)\n numberOfClasses <- 4\n for (k in 1:numberOfClasses) { # each classes\n input <- inputs[, k]\n outputs <- c(\n perceptron(input, weights[, 1], featureQ, sigmoid),\n perceptron(input, weights[, 2], featureQ, sigmoid),\n perceptron(input, weights[, 3], featureQ, sigmoid),\n perceptron(input, weights[, 4], featureQ, sigmoid))\n\n for (m in 1:numberOfClasses) {\n if (m == k && outputs[m] < 0.9) { # reinforce\n correction <- featureQ(input) * learningRate * (1 - outputs[m])\n weights[, m] <- weights[, m] + correction\n numberOfErrors <- numberOfErrors + 1\n }\n\n if (m != k && outputs[m] > 0.1) { # punish\n correction <- featureQ(input) * learningRate * (0 - outputs[m])\n weights[, m] <- weights[, m] + correction\n numberOfErrors <- numberOfErrors + 1\n }\n }\n }\n }\n errors <- c(errors, numberOfErrors)\n}\n\nplot(NA, NA, xlim=c(-20,20), ylim=c(-20,20), xlab=\"x\", ylab=\"y\")\npoints(class0, col = colours[1])\npoints(class1, col = colours[2])\npoints(class2, col = colours[3])\npoints(class3, col = colours[4])\ndrawDecisionBoundaryQ(weights[, 1], xlim = c(-20, 20), ylim = c(-20, 20), length = 100)\ndrawDecisionBoundaryQ(weights[, 2], xlim = c(-20, 20), ylim = c(-20, 20), length = 100)\ndrawDecisionBoundaryQ(weights[, 3], xlim = c(-20, 20), ylim = c(-20, 20), length = 100)\ndrawDecisionBoundaryQ(weights[, 4], xlim = c(-20, 20), ylim = c(-20, 20), length = 100)\ntitle(\"(b) quadratic multiclass perceptron with sigmoid activation function\")\n\ndrawErrors(errors)\ntitle(\"error / iteration\")\n", "meta": {"hexsha": "c77dac805577b6dc3ba06d264f2f1471c36e5739", "size": 11615, "ext": "r", "lang": "R", "max_stars_repo_path": "zweite/main.r", "max_stars_repo_name": "banacorn/neuron", "max_stars_repo_head_hexsha": "e05367a976cb43c607198b5b93ed4d9222e76160", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "zweite/main.r", "max_issues_repo_name": "banacorn/neuron", "max_issues_repo_head_hexsha": "e05367a976cb43c607198b5b93ed4d9222e76160", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "zweite/main.r", "max_forks_repo_name": "banacorn/neuron", "max_forks_repo_head_hexsha": "e05367a976cb43c607198b5b93ed4d9222e76160", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 33.1857142857, "max_line_length": 90, "alphanum_fraction": 0.5284545846, "num_tokens": 3365, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9314625069680098, "lm_q2_score": 0.8128673087708699, "lm_q1q2_score": 0.7571554212600538}} {"text": "#' @export\r\nhomoskedastic_covariance_estimator <- function(X, y){\r\n s.2 <- unbiased_error_variance_estimation(X, y)\r\n \r\n solve(t(X) %*% X) * s.2\r\n}\r\n\r\n#' @export\r\nwhite_heteroskedastic_covariance_estimator <- function(X, y){\r\n e.hat <- c(residual(X, y))\r\n `inv(X'X)` <- solve(t(X) %*% X)\r\n `X'DX` <- t(X) %*% diag(e.hat^2) %*% X\r\n \r\n `inv(X'X)` %*% `X'DX` %*% `inv(X'X)`\r\n}\r\n\r\n#' @export\r\nhinkley_heteroskedastic_covariance_estimator <- function(X, y){\r\n e.hat <- c(residual(X, y))\r\n `inv(X'X)` <- solve(t(X) %*% X)\r\n `X'DX` <- t(X) %*% diag(e.hat^2) %*% X\r\n n <- dim(X)[1]\r\n k <- dim(X)[2]\r\n\r\n n/(n-k) * `inv(X'X)` %*% `X'DX` %*% `inv(X'X)`\r\n}\r\n\r\n#' @export\r\nhorn_heteroskedastic_covariance_estimator <- function(X, y){\r\n e.bar <- c(standardized_residual(X, y))\r\n `inv(X'X)` <- solve(t(X) %*% X)\r\n `X'DX` <- t(X) %*% diag(e.bar^2) %*% X\r\n\r\n `inv(X'X)` %*% `X'DX` %*% `inv(X'X)`\r\n}\r\n\r\n#' @export\r\nmackinnon_heteroskedastic_covariance_estimator <- function(X, y){\r\n e.tilde <- prediction_error(X, y)\r\n `inv(X'X)` <- solve(t(X) %*% X)\r\n `X'DX` <- t(X) %*% diag(e.tilde^2) %*% X\r\n\r\n `inv(X'X)` %*% `X'DX` %*% `inv(X'X)`\r\n}\r\n\r\n\r\n# Notations and Abbreviations\r\n\r\n#' @export\r\nV.hat_beta.hat <- homoskedastic_covariance_estimator\r\n#' @export\r\nvce <- homoskedastic_covariance_estimator\r\n\r\n#' @export\r\nV.hat.hc0_beta.hat <- white_heteroskedastic_covariance_estimator\r\n#' @export\r\nrobust_vce0 <- white_heteroskedastic_covariance_estimator\r\n\r\n#' @export\r\nV.hat.hc1_beta.hat <- hinkley_heteroskedastic_covariance_estimator\r\n#' @export\r\nrobust_vce1 <- hinkley_heteroskedastic_covariance_estimator\r\n\r\n#' @export\r\nV.hat.hc2_beta.hat <- horn_heteroskedastic_covariance_estimator\r\n#' @export\r\nrobust_vce2 <- horn_heteroskedastic_covariance_estimator\r\n\r\n#' @export\r\nV.hat.hc3_beta.hat <- mackinnon_heteroskedastic_covariance_estimator\r\n#' @export\r\nrobust_vce3 <- mackinnon_heteroskedastic_covariance_estimator\r\n", "meta": {"hexsha": "369bd103c3ba6c15b31657101c9f7784b27a34a5", "size": 1959, "ext": "r", "lang": "R", "max_stars_repo_path": "R/covariance_estimation.r", "max_stars_repo_name": "kevinkevin556/econometrics", "max_stars_repo_head_hexsha": "735a25f3eea03d9d1d1d27d90e7c1ef311604c84", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/covariance_estimation.r", "max_issues_repo_name": "kevinkevin556/econometrics", "max_issues_repo_head_hexsha": "735a25f3eea03d9d1d1d27d90e7c1ef311604c84", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/covariance_estimation.r", "max_forks_repo_name": "kevinkevin556/econometrics", "max_forks_repo_head_hexsha": "735a25f3eea03d9d1d1d27d90e7c1ef311604c84", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.8356164384, "max_line_length": 69, "alphanum_fraction": 0.6207248596, "num_tokens": 698, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9284087946129328, "lm_q2_score": 0.8152324871074608, "lm_q1q2_score": 0.7568690106847409}} {"text": "library(ggplot2)\n\n# change these parameters if you wnt\nsamplesPerExperiment <- 32\nnExperiments <- 1000\n\n# generate the experimental data\ncontrols = rnorm(n = samplesPerExperiment*nExperiments, mean = 50, sd = 20)\ntests = rnorm(n = samplesPerExperiment*nExperiments, mean = 60, sd = 20)\ndim(controls) <- c(samplesPerExperiment, nExperiments)\ndim(tests) <- c(samplesPerExperiment, nExperiments)\n\n# this function calculate a p values\npValue <- function(nSamples1, mean1, var1,\n nSamples2, mean2, var2) {\n delta <- mean1 - mean2\n sp2 <- ((nSamples1 - 1) * var1 + (nSamples2 - 1) * var2) / (nSamples1 + nSamples2 - 2)\n stderr <- sqrt(sp2 * (1 / nSamples1 + 1 / nSamples2))\n t <- delta / stderr\n pt(-abs(t), df = 2 * samplesPerExperiment - 2) +\n 1 - pt(abs(t), df = 2 * samplesPerExperiment - 2)\n}\n\n# apply the pValue function to the experimental data\npVector <- mapply(pValue,\n apply(controls, 2, length),\n apply(controls, 2, mean),\n apply(controls, 2, var),\n apply(tests, 2, length),\n apply(tests, 2, mean),\n apply(tests, 2, var))\n\n# plot a histogram\nmyPlot <- ggplot() +\n geom_histogram(aes(x = pVector,\n fill = ifelse(pVector <= 0.05, \"#56B4E9\", \"#E69F00\")),\n binwidth = 0.05,\n color = \"white\") +\n scale_fill_discrete(name = \"Significance\",\n labels = c(\"p <= 0.05\", \"p > 0.05\")) +\n theme(axis.title.x = element_blank()) +\n theme(axis.title.y = element_blank())\n\n# ...profit!\nplot(myPlot)\n\n# print out stuff\nprint(sum(pVector <= 0.05))\nprint(sum(pVector > 0.05))\nprint(summary(pVector))", "meta": {"hexsha": "5ed45104fcc51eef840a07ca7976542e81be6a6b", "size": 1648, "ext": "r", "lang": "R", "max_stars_repo_path": "assets/data/pValues.r", "max_stars_repo_name": "whatdoesthequantsay/whatdoesthequantsay.github.io", "max_stars_repo_head_hexsha": "07624d0759f9db577aa1f3ad2d3f8ae7d91cd924", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "assets/data/pValues.r", "max_issues_repo_name": "whatdoesthequantsay/whatdoesthequantsay.github.io", "max_issues_repo_head_hexsha": "07624d0759f9db577aa1f3ad2d3f8ae7d91cd924", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "assets/data/pValues.r", "max_forks_repo_name": "whatdoesthequantsay/whatdoesthequantsay.github.io", "max_forks_repo_head_hexsha": "07624d0759f9db577aa1f3ad2d3f8ae7d91cd924", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 32.96, "max_line_length": 90, "alphanum_fraction": 0.6122572816, "num_tokens": 494, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9230391685381605, "lm_q2_score": 0.8198933381139645, "lm_q1q2_score": 0.7567936651026906}} {"text": "y=1200\r\nn=2500\r\npie=y/n\r\nsigma=sqrt((pie*(1-pie))/n)\r\npie0=0.44\r\n#test statistic\r\nz=(pie-pie0)/sigma\r\nprint(z)\r\n# critical value\r\nalpha=0.05\r\nz.alpha=qnorm(1-alpha)\r\n#Because the observed value of z exceeds the critical value 1.645, we conclude that the\r\n#percentage of students that participate in binge drinking exceeds the national percentage of 44%\r\nnbar = n + (z.alpha^2)\r\npie_bar=(y+z.alpha)/nbar\r\n\r\nsigma_bar=sqrt((pie_bar*(1-pie_bar))/nbar)\r\nerror_bar=z.alpha*sigma_bar\r\nleft=pie_bar-error_bar\r\nright=pie_bar+error_bar\r\nprint(left)\r\nprint(right)\r\n# the percentage of binge drinkers at the university is, with 95% confidence,between 46% and 50%\r\n", "meta": {"hexsha": "ea8f17ec0cee420bf5b786ed9395aaa8e75f35cb", "size": 653, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH10/EX10.5/Ex10_5.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH10/EX10.5/Ex10_5.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH10/EX10.5/Ex10_5.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 27.2083333333, "max_line_length": 98, "alphanum_fraction": 0.7381316998, "num_tokens": 196, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9669140187510509, "lm_q2_score": 0.782662489091802, "lm_q1q2_score": 0.7567673326534549}} {"text": "=begin\n # sample-jordan-form01.rb\n\n require \"algebra\"\n \n M4 = SquareMatrix(Rational, 4)\n m = M4[\n [-1, 1, 2, -1],\n [-5, 3, 4, -2],\n [3, -1, 0, 1],\n [5, -2, -2, 3]\n ]\n m.jordan_form.display; #=>\n # 2, 0, 0, 0\n # 0, 1, 1, 0\n # 0, 0, 1, 1\n # 0, 0, 0, 1\n puts\n \n #-----------------------------------\n m = M4[\n [3, 1, -1, 1],\n [-3, -1, 3, -1],\n [-2, -2, 0, 0],\n [0, 0, -4, 2]\n ]\n jf, pt, qt, field, modulus = m.jordan_form_info\n p modulus #=> [a^2 + 4]\n jf.display; puts #=>\n # 2, 1, 0, 0\n # 0, 2, 0, 0\n # 0, 0, a, 0\n # 0, 0, 0, -a\n \n m = m.convert_to(jf.class)\n p jf == pt * m * qt #=> true\n \n #-----------------------------------\n m = M4[\n [-1, 1, 2, -1],\n [-5, 3, 4, -2],\n [3, -1, 0, 1],\n [5, -2, -2, 0]\n ]\n jf, pt, qt, field, modulus = m.jordan_form_info\n p modulus #=> [a^3 + 3a - 1, b^2 + ab + a^2 + 3]\n jf.display; puts #=>\n # 2, 0, 0, 0\n # 0, a, 0, 0\n # 0, 0, b, 0\n # 0, 0, 0, -b - a\n \n m = m.convert_to(jf.class)\n p jf == pt * m * qt #=> true\n((<_|CONTENTS>))\n=end\n", "meta": {"hexsha": "131af9ccb4d46df75b34ced5168d2d529609669d", "size": 1144, "ext": "rd", "lang": "R", "max_stars_repo_path": "doc-ja/sample-jordan-form01.rb.v.rd", "max_stars_repo_name": "kunishi/algebra-ruby2", "max_stars_repo_head_hexsha": "ab8e3dce503bf59477b18bfc93d7cdf103507037", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 6, "max_stars_repo_stars_event_min_datetime": "2015-04-25T17:00:02.000Z", "max_stars_repo_stars_event_max_datetime": "2021-07-08T02:59:44.000Z", "max_issues_repo_path": "work/consider/algebra-0.72/doc/sample-jordan-form01.rb.v.rd", "max_issues_repo_name": "rubyworks/stick", "max_issues_repo_head_hexsha": "7e89d1a1ade1db085ddfecf19f774f0ba9bc2b70", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2017-03-10T14:02:43.000Z", "max_issues_repo_issues_event_max_datetime": "2017-03-10T14:02:43.000Z", "max_forks_repo_path": "doc/sample-jordan-form01.rb.v.rd", "max_forks_repo_name": "kunishi/algebra-ruby2", "max_forks_repo_head_hexsha": "ab8e3dce503bf59477b18bfc93d7cdf103507037", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 20.0701754386, "max_line_length": 50, "alphanum_fraction": 0.3426573427, "num_tokens": 598, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9252299550303293, "lm_q2_score": 0.8175744828610095, "lm_q1q2_score": 0.7564444020114366}} {"text": "# @' export\nt_ratio <- function(coef, std_err){\n coef/std_err\n}\n\n# @' export\nf_stat <- function(coef, std_err){\n t_ratio(coef, std_err)^2\n}\n\ncritical_values <- function(distribution, ...){\n quantile_func <- get(paste0(\"q\", distribution))\n\n quantile90 <- quantile_func(p=0.9, ...)\n quantile95 <- quantile_func(p=0.95, ...)\n quantile99 <- quantile_func(p=0.99, ...)\n \n ci_lower_bound90 <- quantile_func(p=0.5*0.1, ...)\n ci_lower_bound95 <- quantile_func(p=0.5*0.05, ...)\n ci_lower_bound99 <- quantile_func(p=0.5*0.01, ...)\n\n ci_upper_bound90 <- quantile_func(p=1-0.5*0.1, ...)\n ci_upper_bound95 <- quantile_func(p=1-0.5*0.05, ...)\n ci_upper_bound99 <- quantile_func(p=1-0.5*0.01, ...)\n\n output <- data.frame(\n critical_values = c(quantile90, quantile95, quantile99),\n ci_lower_bound = c(ci_lower_bound90, ci_lower_bound95, ci_lower_bound99),\n ci_upper_bound = c(ci_upper_bound90, ci_upper_bound95, ci_upper_bound99), \n row.names = c(\"0.9\", \"0.95\", \"0.99\")\n )\n\n return(output)\n}\n\nsignificant_level <- function(f_stat, df){\n crit_values <- critical_values(distribution=\"f\", df1=1, df2=df)\n\n result <- sapply(f_stat, function(f){\n if (f > crit_values[\"0.99\", \"critical_values\"]) '***'\n else if (f > crit_values[\"0.95\", \"critical_values\"]) '**'\n else if (f > crit_values[\"0.9\", \"critical_values\"]) '*'\n else ' '\n })\n}\n\n", "meta": {"hexsha": "86454033bfbfa4e65eeba1f7f41777b82b666428", "size": 1471, "ext": "r", "lang": "R", "max_stars_repo_path": "R/statistical_significance.r", "max_stars_repo_name": "kevinkevin556/econometrics", "max_stars_repo_head_hexsha": "735a25f3eea03d9d1d1d27d90e7c1ef311604c84", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/statistical_significance.r", "max_issues_repo_name": "kevinkevin556/econometrics", "max_issues_repo_head_hexsha": "735a25f3eea03d9d1d1d27d90e7c1ef311604c84", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/statistical_significance.r", "max_forks_repo_name": "kevinkevin556/econometrics", "max_forks_repo_head_hexsha": "735a25f3eea03d9d1d1d27d90e7c1ef311604c84", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 31.2978723404, "max_line_length": 82, "alphanum_fraction": 0.6016315432, "num_tokens": 448, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9304582632076909, "lm_q2_score": 0.8128673155708975, "lm_q1q2_score": 0.7563391106643953}} {"text": "mean.square.error <- function(theta.hat,theta) {\r\n#Purpose: \r\n# Calculates mean squared errors for a matrix of estimates\r\n# where the rows are the replicates and the columns are different\r\n# estimators\r\n#Inputs:\r\n# theta.hat - vector of estimates. Rows = replicates; Cols = estimators.\r\n# theta - true value\r\n#Outputs:\r\n# vector of MSEs - one for each estimator\r\n\r\n#count number of replicates for each estimator\r\n n <- dim(theta.hat)[1]\r\n#count number of estimators\r\n num.ests <- dim(theta.hat)[2]\r\n#create vector for results\r\n MSE.vec <- numeric(num.ests)\r\n \r\n#Work out the sum of squared errors for each estimator:\r\n#Go through each replicate\r\n for(i in 1:n) {\r\n#go through each estimator\r\n for(j in 1:num.ests) \r\n#Add the squared error for this replicate to the running total in MSE.vec\r\n MSE.vec[j] <- MSE.vec[j]+(theta.hat[i,j]-theta)^2\r\n }\r\n#Turn from a sum of squared errors into mean square error by dividing by n\r\n MSE.vec <- MSE.vec/n\r\n \r\n return(MSE.vec)\r\n} ", "meta": {"hexsha": "536b8153d8c9f70601823cc6b58cc174aaf8c2e4", "size": 992, "ext": "r", "lang": "R", "max_stars_repo_path": "Practicals/Practical 3/functions/mean.square.error.r", "max_stars_repo_name": "yc59/2018", "max_stars_repo_head_hexsha": "4c74a67a4d0dadecc4213dd57289120b31806aa6", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Practicals/Practical 3/functions/mean.square.error.r", "max_issues_repo_name": "yc59/2018", "max_issues_repo_head_hexsha": "4c74a67a4d0dadecc4213dd57289120b31806aa6", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Practicals/Practical 3/functions/mean.square.error.r", "max_forks_repo_name": "yc59/2018", "max_forks_repo_head_hexsha": "4c74a67a4d0dadecc4213dd57289120b31806aa6", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 32.0, "max_line_length": 75, "alphanum_fraction": 0.689516129, "num_tokens": 263, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9099070109242131, "lm_q2_score": 0.8311430478583168, "lm_q1q2_score": 0.7562628863272013}} {"text": "### ANOVA\n\nlibrary(ggplot2)\n\n# formulae\n\nDV ~ IV # One-way\n\nDV ~ IV1 + IV2 # Two-way\n\nDV ~ IV1:IV2 # Two-way interaction\n\nDV ~ IV1 + IV2 + IV1:IV2 # Main effects + interaction\n\nDV ~ IV1 * IV2 # The same: Main effects + interaction\n\nDV ~ IV1 + IV2 + IV3 + IV1:IV2\n\nDV ~ (IV1 + IV2 + IV3)^2 # main effects and all possible interactions up to level 2\n\nDV ~ IV1 + Error(subject/IV1) # repeated measures\n\n\n\n# reading data\n\nmydata <- read.csv('shops.csv')\n\n\n# One-way ANOVA\n\nboxplot(price ~ origin, data=mydata)\n\nggplot(mydata, aes(x = origin, y = price)) + \n geom_boxplot()\n\n\n\nfit <- aov(price ~ origin, data=mydata)\nsummary(fit)\n\n\n# Two-way ANOVA\n\nfit1 <- aov(price ~ origin + store, data=mydata)\nsummary(fit1)\n\nmodel.tables(fit1,\"means\")\n\n\n# Interaction\n\npd = position_dodge(0.1)\nggplot(mydata, aes(x = store, y = price, color = origin, group = origin)) + \n stat_summary(fun.data = mean_cl_boot, geom = 'errorbar', width = 0.2, lwd = 0.8, position = pd)+ \n stat_summary(fun.data = mean_cl_boot, geom = 'line', size = 1.5, position = pd) +\n stat_summary(fun.data = mean_cl_boot, geom = 'point', size = 5, position = pd, pch=15) +\n theme_bw()\n\nfit3 <- aov(price ~ origin + store + origin:store, data=mydata)\nsummary(fit3)\n\nfit4 <- aov(price ~ origin * store, data=mydata)\nsummary(fit4)\n\n\n\n# Pairwise comparisons\n\nggplot(mydata, aes(x = food, y = price)) + \n geom_boxplot()\n\nfit5 <- aov(price ~ food, data=mydata)\nsummary(fit5)\n\n\nTukeyHSD(fit5)\n\n\n\n\n# Repeated measures\n\nmydata2 <- read.csv('therapy_data.csv')\nstr(mydata2)\n\nmydata2$subject <- as.factor(mydata2$subject)\n\n\nfit1 <- aov(well_being ~ therapy, data = mydata2)\nsummary(fit1)\nfit1b <- aov(well_being ~ therapy + Error(subject/therapy), data = mydata2)\nsummary(fit1b)\n\n\nfit2 <- aov(well_being ~ therapy*price, data = mydata2)\nsummary(fit2)\n\nggplot(mydata2, aes(x = price, y = well_being)) + \n geom_boxplot()\n\nfit2b <- aov(well_being ~ therapy*price + Error(subject/(therapy*price)), data = mydata2)\nsummary(fit2b)\n\nggplot(mydata2, aes(x = price, y = well_being)) + \n geom_boxplot() + \n facet_grid(~subject)\n\n\nfit3 <- aov(well_being ~ therapy*price*sex, data = mydata2)\nsummary(fit3)\nfit3b <- aov(well_being ~ therapy*price*sex + Error(subject/(therapy*price)), data = mydata2)\nsummary(fit3b)\n\n", "meta": {"hexsha": "ab6484dfe31dd6aa25ff1eebb1b1bb01347f30b8", "size": 2258, "ext": "r", "lang": "R", "max_stars_repo_path": "anova.r", "max_stars_repo_name": "Sokel/R-shchu", "max_stars_repo_head_hexsha": "0b5b48b018bf85caca89fefb1896468f6039568c", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "anova.r", "max_issues_repo_name": "Sokel/R-shchu", "max_issues_repo_head_hexsha": "0b5b48b018bf85caca89fefb1896468f6039568c", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "anova.r", "max_forks_repo_name": "Sokel/R-shchu", "max_forks_repo_head_hexsha": "0b5b48b018bf85caca89fefb1896468f6039568c", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 19.6347826087, "max_line_length": 100, "alphanum_fraction": 0.6767050487, "num_tokens": 738, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9504109728022221, "lm_q2_score": 0.7956581097540519, "lm_q1q2_score": 0.7562021981093257}} {"text": "#Example simultion code\r\n#Author: Len Thomas\r\n#Last updated: 25th October 2013\r\n\r\n#Functions to run a simulation to look at the MSE arising from \r\n# using trimmed means to estimate the mean of a mixture distribution\r\n# See ExampleSimulation.pdf for details\r\n#Some code to drive the simulation is provided in ExampleSimulationDriver.r\r\n\r\n#Note that there are two versions of the functions mix.dist and RMSE\r\n#Have a look at them, and try to decide which is better!...\r\n\r\ndo.sim <- function(mix.par=0.2,mu1=5,sigma1=4,mu2=5,df=4,n=30,\r\n alpha.vec=c(0,0.1,0.2), M=1000) {\r\n#Purpose:\r\n# Runs a simulation to compute the RMSEs for trimmed means from \r\n# samples taken from a 2 point normal and t mixture model\r\n#Inputs:\r\n# mix.par - mixture parameter of the distribution (range 0-1)\r\n# mu1 - mean of the normal component of the mixture\r\n# sigma1 - sd of the normal component of the mixture\r\n# mu2 - mean of the t component of the mixture\r\n# df - degrees of freedom for the t component\r\n# n - size of samples to generate in simulation\r\n# alpha.vec - vector of trimming levels to try (0=no trim i.e. mean, \r\n# 0.5=trim 50th quantile above and below - i.e., median)\r\n# M - number of simultions to run\r\n#Output: List containing elements:\r\n# MSE - vector of the MSEs at each trim level\r\n# ests - matrix with M rows and length(alpha.vec) columns containing the raw estimates\r\n# mu - the true mean of the input distribution\r\n \r\n\r\n #initialize matrix of outputs\r\n est.matrix <- matrix(NA,M,length(alpha.vec)) \r\n #run simulation\r\n for(simulation in 1:M) {\r\n temp <- mix.dist(n,mix.par,mu1,sigma1,mu2,df) \r\n est.matrix[simulation,] <- estimate(temp,alpha.vec) \r\n }\r\n\r\n #work out the expected value of the input distribution\r\n E.Z<-get.E.Z(mix.par,mu1,mu2)\r\n \r\n #Calculate MSEs \r\n mean.square.error <- MSE(est.matrix,E.Z)\r\n\r\n return(list(MSE=mean.square.error, ests=est.matrix, mu=E.Z))\r\n\r\n} \r\n\r\nget.E.Z <- function(mix.par, mu1, mu2){\r\n#Purpose: Returns the expected value of a mixture with mix proportion\r\n# mix.par, and means mu1 and mu2\r\n return(mix.par*mu1+(1-mix.par)*mu2)\r\n}\r\n\r\n\r\nmix.dist <- function(n,mix.par,mu1,sigma1,mu2,df) {\r\n#Purpose: Returns n samples from the mixture distribution\r\n#Inputs:\r\n# n - number of samples to return\r\n# mix.par - pi in the practical notes -- proportion of samples from norm dist\r\n# mu1 - mean of norm dist\r\n# sigma1 - sd of norm dist\r\n# mu2 - mean of t dist\r\n# df - df for t dist\r\n#Outputs:\r\n# vector of n values from the mixture distribution\r\n#Implementation note:\r\n# This version uses vectorization - but wastefully samples from\r\n# both the normal and t for each observation. See below for another\r\n# way to do this. Which is quicker, I wonder?\r\n \r\n #sample n values from a Bernoulli dist, to see which distribution\r\n # each data point comes from\r\n nu <- rbinom(n,1,mix.par)\r\n \r\n #sample values from the normal\r\n X <- rnorm(n,mu1,sigma1)\r\n #sample values from the t\r\n Y <- mu2 + rt(n,df)\r\n \r\n #put them together\r\n Z <- nu*X + (1-nu)*Y\r\n return(Z)\r\n}\r\n\r\nmix.dist.alt <- function(n,mix.par,mu1,sigma1,mu2,df) {\r\n#Purpose: Alternative implementation of routine to sample n values\r\n# from the mixture distribution\r\n#Inputs:\r\n# n - number of samples to return\r\n# mix.par - pi in the practical notes -- proportion of samples from norm dist\r\n# mu1 - mean of norm dist\r\n# sigma1 - sd of norm dist\r\n# mu2 - mean of t dist\r\n# df - df for t dist\r\n#Outputs:\r\n# vector of n values from the mixture distribution\r\n\r\n #create results vector\r\n Z<-numeric(n)\r\n \r\n #go through each observation...\r\n for(i in 1:n){\r\n #...determine if it comes from the normal or t distribution\r\n if(rbinom(1,1,mix.par)==1) {\r\n #normal distribution\r\n Z[i]<-rnorm(1,mu1,sigma1)\r\n } else {\r\n #t distribution\r\n Z[i]<-mu2+rt(1,df)\r\n }\r\n }\r\n\r\n return(Z)\r\n}\r\n\r\n\r\nestimate <- function(x,trim) {\r\n#Purpose: Estimates trimmed means on data x, using a vector of trimming\r\n# levels trim\r\n#Inputs:\r\n# x - data\r\n# trim - vector of trimming levels\r\n#Outputs:\r\n# vector of trimmed means\r\n\r\n #create vector for results\r\n n.trimmed.means<-length(trim)\r\n trimmed.means<-numeric(n.trimmed.means)\r\n\r\n #loop through, calculating trimmed means\r\n for(i in 1:n.trimmed.means) \r\n trimmed.means[i] <- mean(x,trim[i])\r\n\r\n return(trimmed.means)\r\n}\r\n\r\nMSE <- function(theta.hat,theta) {\r\n#Purpose: Calculates mean squared errors for a matrix of estimates\r\n# where the rows are the replicates and the columns are different\r\n# estimators\r\n#Inputs:\r\n# theta.hat - vector of estimates. Rows = replicates; Cols = estimators.\r\n# theta - true value\r\n#Outputs:\r\n# vector of MSEs - one for each estimator\r\n#Implementation note:\r\n# This version uses a double loop. See below for a more vectorized \r\n# version of this function. Which is quicker?\r\n\r\n #count numeber of replicates for each estimator\r\n n <- dim(theta.hat)[1]\r\n #count number of estimators\r\n num.ests <- dim(theta.hat)[2]\r\n #create vector for results\r\n MSE.vec <- numeric(num.ests)\r\n\r\n #Work out the sum of squared errors for each estimator:\r\n #Go through each replicate\r\n for(i in 1:n) {\r\n #go through each estimator\r\n for(j in 1:num.ests) \r\n #Add the sqared error for this replicate of the estimator to\r\n # the running total in MSE.vec\r\n MSE.vec[j] <- MSE.vec[j]+(theta.hat[i,j]-theta)^2\r\n }\r\n #Turn from a sum of squared errors into mean square error by dividing\r\n # by n\r\n MSE.vec <- MSE.vec/n\r\n\r\n return(MSE.vec)\r\n} \r\n\r\nMSE.alt <- function(theta.hat,theta) {\r\n#Purpose: Alternative vectorized implementation of function to\r\n# calculate mean squared errors for a matrix of estimates\r\n# where the rows are the replicates and the columns are different\r\n# estimators\r\n#Inputs:\r\n# theta.hat - vector of estimates. Rows = replicates; Cols = estimators.\r\n# theta - true value\r\n#Outputs:\r\n# vector of MSEs - one for each estimator\r\n\r\n #Declare function to calculate MSE of a vector\r\n MSE.vec <- function(theta.hat.vec, theta) {\r\n #Purpose: calculates MSE of a vector\r\n #Inputs: \r\n # theta.hat.vec - vector of estimates\r\n # theta - true value\r\n #Output: MSE\r\n square.error<-(theta.hat.vec-theta)^2\r\n MSE<-mean(square.error)\r\n return(MSE)\r\n }\r\n\r\n #Apply this function to each column of theta.hat\r\n MSE<-apply(theta.hat,2,MSE.vec,theta)\r\n\r\n return(MSE)\r\n} \r\n", "meta": {"hexsha": "c4637172d5a0c88369c9d176b9799be2a2d2a262", "size": 6333, "ext": "r", "lang": "R", "max_stars_repo_path": "Practicals/Practical 3/functions/ExampleSimulation.r", "max_stars_repo_name": "yc59/2018", "max_stars_repo_head_hexsha": "4c74a67a4d0dadecc4213dd57289120b31806aa6", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Practicals/Practical 3/functions/ExampleSimulation.r", "max_issues_repo_name": "yc59/2018", "max_issues_repo_head_hexsha": "4c74a67a4d0dadecc4213dd57289120b31806aa6", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Practicals/Practical 3/functions/ExampleSimulation.r", "max_forks_repo_name": "yc59/2018", "max_forks_repo_head_hexsha": "4c74a67a4d0dadecc4213dd57289120b31806aa6", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 30.8926829268, "max_line_length": 87, "alphanum_fraction": 0.681035844, "num_tokens": 1726, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9073122313857378, "lm_q2_score": 0.8333245973817158, "lm_q1q2_score": 0.7560855999190261}} {"text": "#Q2. The sum of the squares of the first ten natural numbers is,\r\n#12+22+...+102=385\r\n#The square of the sum of the first ten natural numbers is,\r\n#(1+2+...+10)2=552=3025\r\n#Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is \r\n#3025−385=2640\r\n#.Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.\r\n\r\nsum=0;\r\nsq=0;\r\nres = 0;\r\nn = 10;\r\n\r\nsum = n*(n+1)/2;\r\nsq=(n*(n+1)*(2*n+1))/6;\r\nres=sum*sum-sq;\r\nprint(res)", "meta": {"hexsha": "92fe855170f848a797e4b63867acd01866c4d748", "size": 535, "ext": "r", "lang": "R", "max_stars_repo_path": "Q.2.r", "max_stars_repo_name": "Subr1ata/D.A.-Lab-Assignments", "max_stars_repo_head_hexsha": "75e9eab3483e8650bd0396b0e102c89d0533b1eb", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Q.2.r", "max_issues_repo_name": "Subr1ata/D.A.-Lab-Assignments", "max_issues_repo_head_hexsha": "75e9eab3483e8650bd0396b0e102c89d0533b1eb", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Q.2.r", "max_forks_repo_name": "Subr1ata/D.A.-Lab-Assignments", "max_forks_repo_head_hexsha": "75e9eab3483e8650bd0396b0e102c89d0533b1eb", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 31.4705882353, "max_line_length": 121, "alphanum_fraction": 0.6822429907, "num_tokens": 170, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9381240142763574, "lm_q2_score": 0.8056321936479701, "lm_q1q2_score": 0.7557829075353014}} {"text": "setwd(\"C:/Users/Nina/Desktop/machinelearning_estatistica_R/dataset\")\nlibrary(readxl)\n\n# Problema: Quero prever quanto será o salário com base no passar dos anos \n\n\n# Sep é um separador de coluna e o dec = separador de casas decimais.\ndados <- read.table(\"salary.csv\", header = TRUE,\n sep = \",\", dec = \".\") #Função que lê o arquivo csv e salva em uma base de dados R \n\n# Verifica os nomes das variaveis\nnames(dados)\n\n# Verifica a correlação linear entre duas variáveis quantitativas\ncor(dados$years, dados$salary)\n\n# O output é +0.97. Portanto é uma correlação linear forte e positiva, ou seja, com o passar dos anos aumenta o meu salário\n\n# Realizando o modelo de Regressão Linear\n\n# Obtenha o modelo de regressão linear simples. Com 90% de confiança, há relação linear entre as variáveis?\nregressao <- lm(data=dados,\n salary ~ years) \noptions(scipen=999)\nsummary(regressao)\n\n# De acordo co o output temos BO = 25792.2, significa que quando você tem 0 anos , ou seja, nem nasceu, você já tem um salário assim.\n# Podemos notar que a base de dados não é verossímel a realidade.\n\nregressao$coefficients[1] + regressao$coefficients[2] * 1\n\n# Calcula os valores preditos da varíavel resposta para cada elemento da amostra\nregressao$fitted.values #: calcula os valores preditos da variável resposta(Y) para cada elemento da amostra (faz uma previsão);\n\n# calcula o erro ou os resíduos (valor observado - valor predito) para cada ponto da amostra\nregressao$residuals \n\n# obtém uma estimativa dos coeficientes da regressão.\nregressao$coefficients \n\n# Gerar o gráfico de dispersão - variáveis quantitativas\n\nplot (salary ~ years,pch = 4, data = dados)\n\n# Esta função ajusta a reta do modelo aos dados\nabline(regressao,col=\"red\")\n\n# Aqui a gente consegue ver um raio quadrado bem grande, ou seja, a interpretação disso 95% da variabilidade explicada da variável y pela x.\nsummary(regressao)\n\n\nsetwd(\"C:/Users/Nina/Desktop/machinelearning_estatistica_R/dataset\")\nlibrary(readxl)\n\n# Problema: Quero prever quanto será o salário com base no passar dos anos \n\n\n# Sep é um separador de coluna e o dec = separador de casas decimais.\ndados <- read.table(\"salary.csv\", header = TRUE,\n sep = \",\", dec = \".\") #Função que lê o arquivo csv e salva em uma base de dados R \n\n# Verifica os nomes das variaveis\nnames(dados)\n\n# Verifica a correlação linear entre duas variáveis quantitativas\ncor(dados$years, dados$salary)\n\n# O output é +0.97. Portanto é uma correlação linear forte e positiva, ou seja, com o passar dos anos aumenta o meu salário\n\n# Realizando o modelo de Regressão Linear\n\n# Obtenha o modelo de regressão linear simples. Com 90% de confiança, há relação linear entre as variáveis?\nregressao <- lm(data=dados,\n salary ~ years) \noptions(scipen=999)\nsummary(regressao)\n\n# De acordo co o output temos BO = 25792.2, significa que quando você tem 0 anos , ou seja, nem nasceu, você já tem um salário assim.\n# Podemos notar que a base de dados não é verossímel a realidade.\n\nregressao$coefficients[1] + regressao$coefficients[2] * 1\n\n# Calcula os valores preditos da varíavel resposta para cada elemento da amostra\nregressao$fitted.values #: calcula os valores preditos da variável resposta(Y) para cada elemento da amostra (faz uma previsão);\n\n# calcula o erro ou os resíduos (valor observado - valor predito) para cada ponto da amostra\nregressao$residuals \n\n# obtém uma estimativa dos coeficientes da regressão.\nregressao$coefficients \n\n# Gerar o gráfico de dispersão - variáveis quantitativas\n\nplot (salary ~ years,pch = 4, data = dados)\n\n# Esta função ajusta a reta do modelo aos dados\nabline(regressao,col=\"red\")\n\n# Aqui a gente consegue ver um raio quadrado bem grande, ou seja, a interpretação disso 95% da variabilidade explicada da variável y pela x.\nsummary(regressao)\n\n\n", "meta": {"hexsha": "cdcafad8600cf459d5d36954648df65cce9c5b64", "size": 3838, "ext": "r", "lang": "R", "max_stars_repo_path": "files/regressao_linear_simples.r", "max_stars_repo_name": "Nina-pinheiro/machinelearning_estatistica_R", "max_stars_repo_head_hexsha": "500a34d6ebfd1c3d42e4d7ae25384d0dd8fed737", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 4, "max_stars_repo_stars_event_min_datetime": "2020-07-27T05:26:54.000Z", "max_stars_repo_stars_event_max_datetime": "2020-07-29T02:50:22.000Z", "max_issues_repo_path": "files/regressao_linear_simples.r", "max_issues_repo_name": "Jailsonrs/Data-Science-R", "max_issues_repo_head_hexsha": "45af621fcc16d62e7153cdc9394888d74d2abf1f", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "files/regressao_linear_simples.r", "max_forks_repo_name": "Jailsonrs/Data-Science-R", "max_forks_repo_head_hexsha": "45af621fcc16d62e7153cdc9394888d74d2abf1f", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2020-07-28T11:23:46.000Z", "max_forks_repo_forks_event_max_datetime": "2020-07-28T11:23:46.000Z", "avg_line_length": 37.2621359223, "max_line_length": 140, "alphanum_fraction": 0.7488275143, "num_tokens": 1076, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9324533013520765, "lm_q2_score": 0.8104789086703224, "lm_q1q2_score": 0.7557337340658702}} {"text": "###############\r\n## Section 2 ##\r\n###############\r\n\r\nlibrary(MASS) \r\n\r\nsetwd(\"C:\\\\dc_book\\\\Replication_Files_Element\")\r\n\r\nITN.data <- read.csv(\"ITN_data.csv\", header=TRUE)\r\n\r\n###############\r\n## Table 2.1 ##\r\n###############\r\n\r\n## Logit model\r\n\r\nITN.logit <- glm(useditn ~ malariamessage+education+richest+poorest+pregnant+altitude, family=binomial(link=\"logit\"), data=ITN.data, x=TRUE)\r\nITN.logit.results <- cbind(ITN.logit$coefficients, sqrt(diag(vcov(ITN.logit))), confint.default(ITN.logit, level=0.95))\r\nN <- length(ITN.logit$fitted.values)\r\ncolnames(ITN.logit.results) <- c(\"Coeff\", \"(se)\", \"2.5%\", \"97.5%\")\r\nprint((round(ITN.logit.results, digits=3)))\r\nprint(N)\r\n\r\n###############\r\n## Table 2.2 ##\r\n###############\r\n\r\n## Simulated Coefficients\r\n\r\nbeta <- ITN.logit$coefficients\r\ncovmat.beta <- vcov(ITN.logit)\r\nndraws <- 1000\r\nbetadraw <- mvrnorm(ndraws, beta, covmat.beta)\r\n\r\nmean.x <- colMeans(ITN.logit$x)\r\nsimprobs <- plogis(betadraw%*%mean.x)\r\n\r\nsimcoef.results <- append(quantile(simprobs, probs=c(0.5, 0.025, 0.975)), sd(simprobs))\r\n\r\n## Bootstrapping\r\n\r\nnsamples <- 1000\r\nbetas.boot <- matrix(NA,nsamples,length(beta))\r\n\r\nfor (i in 1:1000) {\r\n\r\n\tITN.data.boot <- ITN.data[sample(seq(1,nrow(ITN.data),1), replace=TRUE),]\r\n\tlogit.boot <- glm(useditn ~ malariamessage+education+richest+poorest+pregnant+altitude, family=binomial(link=\"logit\"), data=ITN.data.boot)\r\n\tbetas.boot[i,] <- logit.boot$coefficients\t\r\n}\r\n\r\nprobs.boot <- plogis(betas.boot%*%mean.x)\r\n\r\nboot.results <- append(quantile(probs.boot, probs=c(0.5, 0.025, 0.975)), sd(probs.boot))\r\n\r\n## Delta Method\r\n\r\nxb <- mean.x %*% beta\r\npredicted.prob <- plogis(xb)\r\n\r\ndeltamethod.var <- (dlogis(xb)^2) * (t(mean.x) %*% covmat.beta %*% mean.x)\r\ndeltamethod.se <- sqrt(deltamethod.var)\r\n\r\ndelta.95ci.u <- predicted.prob + 1.96*deltamethod.se\r\ndelta.95ci.l <- predicted.prob - 1.96*deltamethod.se\r\n\r\ndelta.results <- cbind(predicted.prob, delta.95ci.l, delta.95ci.u, deltamethod.se)\r\n\r\n## Summarize Results\r\n\r\nstatistical.uncertainty <- rbind(simcoef.results, boot.results, delta.results)\r\ncolnames(statistical.uncertainty) <- c(\"Median\", \"2.5%\", \"97.5%\", \"(se)\")\r\nrownames(statistical.uncertainty) <- c(\"Simulated Coefficients\", \"Bootstrap\", \"Delta Method\")\r\n\r\nprint(round(statistical.uncertainty, digits=3))\r\n\r\n", "meta": {"hexsha": "0d01dafa965067f069cf5c8c0c6f58c003ead303", "size": 2283, "ext": "r", "lang": "R", "max_stars_repo_path": "R Code/Section2.r", "max_stars_repo_name": "GarrettGlasgow/interpreting-discrete-choice-models", "max_stars_repo_head_hexsha": "918a5cc6ee3b291c8ae849f7caa474849b451b22", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R Code/Section2.r", "max_issues_repo_name": "GarrettGlasgow/interpreting-discrete-choice-models", "max_issues_repo_head_hexsha": "918a5cc6ee3b291c8ae849f7caa474849b451b22", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R Code/Section2.r", "max_forks_repo_name": "GarrettGlasgow/interpreting-discrete-choice-models", "max_forks_repo_head_hexsha": "918a5cc6ee3b291c8ae849f7caa474849b451b22", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2022-01-21T12:26:06.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-21T12:26:06.000Z", "avg_line_length": 29.6493506494, "max_line_length": 142, "alphanum_fraction": 0.6513359615, "num_tokens": 729, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8933094003735664, "lm_q2_score": 0.8459424353665382, "lm_q1q2_score": 0.7556883296878367}} {"text": "## Author: Sergio García Prado\n## Title: Statistical Inference - Non parametric Tests - Exercise 08\n\nrm(list = ls())\n\nx1 <- c(1, 3, 3) # c('A', 'C', 'C')\nx2 <- c(2, 2, 3) # c('B', 'B', 'C')\n\n\n(s <- (x2 - x1)[x2 != x1])\n# 1 -1\n\n(n <- length(s))\n# 2\n\n(V <- sum((s > 0) * rank(abs(s))))\n# 1.5\n\n\n(V.mean <- n * (n + 1) / 4)\n# 1.5\n\n(V.var <- n * (n + 1) * (2 * n + 1) / 24)\n# 1.25\n\n## Asymptotic pvalue (with continuity correction, without tie correction)\n1 - pnorm(V - 0.5, mean = V.mean, sd = sqrt(V.var))\n# 0.672639576990711\n\n## Asymptotic pvalue (with continuity correction, with tie correction)\n(ties <- table(abs(s)))\n# 1\n# 2\n\n(V.var.corrected <- V.var - sum(ties ^ 3 - ties) / 48)\n# 1.125\n\n1 - pnorm(V - 0.5, mean = V.mean, sd = sqrt(V.var.corrected))\n#0.681324055883031\n\n## Exact pvalue (not valid with ties)\n1 - psignrank(V - 1, n)\n# 0.5\n\nwilcox.test(x1, x2, paired = TRUE, alternative = \"greater\", exact = FALSE)\n# Wilcoxon signed rank test with continuity correction\n#\n# data: x1 - x2\n# V = 1.5, p-value = 0.6813\n# alternative hypothesis: true location is greater than 0\n", "meta": {"hexsha": "13bc70d7c3329c2aae009f20525c2d7504782d0f", "size": 1081, "ext": "r", "lang": "R", "max_stars_repo_path": "statistical-inference/non-parametric/exercise-08.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "statistical-inference/non-parametric/exercise-08.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "statistical-inference/non-parametric/exercise-08.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 21.1960784314, "max_line_length": 75, "alphanum_fraction": 0.591119334, "num_tokens": 421, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9241418158002492, "lm_q2_score": 0.817574478416099, "lm_q1q2_score": 0.7555547630353954}} {"text": "#' Compute Efficient Frontier of Mean Variance Optimization\r\n#' @param returns\r\n#' @param cset\r\n#' @param list.arg\r\n#' @param npoints\r\n#' @author Kirk Li \\email{kirkli@@stat.washington.edu} \r\n#' @seealso \\code{\\link{efrontPlot}}\r\n#' @keywords efficient frontier\r\n#' @examples\r\n#' @export\r\n\r\nefrontMV = function(returns,cset = NULL, list.arg= NULL, npoints = 10)\r\n{\r\n\t\r\n\trequire(quadprog)\r\n\trequire(Rglpk)\r\n\trequire(xts)\r\n\t\r\n if(is.null(cset))\r\n {\r\n mu = apply(returns,2,mean)\r\n mu.min = minmu(returns)\r\n mu.max = 1.2*max(mu)} else\r\n {\r\n if (any(c(\"turnover.hobbs\",\"turnover\",\"propcost\") %in% cset$clist.names)){ # find max mu without turnover/propcost constraint, since Rglpk doesn't work with turnover/propcost\r\n if(length(cset$clist.names)>1){\r\n\t\r\n index.mu <- which (cset$clist.names %in% c(\"turnover.hobbs\",\"turnover\",\"propcost\"))\r\n clist.mu <- c(cset$clist.names[-index.mu],\"sum\") \r\n cset.mu <- combine.cset(clist=clist.mu,returns=returns,list.arg,verbose=F)\r\n mu.min = minmu(returns,cset.mu)\r\n \r\nmu.max = .999*maxmu(returns,cset.mu)\r\n } else{mu = apply(returns,2,mean)\r\n mu.min = minmu(returns)\r\n mu.max = 1.2*max(mu)}\r\n } \r\n else {\r\n mu.min = minmu(returns)\r\n mu.max = .999*maxmu(returns,cset)\r\n }\r\n }\r\n p = ncol(returns)\r\n efront = matrix(rep(0,npoints*(p+2)),ncol = p+2)\r\n muvals = seq(mu.min,mu.max,length.out = npoints)\r\n for(i in 1:npoints){\r\n if(is.null(cset))\r\n {efront[i,] = mvo(returns,muvals[i],wts.only = F)} else\r\n {\r\n efront[i,] = tryCatch(mvo(returns,muvals[i],cset,wts.only = F),error=function(e)return(NA))\r\n efront[i,] = as.numeric( efront[i,] )\r\n }}\r\n dimnames(efront)[[2]] = c(\"MU\",\"VOL\",dimnames(returns)[[2]])\r\n if(any(is.na(efront))){\r\n print(\"turnover/propcost constraints reduced the max mean return in efficient frontier plot\")\r\n # violate\r\n efront<-efront[-which(apply(efront,1,function(x)any(is.na(x)))),]}\r\n efront\r\n}\r\n\r\n\r\n\r\n#' Plot Efficient Frontier of Mean Variance Optimization\r\n#' @param returns\r\n#' @param cset\r\n#' @param mu.min\r\n#' @param mu.max\r\n#' @param rf\r\n#' @param npoints\r\n#' @param wts.xlab\r\n#' @param printout\r\n#' @param bar.ylim\r\n#' @param list.arg\r\n#' @param is.fancy\r\n#' @author Kirk Li \\email{kirkli@@stat.washington.edu} \r\n#' @seealso \\code{\\link{efrontPlot}}\r\n#' @keywords efficient frontier\r\n#' @examples\r\n#' @export\r\nefrontPlot = function(returns,cset = NULL,mu.min = NULL, mu.max = NULL, rf = NULL,\r\n npoints = 10,wts.plot = T, wts.xlab=\"VOL\",printout = F,bar.ylim = c(0,2),\r\n list.arg=NULL, is.fancy=TRUE)\r\n{\r\n if(is.null(cset))\r\n {efront = efrontMV(returns,cset = NULL, list.arg=list.arg, npoints)} else\r\n {efront = efrontMV(returns,cset,list.arg=list.arg, npoints)}\r\n\tif(nrow(efront)<=1) stop(\"no solution, consider relaxing constraints\")\r\n if(printout) print(efront)\r\n # Set smart x and y plotting region limits\r\n sigma = apply(returns,2,sd);mu = apply(returns,2,mean)\r\n xlim = c(0,max(sigma));ylim = range(mu);ylim[1] = ylim[1]-.05*diff(ylim)\r\n ylim[1] = min(min(efront[,1]),ylim[1])\r\n ylim[2] = max(max(efront[,1]),ylim[2])\r\n if(wts.plot) {par(mfrow = c(1,2), mgp= c(4, 2, 0), mar=c(8,6,4,2)+0.1)}\r\n plot(efront[,2],efront[,1],type = \"l\",col = 4,lwd = 2, xlab = \"VOL\",ylab = \"MU\", xlim = xlim,\r\n ylim = ylim, main = \"MV Efficient Frontier\")\r\n points(sigma,mu,pch = 20)\r\n text(sigma,mu, labels = dimnames(returns)[[2]],pos = 1, cex = .7)\r\n # If risk-free rate is supplied, get Sharpe ratio and plot tangent line\r\n if(!is.null(rf))\r\n {sr = (efront[,1]-rf)/efront[,2]\r\n i.srmax = which.max(sr);srmax = sr[i.srmax]\r\n abline(rf,srmax,lty = 2)\r\n # Plot points risk-free rate and tangency portfolio\r\n points(0,rf,pch = 16)\r\n points(efront[i.srmax,2],efront[i.srmax,1],pch = 16)\r\n # Plot point at minimum variance portfolio\r\n i.minvol = which.min(efront[,2])\r\n points(efront[i.minvol,2],efront[i.minvol,1],pch = 16)\r\n \r\n if(is.fancy){ #display parameter values in ef plot\r\n para.to.dis <- unique(unlist(sapply(cset$clist.names,function(x){\r\n clist.names.i <- paste(\"cset.\",x,sep=\"\")\r\n names(formals(clist.names.i))})))\r\n para.to.dis <- para.to.dis[para.to.dis %in% c(\"toc\",\"ptc\")] # only display these two parameters\r\n to.dis <- list.arg[para.to.dis]\r\n temp1 <- gsub(\"\\\\)\",\"\",gsub(\"\\\\(\",\"\",gsub(\" c\",\" \",paste(names(to.dis),to.dis))))\r\n temp1 <- sub(\"[[:space:]]\",\" = \",temp1)\r\n temp1 <- c(temp1, paste(\"SRmax =\",round(srmax,3),sep = \"\"),\r\n paste(\"rf =\",round(rf,3),sep = \"\"))\r\n temp1 <- temp1[unlist(lapply(temp1, function(x){nchar(x)<=50}))]\r\n legend(\"topleft\",legend=paste(temp1),bty = \"n\",y.intersp=0.8, xjust=0, x.intersp=-0.5)\r\n } else{ \r\n legend(\"topleft\",inset = c(0,.05),paste(\"SRmax =\",round(srmax,3),sep = \"\"),bty = \"n\")\r\n legend(\"topleft\",inset = c(0,.1),paste(\"rf =\",round(rf,3),sep = \"\"),bty = \"n\")}\r\n }\r\n wts.efront = t(efront); p = nrow(wts.efront)-2\r\n# MU <- efront[,\"MU\"]\r\n# SD <- efront[,\"SD\"]\r\n if(wts.plot)\r\n {\r\n barplotWts(wts.efront,legend.text = T,col = topo.colors(p),ylab = \"WEIGHTS\",xlab = wts.xlab, bar.ylim = bar.ylim)\r\n }\r\n par(mfrow = c(1,1))\r\n}\r\n\r\n", "meta": {"hexsha": "7a18d43079adf4259213d7c376d345b346a3a79c", "size": 5392, "ext": "r", "lang": "R", "max_stars_repo_path": "R/efront.constrained.r", "max_stars_repo_name": "kecoli/PCRM", "max_stars_repo_head_hexsha": "6603978752abbf33b40c0ea2ca4706d0a9393e2a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2019-09-15T15:17:44.000Z", "max_stars_repo_stars_event_max_datetime": "2019-09-15T15:17:44.000Z", "max_issues_repo_path": "R/efront.constrained.r", "max_issues_repo_name": "kecoli/PCRM", "max_issues_repo_head_hexsha": "6603978752abbf33b40c0ea2ca4706d0a9393e2a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/efront.constrained.r", "max_forks_repo_name": "kecoli/PCRM", "max_forks_repo_head_hexsha": "6603978752abbf33b40c0ea2ca4706d0a9393e2a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 39.3576642336, "max_line_length": 181, "alphanum_fraction": 0.5834569733, "num_tokens": 1742, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9184802462567087, "lm_q2_score": 0.8221891370573388, "lm_q1q2_score": 0.7551644810740152}} {"text": "\r\n#Task 1:\r\ndistance = function(x)\r\n{\r\n x = as.matrix(x)\r\n u = apply(x*x,1,sum) %*% matrix(1.0,1,nrow(x))\r\n sqrt(abs(u + t(u) - 2 * x %*% t(x)))\r\n}\r\n\r\nordering = function(mim)\r\n{\r\n Non = nrow(mim) + 1\r\n ordering = rep(0,Non)\r\n ordering[1] = m[Non-1,1]\r\n ordering[2] = m[Non-1,2]\r\n location = 2\r\n for(i in seq(Non-2,1))\r\n {\r\n for(j in seq(1,location))\r\n {\r\n if(ordering[j] == i)\r\n {\r\n ordering[j] = mim[i,1]\r\n if(j==location)\r\n {\r\n location = location + 1\r\n ordering[location] = mim[i,2]\r\n } else\r\n {\r\n location = location + 1\r\n for(k in seq(loc, j+2)) ordering[k] = ordering[k-1]\r\n ordering[j+1] = mim[i,2]\r\n }\r\n }\r\n }\r\n }\r\n -ordering\r\n}\r\n\r\nhi_clust = function(d, method=c(\"single\",\"complete\",\"average\",\"centroid\"))\r\n{\r\n if(!is.matrix(d)) d = as.matrix(d)\r\n \r\n method_function = switch(match.arg(method),\r\n single = min,\r\n complete = max,\r\n average = mean,\r\n centroid = median)\r\n N = nrow(d)\r\n diag(d)=Inf\r\n n = -(1:N) \r\n m = matrix(0,nrow=N-1, ncol=2) \r\n h = rep(0,N-1) \r\n for(j in seq(1,N-1))\r\n {\r\n \r\n h[j] = min(d)\r\n i = which(d - h[j] == 0, arr.ind=TRUE)\r\n i = i[1,,drop=FALSE]\r\n p = n[i]\r\n p = p[order(p)]\r\n m[j,] = p\r\n grp = c(i, which(n %in% n[i[1,n[i]>0]]))\r\n n[grp] = j\r\n r = apply(d[i,],2,method_function)\r\n d[min(i),] = d[,min(i)] = r\r\n d[min(i),min(i)] = Inf\r\n d[max(i),] = d[,max(i)] = Inf\r\n }\r\n \r\n structure(list(merge = m, height = h, order = iorder(m),\r\n labels = rownames(d), method = method, \r\n call = match.call(), dist.method = \"euclidean\"), \r\n class = \"hclust\")\r\n}\r\n\r\ni=seq(1,by=3,length.out=50)\r\nx=as.matrix(iris[i,1:4])\r\nh=hclust(dist(x),method=\"single\")\r\nh1=hi_clust(dist(x),method=\"single\")\r\n#print(cbind(h$merge[1:22,],h1$merge[1:22,]))\r\nplot(h1)\r\n\r\nh=hclust(dist(x),method=\"complete\")\r\nh2=hi_clust(dist(x),method=\"complete\")\r\n#print(cbind(h$merge[1:22,],h1$merge[1:22,]))\r\nplot(h2)\r\n\r\nh=hclust(dist(x),method=\"average\")\r\nh3=hi_clust(dist(x),method=\"average\")\r\n#print(cbind(h$merge[1:22,],h1$merge[1:22,]))\r\nplot(h3)\r\n\r\n\r\nh=hclust(dist(x),method=\"centroid\")\r\nh4 = hi_clust(dist(x),method=\"centroid\")\r\n#print(cbind(h$merge[1:22,],h1$merge[1:22,]))\r\nplot(h4)\r\n\r\n\r\n\r\n#Task 2:\r\n#loading the dataset\r\nfile_data <- read.delim(\"nci.data.txt\", header=FALSE, sep=\" \")\r\nt(file_data)\r\nfile_trans <- t(file_data)\r\nfile_usable <- file_trans[complete.cases(file_trans), ]\r\n\r\n#Task 3:\r\n#K-means clustering\r\n#The kmeans() function performs K-means clustering in R.\r\n\r\n\r\n\r\n#K = 1\r\nset.seed(1)\r\nkm.out <- kmeans(file_trans, 1,nstart = 20)\r\nkm.out$cluster\r\n\r\n\r\n#K = 2\r\nset.seed(1)\r\nkm.out = kmeans(file_trans, 2, nstart=20)\r\nkm.out$cluster\r\n\r\n#K = 3\r\nset.seed(2)\r\nkm.out = kmeans(file_trans, 2, nstart=20)\r\nkm.out$cluster\r\n\r\n#K = 4\r\nset.seed(2)\r\nkm.out = kmeans(file_trans, 2, nstart=20)\r\nkm.out$cluster\r\n", "meta": {"hexsha": "e7ff6a45572dca60408bb053507e977cefa6ae7a", "size": 3062, "ext": "r", "lang": "R", "max_stars_repo_path": "Hierarchical CLustering/HC.r", "max_stars_repo_name": "srivastavaprashant/Data-Science", "max_stars_repo_head_hexsha": "9d959554a878e5a18b705bcf02e73b168db7af05", "max_stars_repo_licenses": ["Unlicense"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-05-19T09:31:25.000Z", "max_stars_repo_stars_event_max_datetime": "2021-05-19T09:31:25.000Z", "max_issues_repo_path": "Hierarchical CLustering/HC.r", "max_issues_repo_name": "srivastavaprashant/Data-Science", "max_issues_repo_head_hexsha": "9d959554a878e5a18b705bcf02e73b168db7af05", "max_issues_repo_licenses": ["Unlicense"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Hierarchical CLustering/HC.r", "max_forks_repo_name": "srivastavaprashant/Data-Science", "max_forks_repo_head_hexsha": "9d959554a878e5a18b705bcf02e73b168db7af05", "max_forks_repo_licenses": ["Unlicense"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.6814814815, "max_line_length": 75, "alphanum_fraction": 0.5202482038, "num_tokens": 1024, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9263037262250327, "lm_q2_score": 0.8152324803738429, "lm_q1q2_score": 0.7551528843099664}} {"text": "# Euler/Milstein\n\nr <- 2; K <- 1; beta <- 0.25; Xzero <- 0.5; # problem parameters\nT <- 1; N <- 2^(11); dt <- T/N; # \nM <- 500; # number of paths sampled\nR <- [1; 16; 32; 64; 128]; # Milstein stepsizes are R*dt\n\ndW <- sqrt(dt)* runif(1, M, N);\nXmil <- double(M, 5);\nfor p = 1:5\n Dt = R[p]*dt;\n L = N/R[p];\n Xtemp = Xzero*rep(M,1);\n for j = 1:L\n Winc = sum(dW(:, R[p]*(j-1)+1:R[p]*j),2);\n Xtemp = Xzero + Dt*r*Xtemp.*(K-Xtemp) + beta*Xtemp.*Winc + .5*beta^2*Xtemp.*(Winc.^2 - Dt);\n end\n Xmil(:,p) <- Xtemp; #store MIlstein solution at t=1\nend\n\nXref = Xmil(:,1); # Reference solution\nXerr = abs(Xmil(:,2:5) - repmat (Xref,1,4)); # Error in each path\nmean(Xerr); # Mean pathwise errors\nDtvals = dt*R(2:5); # Milstein timesteps used\n\nsubplot(224)\nplot(Dtvals, mean(Xerr), log = \"xy\", type = \"l\");\nlines(Dtvals, Dtvals, log = \"xy\");\naxis([1e-3 1e-1 1e-4 1])\nxlabel('\\Delta t')\nylabel('Sample average of | X(T) - X_L|')\nmain('milstein', 'FontSize', 10)", "meta": {"hexsha": "999f43e7f76b8d24782c641e58ab5a18889ca09c", "size": 1146, "ext": "r", "lang": "R", "max_stars_repo_path": "simulations/c/euler-milstein.r", "max_stars_repo_name": "SUNY-SDE-2015/REU15", "max_stars_repo_head_hexsha": "a54ace642d8696250c7fa0bf574b16a931ec91c9", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "simulations/c/euler-milstein.r", "max_issues_repo_name": "SUNY-SDE-2015/REU15", "max_issues_repo_head_hexsha": "a54ace642d8696250c7fa0bf574b16a931ec91c9", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 2, "max_issues_repo_issues_event_min_datetime": "2015-06-04T17:55:32.000Z", "max_issues_repo_issues_event_max_datetime": "2015-07-09T15:38:17.000Z", "max_forks_repo_path": "simulations/c/euler-milstein.r", "max_forks_repo_name": "SUNY-SDE-2015/REU15", "max_forks_repo_head_hexsha": "a54ace642d8696250c7fa0bf574b16a931ec91c9", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 35.8125, "max_line_length": 99, "alphanum_fraction": 0.482547993, "num_tokens": 406, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8947894520743981, "lm_q2_score": 0.8438951064805861, "lm_q1q2_score": 0.7551084399360295}} {"text": "#' Area under the curve (AUC)\n#'\n#' @description Calculates AUC\n#'\n#' @param x numeric vector\n#' @param y numeric vector\n#' @param limits numeric range for integration (default = x range)\n#'\n#' @return auc\n#' @export\n#'\n#' @examples\n#'\n#' x <- seq(-3,3,l = 100)\n#'\n#' y <- dnorm(x)\n#'\n#' plot(x,y)\n#'\n#' auc(x,y)\n#'\n\nauc <- function(x,y, limits = NULL) {\n\n if(is.numeric(x) == F){\n stop(\"x must be numeric\")\n }\n\n if(is.numeric(y) == F){\n stop(\"y must be numeric\")\n }\n\n if((is.numeric(limits) == F) & (is.null(limits) == F)){\n stop(\"limits must be numeric or NULL\")\n }\n\n if((length(limits) != 0) & (length(limits) != 2)){\n stop(\"limits must be of length 2 or NULL\")\n }\n\n tryCatch(\n {\n if(is.null(limits) == T){\n r <- range(x)\n }else{\n r <- limits\n }\n integrate(approxfun(x,y), r[1], r[2])$value\n },\n error = function(e) return(NA_real_)\n )\n\n}\n", "meta": {"hexsha": "5ddcb865585acc404d85e0e660246411ea799c0b", "size": 908, "ext": "r", "lang": "R", "max_stars_repo_path": "R/auc.r", "max_stars_repo_name": "larissabf/relper", "max_stars_repo_head_hexsha": "fc6ed8006190fdb829ebbf8b2f24b3c8ef39c3a4", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/auc.r", "max_issues_repo_name": "larissabf/relper", "max_issues_repo_head_hexsha": "fc6ed8006190fdb829ebbf8b2f24b3c8ef39c3a4", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/auc.r", "max_forks_repo_name": "larissabf/relper", "max_forks_repo_head_hexsha": "fc6ed8006190fdb829ebbf8b2f24b3c8ef39c3a4", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 16.8148148148, "max_line_length": 66, "alphanum_fraction": 0.5341409692, "num_tokens": 296, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8991213718636754, "lm_q2_score": 0.8397339736884712, "lm_q1q2_score": 0.7550227624233138}} {"text": "#Suppose a coin toss turns up 12 heads out of 20 trials. \r\n#At .05 significance level, can one reject the null hypothesis\r\n#that the coin toss is fair?\r\n\r\npbar = 12/20\r\np0 = 0.5\r\n\r\nn = 20\r\n\r\nz = (pbar-p0) / sqrt(p0*(1-p0)/n)\r\n\r\nz # 0.89\r\n\r\nalpha = .05\r\n\r\nz.half.alpha = qnorm(1-alpha/2)\r\n\r\n#aceptamos\r\nc(-z.half.alpha,z.half.alpha)\r\n\r\n\r\npval = 2* pnorm(z,lower.tail = FALSE)\r\npval\r\n\r\nprop.test(12,20,p=0.5,correct = FALSE)", "meta": {"hexsha": "b1a8548e681a414b3e44cfe4cb8b8458ac9047bf", "size": 422, "ext": "r", "lang": "R", "max_stars_repo_path": "Parcial/1. Prueba de hipotesis/TwoTailedProportion.r", "max_stars_repo_name": "jchudb93/Exp-Numerica", "max_stars_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Parcial/1. Prueba de hipotesis/TwoTailedProportion.r", "max_issues_repo_name": "jchudb93/Exp-Numerica", "max_issues_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Parcial/1. Prueba de hipotesis/TwoTailedProportion.r", "max_forks_repo_name": "jchudb93/Exp-Numerica", "max_forks_repo_head_hexsha": "c288c9e73d9770fd49fd6646984a1c2ea6c893c0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 16.88, "max_line_length": 63, "alphanum_fraction": 0.6279620853, "num_tokens": 156, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9489172673767974, "lm_q2_score": 0.7956581024858786, "lm_q1q2_score": 0.7550137123771078}} {"text": "# linear regression to get estimate forage fill value in ration depending on energy::fillvalue\n# UFL:FV (FV either in UEL or ULB) ration.\n# Based on feed tables in\n# Agabriel, J. (2010). Alimentation des bovins, ovins et caprins. Besoins des animaux - Valeurs\n# des aliments. Tables INRA 2010. Editions Quae, France.\n\nM <- as.matrix(read.csv(\"FV_f.csv\", header = TRUE, sep = \";\", dec = \".\"))\nUEL <- as.numeric(M[,\"UEL\"])\nUEB <- as.numeric(M[,\"UEB\"])\nUFL_UEL <- as.numeric(M[,\"UFL_UEL\"])\nUFL_UEB <- as.numeric(M[,\"UFL_UEB\"])\n\ncor(UFL_UEL, UEL)\nfit <- lm(UEL ~ UFL_UEL)\n#pdf(\"UEL_f.pdf\")\npng(\"UEL_f.png\", width = 500, height = 500, units = \"px\")\nplot(UFL_UEL, UEL)\nabline(fit)\ns <- summary(fit)\nlm_coef <- round(coef(fit), 3)\nmtext(bquote(UEL == .(lm_coef[2])*UFL/UEL + .(lm_coef[1])), adj=1, padj=0)\nmtext(bquote(r^2 == .(round(s$r.squared, 3))), adj=0, padj=0)\nmtext(bquote(n == .(nrow(M))), adj=0.15, padj=0)\nprint(s)\ndev.off()\n\ncor(UFL_UEB, UEB)\nfit <- lm(UEB ~ UFL_UEB)\n#pdf(\"UEB_f.pdf\")\npng(\"UEB_f.png\", width = 500, height = 500, units = \"px\")\nplot(UFL_UEB, UEB)\nabline(fit)\ns <- summary(fit)\nlm_coef <- round(coef(fit), 3)\nmtext(bquote(UEB == .(lm_coef[2])*UFL/UEB + .(lm_coef[1])), adj=1, padj=0)\nmtext(bquote(r^2 == .(round(s$r.squared, 3))), adj=0, padj=0)\nmtext(bquote(n == .(nrow(M))), adj=0.15, padj=0)\nprint(s)\ndev.off()\n", "meta": {"hexsha": "ba439fdd530b0bd7d00463da548b7fe8b630d20b", "size": 1334, "ext": "r", "lang": "R", "max_stars_repo_path": "doc/FV_f/FV_f.r", "max_stars_repo_name": "BenLatham/dairy.py", "max_stars_repo_head_hexsha": "4b67b7fae3512327f4b310f1d07425a34e87d160", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 6, "max_stars_repo_stars_event_min_datetime": "2015-03-12T18:27:25.000Z", "max_stars_repo_stars_event_max_datetime": "2021-01-31T00:30:28.000Z", "max_issues_repo_path": "doc/FV_f/FV_f.r", "max_issues_repo_name": "BenLatham/dairy.py", "max_issues_repo_head_hexsha": "4b67b7fae3512327f4b310f1d07425a34e87d160", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2020-06-03T08:37:36.000Z", "max_issues_repo_issues_event_max_datetime": "2020-06-03T16:09:18.000Z", "max_forks_repo_path": "doc/FV_f/FV_f.r", "max_forks_repo_name": "BenLatham/dairy.py", "max_forks_repo_head_hexsha": "4b67b7fae3512327f4b310f1d07425a34e87d160", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2016-07-12T08:42:14.000Z", "max_forks_repo_forks_event_max_datetime": "2021-07-20T06:05:30.000Z", "avg_line_length": 33.35, "max_line_length": 95, "alphanum_fraction": 0.6446776612, "num_tokens": 530, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9399133531922388, "lm_q2_score": 0.8031737892899222, "lm_q1q2_score": 0.7549137694876075}} {"text": "#!/usr/bin/Rscript\n\nrequire(deSolve)\n\n## ==============================================================================\n## Example: Numerical solution of the susceptible (X), infected (Y) resistant (Z)\n## epidemiological model\n## ==============================================================================\n\nparameters <- c(beta = 0.01,\n gamma = 0.01,\n m = 0.1)\n\nstate <- c(X = 100, Y = 1, Z = 0)\n\n## the ODE system\n\nlorenz <- function(t, state, parameters) {\n with(as.list(c(state, parameters)),{\n\n# rate of change\n\n dX <- -beta*X*Y + gamma*Z\n dY <- beta * X * Y - m*Y \n dZ <- m*Y - gamma * Z\n\n# return the rate of change\n\n list(c(dX, dY, dZ))\n\n })\n\n}\n\ntimes <- seq(0, 100, by = 0.01)\n\nout <- ode(y = state, times = times, func = lorenz, parms = parameters)\n\nhead(out)\n\npar(oma = c(0, 0, 3, 0))\nplot(out, xlab = \"time\", ylab = \"-\")\nplot(out[, \"X\"], out[, \"Z\"], pch = \".\")\nmtext(outer = TRUE, side = 3, \"SIR Model\", cex = 1.5)\n", "meta": {"hexsha": "0ae53d864e59c5f93e458a6b044dcef221df0aea", "size": 994, "ext": "r", "lang": "R", "max_stars_repo_path": "simple_sir.r", "max_stars_repo_name": "siglun/etudes", "max_stars_repo_head_hexsha": "d78a76d9e6a58192041483b3ac90e9d2f5eb84fd", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "simple_sir.r", "max_issues_repo_name": "siglun/etudes", "max_issues_repo_head_hexsha": "d78a76d9e6a58192041483b3ac90e9d2f5eb84fd", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "simple_sir.r", "max_forks_repo_name": "siglun/etudes", "max_forks_repo_head_hexsha": "d78a76d9e6a58192041483b3ac90e9d2f5eb84fd", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.0888888889, "max_line_length": 81, "alphanum_fraction": 0.4466800805, "num_tokens": 295, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9579122696813392, "lm_q2_score": 0.7879312031126512, "lm_q1q2_score": 0.754768967126388}} {"text": "##PROJET: Manipulation de polynomes\n\n#1) Quelle serait la représentation creuse sous forme de liste du polynome 2+x^4−3x^5 ? list(c(2, 0), c(1, 4), c(-3, 5))\n#2) Et sa représentation dense ? c(2, 0, 0, 0, 1, -3)\n#3) Quand choisit-on de travailler plutot en représentation creuse ? Quand on souhaite travailler avec les degrés\n#4) Quelle est la représentation la plus économique en terme d’espace mémoire ? Representation dense\n\n# SOURCES :\n# http://www.i3s.unice.fr/~malapert/R/pdf/A4-Polynomes.pdf\n# https://www.youtube.com/watch?v=Z393AcN_Gz0 (Horner methode comprehension)\n\n# Pour executer le programme faire Rscript ./polynomes.r\n# Ou l'executer dans Rstudio.\n# Va executer toutes les demonstrations de l'activite.\n\n# Vous devez avoir installer le package 'polynom' sinon il y aura une erreur.\n\n# Pour utiliser les fonctions une a une\n# (cf. Activite_manipulation_des_polynomes.pdf)\n# qui est une documentation du code.\np <- list(c(2,5), c(-1,4),c(-2,1))\nq <- list(c(1,4), c(7,2),c(-1,0))\n\n# indique si le polynome est nul\nis_poly0 <- function(p) length(p) == 0\n\n# renvoyant le degre d’un monome ou d’un polynome.\ndegre <- function(mp) {\n if(is_poly0(mp)) return(-Inf)\n if (is.list(mp)) mp <- mp[[1]]\n if (is.vector(mp) && length(mp) == 2) return(mp[2])\n else return(NULL)\n}\n\n# renvoyant le coefficient d’un monome ou d’un polynome.\ncoeff <- function(mp) {\n if(is_poly0(mp)) return(-Inf)\n if (is.list(mp)) mp <- mp[[1]]\n if (is.vector(mp) && length(mp) == 2) return(mp[1])\n else return(NULL)\n}\n\n# renvoyant une chaîne de caractères représentant le polynome creux sous la forme ∑aiX^i\npoly2str <- function(p){\n if(length(p) == 0){\n return (\"\")\n }\n acc = \"\"\n for(e in p){\n acc = paste(acc, e[1], \"*X^\", e[2], \" + \", sep=\"\")\n }\n return(substr(acc, 0, nchar(acc) - 3))\n}\n\n# multiplication par un scalaire k d’un polynome\nmult_ext <- function(p, k) {\n return(lapply(p, function(x) c(k*x[1], x[2])))\n}\n\n# transforme un polynome plein en un polynome creux\nmake_poly <- function(x) {\n poly_creux <- list()\n power <- length(x) - 1\n j <- 1\n for (i in length(x):1) {\n if (x[i] != 0) {\n poly_creux[[j]] <- c(x[i], power)\n j <- j + 1\n }\n power <- power - 1\n }\n return(poly_creux)\n}\n\n# générant un polynome aléatoire de degré inférieur à n\n# et dont les coefficients sont tirés dans le vecteur coeffs\nrand_poly <- function(n, coeffs) {\n poly <- list()\n len_poly <- sample(1:n-1, 1)\n j <- 1\n for (i in len_poly:1) {\n rand_coeff <- sample(coeffs, 1)\n if (rand_coeff != 0) {\n poly[[j]] <- c(rand_coeff, i)\n j <- j + 1\n }\n }\n if (length(poly) == 0) return(rand_poly(n, coeffs))\n return(poly)\n}\n\n# trie une liste de monomes par degré décroissant\nsort_monoms <- function(p) {\n for (i in 1:length(p)) {\n for (j in i:length(p)) {\n if (p[[i]][2] < p[[j]][2]) {\n x <- p[[i]]\n p[[i]] <- p[[j]]\n p[[j]] <- x\n }\n }\n }\n return(p)\n}\n\n# somme les termes de même degré, et supprime les termes dont le coefficient est nulle\nmerge_monoms <- function(p) {\n monoms <- list(p[[1]])\n l_p <- length(p)\n i <- 2\n j <- 1\n # Additionne les monoms entre eux\n while (i <= l_p) {\n if (monoms[[j]][2] == p[[i]][2] && i != j) {\n monoms[[j]] <- c(monoms[[j]][1] + p[[i]][1], p[[i]][2])\n } else {\n j <- j + 1\n monoms[[j]] <- p[[i]]\n }\n i <- i + 1\n }\n k <- 1\n # Enlève les monoms de coeff nulle\n while (k <= length(monoms)) {\n if (monoms[[k]][1] == 0) {\n monoms[[k]] <- NULL\n next\n }\n k <- k + 1\n }\n return(monoms)\n}\n\n# Addition de deux polynomes\nadd <- function(p, q) {\n combine <- c(p, q) # combine 2 listes\n return(merge_monoms(sort_monoms(combine)))\n}\n\n# Soustraction de 2 polynomes\nsub <- function(p,q) add(p,mult_ext(q,-1))\n\n# polynome dérivé du polynome p\nderiv <- function(p) {\n drv <- list()\n for (i in p) {\n if (i[[2]] == 1) {\n drv <- c(drv, list(c(i[[1]], 0)))\n }\n else if (i[[2]] == 0) {\n i <- NULL\n }\n else {\n drv <- c(drv, list(c(i[[2]] * i[[1]], i[[2]] - 1)))\n }\n }\n return(drv)\n}\n\n# primitive du polynome p\ninteg <- function(p) {\n integ <- list()\n for (c in p) {\n integ <- c(integ, list(c(c[[1]] / (c[[2]] + 1), c[[2]] + 1)))\n }\n return(integ)\n}\n\n# Multiplication de 2 monomes\nmult_monoms <- function(m1, m2) {\n return(list(c(m1[1] * m2[1], m1[2] + m2[2])))\n}\n\n# Multiplication d'un polynome par un monome\nmult_poly_mono <- function(p, m) {\n return(lapply(p, function(x) c(m[1]*x[1], m[2] + x[2])))\n}\n\n# Multiplication interne de deux polynomes\nmult <- function(p, q) {\n res <- list()\n # S'appuyant sur la methode vu dans le cours de l'activite\n for (monom in q) {\n res <- add(res, mult_poly_mono(p, monom))\n }\n return(res)\n}\n\n# Valeur d'un polynome en un point x version naive\npolyval <- function(p, x) {\n res <- c()\n for (monom in p) {\n res <- c(res, c(monom[1] * x ** monom[2]))\n }\n return(sum(res))\n}\n\n# Fonction personnel pour faire polyhorn\n# qui convertir un polynome creux a dense\ncreux_to_dense <- function(p) {\n degre <- degre(p)\n res <- c()\n old <- p[[1]][2]\n i <- 1\n j <- 1\n while (i <= length(p)) {\n if (old - p[[j]][2] >= 2) {\n res <- c(res, 0)\n old <- old - 1\n next\n }\n else {\n res <- c(res, p[[j]][1])\n j <- j + 1\n }\n old <- p[[i]][2]\n i <- i + 1\n }\n adjust <- degre - length(res) + 1\n if (adjust > 0) res <- c(res, numeric(adjust))\n return(rev(res))\n}\n\n# Valeur d'un polynome en un point x version Horner\npolyhorn <- function(p, x) {\n # Verification que le polynome p est un polynome creux, si oui conversion en dense\n if (is.list(p)) p <- creux_to_dense(p)\n len_p <- length(p)\n res <- p[[len_p]][1]\n for (i in (len_p-1):1) {\n res <- (res * x) + p[[i]][1]\n }\n return(res)\n}\n\n# construit la fonction polynome associee a p\nfpoly <- function(p) {\n return( function(x) {polyval(p, x)}) # on peut faire pareil avec polyhorn\n}\n\n# dessine les courbes de la primitive, derivee et du polynome\ndessiner <- function(p, x) {\n cols <- c(\"green\", \"red\", \"blue\")\n finteg <- fpoly(integ(p))\n fderiv <- fpoly(deriv(p))\n fpoly_p <- fpoly(p)\n\n integ <- sapply(x, finteg)\n derivate <- sapply(x, fderiv)\n poly_p <- sapply(x, fpoly_p)\n matplot(x, cbind(integ, derivate, poly_p), t=\"l\", lwd=1.5, lty=1, xlab=\"x\", ylab=\"y\", col=cols)\n legend(\"topleft\", inset=.05, legend=c(\"Primitive\", \"Derivee\", \"Polynome\"), horiz=FALSE, lwd=2, lty=1, col=cols)\n}\n\n# tout les cas de test de l'activite polynome\n# sont effectue dans cette fonction\ndemonstration <- function() {\n stopifnot(\"2*X^5 + -1*X^4 + -2*X^1\" == poly2str(p))\n stopifnot(poly2str(mult_ext(p,-2)) == \"-4*X^5 + 2*X^4 + 4*X^1\")\n stopifnot(poly2str(make_poly(c(0, -2, 0, 0, -1, 2))) == \"2*X^5 + -1*X^4 + -2*X^1\")\n stopifnot(poly2str(make_poly(c(-1, 0, -7, 0, 1))) == \"1*X^4 + -7*X^2 + -1*X^0\")\n stopifnot(poly2str(add(p, list())) == \"2*X^5 + -1*X^4 + -2*X^1\")\n stopifnot(poly2str(add(list(), q)) == \"1*X^4 + 7*X^2 + -1*X^0\")\n stopifnot(poly2str(add(p,q)) == \"2*X^5 + 7*X^2 + -2*X^1 + -1*X^0\")\n stopifnot(poly2str(sub(p,p)) == \"\")\n stopifnot(poly2str(sub(p,q)) == \"2*X^5 + -2*X^4 + -7*X^2 + -2*X^1 + 1*X^0\")\n stopifnot(poly2str(sub(q,p)) == \"-2*X^5 + 2*X^4 + 7*X^2 + 2*X^1 + -1*X^0\")\n stopifnot(poly2str(integ(p)) == \"0.333333333333333*X^6 + -0.2*X^5 + -1*X^2\")\n stopifnot(poly2str(integ(q)) == \"0.2*X^5 + 2.33333333333333*X^3 + -1*X^1\")\n stopifnot(poly2str(deriv(p)) == \"10*X^4 + -4*X^3 + -2*X^0\")\n stopifnot(poly2str(deriv(q)) == \"4*X^3 + 14*X^1\")\n p1 <- make_poly(c(1,1))\n p2 <- make_poly(c(-1,1))\n p3 <- make_poly(c(1,-1,1))\n stopifnot(poly2str(mult(p1,p2)) == \"1*X^2 + -1*X^0\")\n stopifnot(poly2str(mult(p3,p3)) == \"1*X^4 + -2*X^3 + 3*X^2 + -2*X^1 + 1*X^0\")\n cat('---TEST CASES DE L\\'ACTIVITE POLYNOME---\\n')\n cat('TEST CASE : poly2str(p) == \"2*X^5 + -1*X^4 + -2*X^1\" TRUE\\n')\n cat('TEST CASE : poly2str(mult_ext(p,-2)) == \"-4*X^5 + 2*X^4 + 4*X^1\" TRUE\\n')\n cat('TEST CASE : poly2str(make_poly(c(0, -2, 0, 0, -1, 2))) == \"2*X^5 + -1*X^4 + -2*X^1\" TRUE\\n')\n cat('TEST CASE : poly2str(make_poly(c(-1, 0, -7, 0, 1))) == \"1*X^4 + -7*X^2 + -1*X^0\" TRUE\\n')\n cat('TEST CASE : poly2str(rand_poly(5,0:3)) = ', poly2str(rand_poly(5,0:3)), '\\n')\n cat('TEST CASE : poly2str(rand_poly(10,0:1)) = ', poly2str(rand_poly(10,0:1)), '\\n')\n cat('TEST CASE : poly2str(add(p, list())) == \"2*X^5 + -1*X^4 + -2*X^1\" TRUE\\n')\n cat('TEST CASE : poly2str(add(list(), q)) == \"1*X^4 + 7*X^2 + -1*X^0\" TRUE\\n')\n cat('TEST CASE : poly2str(add(p,q)) == \"2*X^5 + 7*X^2 + -2*X^1 + -1*X^0\" TRUE\\n')\n cat('TEST CASE : poly2str(sub(p,p)) == \"\" TRUE\\n')\n cat('TEST CASE : poly2str(sub(p,q)) == \"2*X^5 + -2*X^4 + -7*X^2 + -2*X^1 + 1*X^0\" TRUE\\n')\n cat('TEST CASE : poly2str(sub(q,p)) == \"-2*X^5 + 2*X^4 + 7*X^2 + 2*X^1 + -1*X^0\" TRUE\\n')\n cat('TEST CASE : poly2str(integ(p)) == \"0.333333333333333*X^6 + -0.2*X^5 + -1*X^2\" TRUE\\n')\n cat('TEST CASE : poly2str(integ(q)) == \"0.2*X^5 + 2.33333333333333*X^3 + -1*X^1\" TRUE\\n')\n cat('TEST CASE : poly2str(deriv(p)) == \"10*X^4 + -4*X^3 + -2*X^0\" TRUE\\n')\n cat('TEST CASE : poly2str(deriv(q)) == \"4*X^3 + 14*X^1\" TRUE\\n')\n cat('TEST CASE : poly2str(mult(p1,p2)) == \"1*X^2 + -1*X^0\" TRUE\\n')\n cat('TEST CASE : poly2str(mult(p3,p3)) == \"1*X^4 + -2*X^3 + 3*X^2 + -2*X^1 + 1*X^0\" TRUE\\n')\n cat('---TEST POLYNOMES P EN UN POINT X---\\n')\n cat('UTILISATION DE POLYVAL\\n')\n print(poly2str(p))\n for(i in -1:1) {\n print(paste(\"p(\",i,\") = \",polyval(p,i), sep=\"\"))\n }\n print(poly2str(q))\n for(i in -1:1) {\n print(paste(\"q(\",i,\") = \",polyval(q,i), sep=\"\"))\n }\n cat('UTALISATION DE POLYHORN\\n')\n print(poly2str(p))\n for(i in -1:1) {\n print(paste(\"p(\",i,\") = \",polyhorn(p,i), sep=\"\"))\n }\n print(poly2str(q))\n for(i in -1:1) {\n print(paste(\"q(\",i,\") = \",polyhorn(q,i), sep=\"\"))\n }\n cat('dessiner(p, x) -> (voir plot)\\n')\n x <- seq(-2,4,length.out=1000)\n p1 <- make_poly(c(-1,-1,1))\n dessiner(p1,x)\n}\n\ndemonstration()\n\n### N'AFFICHE PAS COMME DANS L'EXEMPLE DE L'ACTIVITE MAIS A LES MEMES RESULTAT\n### EN COMPARANT vh, vn et vr ci-dessous (sachant que polyhorn et polyval fonctionnent bien avec de multiple tests)\nx <- seq(2-0.02,2.02,length.out=1001)\nvec <- c(-2,0,1)\n## p(x) = (x^2-2)^16\np1 <- make_poly(vec)\nfor(i in 1:4) {\n p1 <- mult(p1,p1)\n}\n## Evaluate p using our methods (observed)\nvn <- sapply(x, polyval, p=p1)\nvh <- sapply(x, polyhorn, p=p1)\n\n\nlibrary(\"polynom\")\n## Evaluate p using R package (expected)\npr <-as.polynomial(c(-2,0,1))\n## p is an R object ! I directly used the power operator.\npr <- pr ** 16\n## I also use a generic function\nvr <- predict(pr,x)\n\n## Last, visualize the results\ncols <- c(\"red\", \"gold\")\nmatplot(x, cbind(vn-vr,vh-vr),t=\"l\", lwd=2, lty=1,col=cols, xlab=\"x\",ylab=\"P(x)-P^R(x)\")\nlegend(\"topleft\", inset=.05, legend=c(\"Naive\", \"Horner\"), horiz=TRUE, lwd=2, lty=1, col=cols)", "meta": {"hexsha": "422de5393912ea883157286da7f98d972dbc8894", "size": 11374, "ext": "r", "lang": "R", "max_stars_repo_path": "polynomes.r", "max_stars_repo_name": "takitsu21/polynomial-library", "max_stars_repo_head_hexsha": "08edbb2c8e5745b4290264675349e84cb364f1ac", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "polynomes.r", "max_issues_repo_name": "takitsu21/polynomial-library", "max_issues_repo_head_hexsha": "08edbb2c8e5745b4290264675349e84cb364f1ac", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "polynomes.r", "max_forks_repo_name": "takitsu21/polynomial-library", "max_forks_repo_head_hexsha": "08edbb2c8e5745b4290264675349e84cb364f1ac", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 32.683908046, "max_line_length": 120, "alphanum_fraction": 0.5463337436, "num_tokens": 4205, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.923039160069787, "lm_q2_score": 0.8175744695262775, "lm_q1q2_score": 0.7546532516460369}} {"text": "true.lambda <- 2.4\ntrue.mu <- .000000005\nN0 <- 2\ny0 <- statmod::rinvgauss(N0, mean = true.mu, shape = true.lambda)\n\na_0 <- .9\n\nlog(prod(statmod::dinvgauss(y0, mean = true.mu, shape = true.lambda)^a_0) )\na_0* sum(statmod::dinvgauss(y0, mean = true.mu, shape = true.lambda, log = TRUE))\nsum(a_0 * statmod::dinvgauss(y0, mean = true.mu, shape = true.lambda, log = TRUE))\n\nlogP <- sum(log(y0))\nS <- sum(y0)\nSprime <- sum(1/y0)\n\na_0 * N0 * .5 * ( log(true.lambda) - log(2*pi) ) -3/2 * a_0 * logP + (a_0*N0*true.lambda)/true.mu -(a_0*S*true.lambda)/(2*true.mu^2)-(a_0*Sprime*true.lambda)/2\na_0 * N0 * .5 * ( log(true.lambda) - log(2*pi) ) -3/2 * a_0 * logP + true.lambda * ( (a_0*N0)/true.mu -(a_0*S)/(2*true.mu^2)-(a_0*Sprime)/2 ) \na_0 * N0 * .5 * ( log(true.lambda) - log(2*pi) ) -3/2 * a_0 * logP - ( -(a_0*N0)/true.mu +(a_0*S)/(2*true.mu^2) + (a_0*Sprime)/2 ) * true.lambda \n\n-(a_0*N0)/true.mu +(a_0*S)/(2*true.mu^2) + (a_0*Sprime)/2\n", "meta": {"hexsha": "25c506d9f625c8cd39d0e238deddcd186ab5fbad", "size": 937, "ext": "r", "lang": "R", "max_stars_repo_path": "code/extra/test_invgauss.r", "max_stars_repo_name": "maxbiostat/propriety_power_priors", "max_stars_repo_head_hexsha": "43a9dc7bd007d5647bc453cd8a875e82c16ad6eb", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "code/extra/test_invgauss.r", "max_issues_repo_name": "maxbiostat/propriety_power_priors", "max_issues_repo_head_hexsha": "43a9dc7bd007d5647bc453cd8a875e82c16ad6eb", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 7, "max_issues_repo_issues_event_min_datetime": "2020-05-29T19:11:11.000Z", "max_issues_repo_issues_event_max_datetime": "2020-08-29T15:58:08.000Z", "max_forks_repo_path": "code/extra/test_invgauss.r", "max_forks_repo_name": "maxbiostat/propriety_power_priors", "max_forks_repo_head_hexsha": "43a9dc7bd007d5647bc453cd8a875e82c16ad6eb", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 44.619047619, "max_line_length": 160, "alphanum_fraction": 0.5955176094, "num_tokens": 409, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9511422199928904, "lm_q2_score": 0.793105951184112, "lm_q1q2_score": 0.7543565550988293}} {"text": "\nblockMiss = function(n){\n # n = length of song\n\n nsections = sqrt(n)\t# quick way to determine number of sections in the song\n\n mix = c(0.3,0.4,0.2,0.1)\t# mixture probabilities of difficulty of a section: Easy, Medium ,Hard, Very Hard\n missprop = c(0.01,0.05,0.25,0.5)\t# Probability of missing a note for each of the four types of sections\n\n sectiontype = sample(1:4,nsections,mix,replace=T)\t# randomly assign a difficulty to each section with probability from the mix vector\n\n sectionsize = rmultinom(1,n,rep(1,nsections))[,1]\t# randomly allocate section sizes for song using multinomial distribution\n\n song = numeric(n)\n\n notes = 0\n for(i in 1:nsections){\n song[(notes+1):(notes + sectionsize[i])] = rbinom(sectionsize[i],1,missprop[sectiontype[i]])\n notes = notes + sectionsize[i]\n }\n\n return(song)\n \n}\n\n\nx = matrix(0,200,100)\n\nfor(j in 1:100){\n\tx[,j] = blockMiss(200)\n}\n\nwrite(t(x),\"p.varies_block_n200_r100.txt\",ncol=200) # each row in this file is a different simulated song\n\ny = matrix(0,600,100)\nfor(j in 1:100){\n\ty[,j] = blockMiss(600)\n}\n\nwrite(t(y),\"p.varies_block_n600_r100.txt\",ncol=600) # each row in this file is a different simulated song\n", "meta": {"hexsha": "f649115f6462e44a2104aad241f18628ff15e66b", "size": 1174, "ext": "r", "lang": "R", "max_stars_repo_path": "GHSupplementaryFiles/AppendixD/blockSim.r", "max_stars_repo_name": "iramler/guitar_hero_jse", "max_stars_repo_head_hexsha": "daaa66120705cd66d517bd35a66d4151683f9480", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "GHSupplementaryFiles/AppendixD/blockSim.r", "max_issues_repo_name": "iramler/guitar_hero_jse", "max_issues_repo_head_hexsha": "daaa66120705cd66d517bd35a66d4151683f9480", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "GHSupplementaryFiles/AppendixD/blockSim.r", "max_forks_repo_name": "iramler/guitar_hero_jse", "max_forks_repo_head_hexsha": "daaa66120705cd66d517bd35a66d4151683f9480", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 28.6341463415, "max_line_length": 135, "alphanum_fraction": 0.6984667802, "num_tokens": 369, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9362850093037732, "lm_q2_score": 0.8056321889812552, "lm_q1q2_score": 0.7543013415557337}} {"text": "# The probability of observing y successes in n trials of a binomial experiment \r\n# number of trials\r\nn<-20\r\n# let probability of success on a single trial be z\r\nz<-0.85\r\n# probability that 18 or more of the 20 seeds will germinate?\r\ny<-18\r\nprobability_for18seeds<-(factorial(n))/(factorial(y)*factorial(n-y))*(z^y)*(1-z)^(n-y)\r\ny<-19\r\nprobability_for19seeds<-(factorial(n))/(factorial(y)*factorial(n-y))*(z^y)*(1-z)^(n-y)\r\ny<-20\r\nprobability_for20seeds<-(factorial(n))/(factorial(y)*factorial(n-y))*(z^y)*(1-z)^(n-y)\r\ntotal_probability<-probability_for18seeds+probability_for19seeds+probability_for20seeds\r\nprint(total_probability)", "meta": {"hexsha": "f85ea509ca7a10f2f637e73864d5455e77febc5e", "size": 633, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH4/EX4.7/Ex4_7.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH4/EX4.7/Ex4_7.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH4/EX4.7/Ex4_7.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 45.2142857143, "max_line_length": 88, "alphanum_fraction": 0.7345971564, "num_tokens": 190, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9702399051935107, "lm_q2_score": 0.7772998611746912, "lm_q1q2_score": 0.7541673436130614}} {"text": "\n#' @name GLMGA\n#' @rdname GLMGA\n#' @title The GLMGA distribution\n#'\n#' @param y vector of quantiles.\n#' @param u vector of probabilities.\n#' @param sigma parameter of GLMGA distribution.\n#' @param a parameter of GLMGA distribution.\n#' @param b parameter of GLMGA distribution.\n#' @param log logical; if TRUE, probabilities/densities p are returned as log(p).\n#' @param n number of observations. If length(n) > 1, the length is taken to be the number required.\n#' @importFrom stats runif\n#' @importFrom stats pbeta\n#' @description Density (\\code{dGLMGA}), distribution function (\\code{pGLMGA}), quantile function (\\code{qGLMGA}) and random generation (\\code{rGLMGA}) for the GLMGA distribution with parameters sigma, a and b.\n#' @references Zhengxiao Li, Jan Beirlant, Shengwang Meng. Generalizing The Log-Moyal Distribution And Regression Models For Heavy-Tailed Loss Data. ASTIN Bulletin: The Journal of the IAA, 11(1):57-99, 2021.\n#' @details\n#' The GLMGA distribution with parameters (sigma, a, b) has density\n#' \\deqn{f(y)=\\frac{(2b)^a}{\\sigma B(a,\\frac{1}{2})}\\frac{y^{-(\\frac{1}{2\\sigma}+1)}}{(y^{-\\frac{1}{\\sigma}}+2b)^{a + \\frac{1}{2}}},}\n#' for \\eqn{y>0,\\sigma>0, a>0, b>0}.\n#'\n#' The cumulative distribution function \\eqn{F(y)} is\n#'\n#' \\deqn{F(y)=1-I_{\\frac{1}{2},a}(\\frac{y^{-1/\\sigma}}{y^{-1/\\sigma}+2b}).}\n#'\n#' Here \\eqn{I_{m,n}()} is the beta cumulative distribution function (or regularized incomplete beta function) with parameters shape1 = m and shape2 = n\n#' implemented by R's \\code{\\link[stats]{pbeta}} and defined in its help.\n#'\n#' The quantile function \\eqn{F^{-1}(u)} is\n#'\n#' \\deqn{(2b)^{-\\sigma}[\\frac{I^{-1}_{\\frac{1}{2},a}(1-p)}{1-I^{-1}_{\\frac{1}{2},a}(1-p)}]^{-\\sigma},}\n#' where \\eqn{u \\in (0,1)}, and \\eqn{I_{m,n}^{-1}()} denotes the inverse of the beta cumulative distribution function (or regularized incomplete beta function)\n#' with parameters shape1 = m and shape2 = n\n#' implemented by R's \\code{\\link[stats]{qbeta}}.\n#'\n#'\n#'\n#' @return\n#' \\code{dGLMGA} gives the density, \\code{pGLMGA} gives the distribution function, \\code{qGLMGA} gives the quantile function, and \\code{rGLMGA} generates random deviates.\n#'\n#' Invalid arguments will result in return value NaN, with a warning.\n#'\n#' The length of the result is determined by n for rgamma, and is the maximum of the lengths of the numerical arguments for the other functions.\n#'\n#' The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.\n#'\n#'\nNULL\n\n\n\n\n#' @rdname GLMGA\n#' @export\n#' @examples\n#' # density function at value 0.5 and 0.1\n#' dGLMGA(c(0.5, 0.1), sigma = 2, a = 2, b = 3, log = FALSE)\ndGLMGA <- function(y, sigma, a, b, log = FALSE) {\n if (log == FALSE) {\n exp(-0.5 * log(2 * pi) - log(sigma) + a * log(b) + lgamma(a + 0.5) - lgamma(a) - (1 / (2 * sigma) + 1) * log(y) - (a + 0.5) * log(0.5 * (1 / y)^(1 / sigma) + b))\n } else if (log == TRUE) {\n -0.5 * log(2 * pi) - log(sigma) + a * log(b) + lgamma(a + 0.5) - lgamma(a) - (1 / (2 * sigma) + 1) * log(y) - (a + 0.5) * log(0.5 * (1 / y)^(1 / sigma) + b)\n }\n}\n\n\n#' @rdname GLMGA\n#' @export\n#'\n#' @examples\n#' # cdf at value 10 and 20.\n#' pGLMGA(c(10, 20), sigma = 2, a = 2, b = 3)\npGLMGA <- function(y, sigma, a, b) {\n z <- y^(-1 / sigma) / (y^(-1 / sigma) + 2 * b)\n p <- 1 - pbeta(z, shape1 = 0.5, shape2 = a)\n p\n}\n\n\n#' @rdname GLMGA\n#' @export\n#'\n#' @examples\n#' # quantile function at level 50% and 10%\n#' qGLMGA(c(0.5, 0.1), sigma = 2, a = 2, b = 3)\nqGLMGA <- function(u, sigma, a, b) {\n c <- (2 * b)^(-sigma)\n # I <- pbeta(u, shape1 = 0.5, shape2 = a)\n Iinv <- qbeta(1 - u, shape1 = 0.5, shape2 = a)\n c * (Iinv / (1 - Iinv))^(-sigma)\n}\n\n\n#' @rdname GLMGA\n#' @export\n#' @examples\n#' # simulate 10 samples from GLMGA distribution with parameters (2, 2, 3)\n#' rGLMGA(n = 10, sigma = 2, a = 2, b = 3)\nrGLMGA <- function(n, sigma, a, b) {\n u <- runif(n, min = 0, max = 1)\n qGLMGA <- Vectorize(qGLMGA)\n r <- qGLMGA(u, sigma = sigma, a = a, b = b)\n r\n}\n\n\n#' #' Sum of vector elements\n#' #'\n#' #' \\code{sum} returns the sum of all the values present in its arguments.\n#' #'\n#' #' This is a generic function: methods can be defined for it directly\n#' #' or via the \\code{\\link{Summary}} group generic. For this to work properly,\n#' #' the arguments \\code{...} should be unnamed, and dispatch is on the\n#' #' first argument.\n#' #'\n#' #' @param ... Numeric, complex, or logical vectors.\n#' #' @param na.rm A logical scalar. Should missing values (including NaN)\n#' #' be removed?\n#' #' @return If all inputs are integer and logical, then the output\n#' #' will be an integer. If integer overflow\n#' #' \\url{https://en.wikipedia.org/wiki/Integer_overflow} occurs, the output\n#' #' will be NA with a warning. Otherwise it will be a length-one numeric or\n#' #' complex vector.\n#' #'\n#' #' Zero-length vectors have sum 0 by definition. See\n#' #' \\url{https://en.wikipedia.org/wiki/Empty_sum} for more details.\n#' #' @examples\n#' #' sum(1:10)\n#' #' sum(1:5, 6:10)\n#' #' sum(F, F, F, T, T)\n#' #'\n#' #' sum(.Machine$integer.max, 1L)\n#' #' sum(.Machine$integer.max, 1)\n#' #'\n#' #' \\dontrun{\n#' #' sum(\"a\")\n#' #' }\n#' sum <- function(..., na.rm = TRUE) {}\n", "meta": {"hexsha": "72db80e0405a747e582ef39c03806921745f69db", "size": 5215, "ext": "r", "lang": "R", "max_stars_repo_path": "R/GLMGA-distribution.r", "max_stars_repo_name": "lizhengxiao/rMGLReg", "max_stars_repo_head_hexsha": "8823d8a0409616ddb3bb75cdba436865dd979604", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/GLMGA-distribution.r", "max_issues_repo_name": "lizhengxiao/rMGLReg", "max_issues_repo_head_hexsha": "8823d8a0409616ddb3bb75cdba436865dd979604", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 2, "max_issues_repo_issues_event_min_datetime": "2021-08-10T13:04:07.000Z", "max_issues_repo_issues_event_max_datetime": "2021-11-23T11:13:27.000Z", "max_forks_repo_path": "R/GLMGA-distribution.r", "max_forks_repo_name": "lizhengxiao/rMGLReg", "max_forks_repo_head_hexsha": "8823d8a0409616ddb3bb75cdba436865dd979604", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 37.5179856115, "max_line_length": 210, "alphanum_fraction": 0.6222435283, "num_tokens": 1816, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9196425223682085, "lm_q2_score": 0.8198933315126792, "lm_q1q2_score": 0.7540087714651941}} {"text": "## Plotting Sierpinski carpet fractal v.2. aev 4/2/17\n## ord - order, fn - file name, ttl - plot title, clr - color\npSierpinskiC2 <- function(ord, fn=\"\", ttl=\"\", clr=\"brown\") {\n m=640; abbr=\"SCR2\"; dftt=\"Sierpinski carpet fractal v.2\";\n cat(\" *** START\", abbr, date(), \"\\n\");\n if(fn==\"\") {pf=paste0(abbr,\"o\", ord)} else {pf=paste0(fn, \".png\")};\n if(ttl!=\"\") {dftt=ttl}; ttl=paste0(dftt,\", order \", ord);\n cat(\" *** Plot file:\", pf,\".png\", \"title:\", ttl, \"\\n\");\n S = matrix(1,1,1);\n for (i in 1:ord) {\n Q = cbind(S,S,S); R = cbind(S,0*S,S); S = rbind(Q,R,Q);\n }\n plotmat(S, pf, clr, ttl);\n cat(\" *** END\", abbr, date(), \"\\n\");\n}\n## Executing:\npSierpinskiC2(5);\n", "meta": {"hexsha": "06b697e389c4a1d8722b8d232eeb67c65369b198", "size": 673, "ext": "r", "lang": "R", "max_stars_repo_path": "Task/Sierpinski-carpet/R/sierpinski-carpet-2.r", "max_stars_repo_name": "LaudateCorpus1/RosettaCodeData", "max_stars_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Sierpinski-carpet/R/sierpinski-carpet-2.r", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Sierpinski-carpet/R/sierpinski-carpet-2.r", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 37.3888888889, "max_line_length": 69, "alphanum_fraction": 0.5497771174, "num_tokens": 267, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.897695292107347, "lm_q2_score": 0.839733963661418, "lm_q1q2_score": 0.7538252258014969}} {"text": "x <- c(-12, 1, 16)\r\ny <- c(-19, -14, -9, 8)\r\n\r\nprob.x <- c(0.35, 0.3, 0.35)\r\n\r\nprob.y_x <- c(0.2, 0.33, 0.23, 0.17,\r\n 0.25, 0.25, 0.22, 0.28,\r\n 0.23, 0.25, 0.23, 0.29)\r\n\r\nparametro_a <- -0.41\r\nparametro_b <- 0.56\r\nparametro_c <- 0.15\r\nparametro_d <- 0.35\r\n\r\nmat.y_x <- matrix(data = prob.y_x, ncol = length(y), nrow = length(x), byrow = TRUE);\r\n\r\nprob.xy <- c()\r\n\r\nfor( i in 1:length(x) ){\r\n \r\n for( j in 1:length(y) ){\r\n \r\n prob.xy <- c(prob.xy, mat.y_x[i,j] * prob.x[i]);\r\n \r\n }\r\n \r\n}\r\n\r\nmat.xy <- matrix(data = prob.xy, ncol = length(y), nrow = length(x), byrow = TRUE);\r\n\r\nprob.y <- c(sum(mat.xy[1:3,1]),sum(mat.xy[1:3,2]),sum(mat.xy[1:3,3]),sum(mat.xy[1:3,4]))\r\n\r\ne.x <- sum(x*prob.x)\r\ne.y <- sum(y*prob.y)\r\n\r\ne.xy <- c()\r\nfor(i in 1:length(x)) {\r\n for(j in 1:length(y)) {\r\n e.xy <- c(e.xy, mat.xy[i,j]*x[i]*y[j])\r\n }\r\n}\r\ne.xy <- sum(e.xy)\r\ncov <- e.xy - e.x*e.y\r\n\r\ncov2 <- cov*parametro_a*parametro_c\r\n\r\nvar.x <- sum(x^2*prob.x)-e.x^2\r\nvar.y <- sum(y^2*prob.y)-e.y^2\r\n\r\nro <- cov/sqrt(var.x*var.y)\r\n\r\nsgn.ac <- parametro_a*parametro_c/abs(parametro_a*parametro_c)\r\n\r\ncat(\"X\\n\")\r\nprint(x)\r\nprint(prob.x)\r\ncat(\"\\nY\\n\")\r\nprint(y)\r\nprint(prob.y)\r\ncat(\"\\nCongiunta\\n\")\r\nprint(mat.xy)\r\ncat(\"\\nE(XY)\\n\")\r\nprint(e.xy)\r\ncat(\"\\nE(X)\\n\")\r\nprint(e.x)\r\ncat(\"\\nE(Y)\\n\")\r\nprint(e.y)\r\ncat(\"\\nCovarianza\\n\")\r\nprint(cov)\r\ncat(\"\\nCovarianza della combinazione lineare\\n\")\r\nprint(cov2)\r\ncat(\"\\nVar(X)\\n\")\r\nprint(var.x)\r\ncat(\"\\nVar(Y)\\n\")\r\nprint(var.y)\r\ncat(\"\\nRo\\n\")\r\nprint(ro)\r\ncat(\"\\nRo della comb. lineare\\n\")\r\nprint(sgn.ac*ro)", "meta": {"hexsha": "a2639284e5bae23228dbbf2dbf56da5292311bca", "size": 1560, "ext": "r", "lang": "R", "max_stars_repo_path": "code/Esercizio 47.r", "max_stars_repo_name": "mfranzil/PSUniTN", "max_stars_repo_head_hexsha": "c4baecf5b01fb7cc2cfc66f4881ae47451475dac", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "code/Esercizio 47.r", "max_issues_repo_name": "mfranzil/PSUniTN", "max_issues_repo_head_hexsha": "c4baecf5b01fb7cc2cfc66f4881ae47451475dac", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "code/Esercizio 47.r", "max_forks_repo_name": "mfranzil/PSUniTN", "max_forks_repo_head_hexsha": "c4baecf5b01fb7cc2cfc66f4881ae47451475dac", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 19.746835443, "max_line_length": 89, "alphanum_fraction": 0.5358974359, "num_tokens": 614, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9273632856092014, "lm_q2_score": 0.8128673133042217, "lm_q1q2_score": 0.7538233024301272}} {"text": "=begin\n # sample-factorize01.rb\n\n require \"algebra\"\n \n P = Polynomial(Integer, \"x\")\n x = P.var\n f = 8*x**7 - 20*x**6 + 6*x**5 - 11*x**4 + 44*x**3 - 9*x**2 - 27\n p f.factorize #=> (2x - 3)^3(x^2 + x + 1)^2\n((<_|CONTENTS>))\n=end\n", "meta": {"hexsha": "fcb7b3b5e0e1916e9fe05f245796e441dd6a0abf", "size": 234, "ext": "rd", "lang": "R", "max_stars_repo_path": "doc-ja/sample-factorize01.rb.v.rd", "max_stars_repo_name": "kunishi/algebra-ruby2", "max_stars_repo_head_hexsha": "ab8e3dce503bf59477b18bfc93d7cdf103507037", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 6, "max_stars_repo_stars_event_min_datetime": "2015-04-25T17:00:02.000Z", "max_stars_repo_stars_event_max_datetime": "2021-07-08T02:59:44.000Z", "max_issues_repo_path": "work/consider/algebra-0.72/doc/sample-factorize01.rb.v.rd", "max_issues_repo_name": "rubyworks/stick", "max_issues_repo_head_hexsha": "7e89d1a1ade1db085ddfecf19f774f0ba9bc2b70", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2017-03-10T14:02:43.000Z", "max_issues_repo_issues_event_max_datetime": "2017-03-10T14:02:43.000Z", "max_forks_repo_path": "doc/sample-factorize01.rb.v.rd", "max_forks_repo_name": "kunishi/algebra-ruby2", "max_forks_repo_head_hexsha": "ab8e3dce503bf59477b18bfc93d7cdf103507037", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 19.5, "max_line_length": 65, "alphanum_fraction": 0.5042735043, "num_tokens": 109, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9504109770159682, "lm_q2_score": 0.7931059536292271, "lm_q1q2_score": 0.7537766042659348}} {"text": "library(stats)\r\n\r\ncreate_model <- function(input,resp,name) {\r\n fit <- nls(resp~exp(a+b*input),start = list(a=log(20),b=-0.001))\r\n B <- coef(fit)\r\n n <- length(input)\r\n d <- 2\r\n \r\n \r\n pred <- function(x) {\r\n #Generate predictions\r\n return(exp(B[\"a\"]+B[\"b\"]*x))\r\n }\r\n sig.est = sqrt(sum((resp-pred(input))^2)/(n-d))\r\n \r\n #Linearize model for confidence and prediction\r\n #f(x|B) ~ f(x|B_hat) + gradient(f(x|B_hat)*(B - B_hat)\r\n #y~f(x|B)+e <=> g = gradient()(a,b)\r\n # z = y - g + g*B\r\n mdiv <- deriv(y~exp(a+b*x),c(\"a\",\"b\"),function(a,b,x){})\r\n G <- mdiv(a=B[\"a\"],b=B[\"b\"],input)\r\n G <- attr(G,\"gradient\")\r\n z <- resp - pred(input) + G%*%B\r\n \r\n #Find linear standard error\r\n var.lin <- ((sig.est^2)*solve(t(G)%*%G))\r\n se.lin <- sqrt(diag(var.lin))\r\n \r\n #Model parameters of lineraized version can be treated\r\n #linearly\r\n \r\n #Confidence of parameters\r\n level <- 0.95\r\n alpha <- 1-level\r\n B.ci <- cbind(B + qt(alpha/2,n-d)*se.lin, B + qt(1-alpha/2,n-d)*se.lin)\r\n row.names(B.ci) <- names(B)\r\n colnames(B.ci) <- c(paste0((1-level)/2*100,\"%\"),paste0((1+level)/2 * 100,\"%\"))\r\n \r\n #Confidence\r\n input.new <- seq(0,100,1)\r\n pred.input.new <- pred(input.new)\r\n grad2 <- mdiv(a=B[\"a\"],b=B[\"b\"],input.new)\r\n G2 <- attr(grad2,\"gradient\")\r\n GS <- rowSums((G2%*%vcov(fit))*G2)\r\n delta <- sqrt(GS)*qt(1-alpha/2, n-d)\r\n df.delta <- data.frame(odometer=input.new,price = pred.input.new,\r\n lwr.conf = pred.input.new-delta,upr.conf = pred.input.new+delta)\r\n \r\n #Prediction\r\n sig2.est <- summary(fit)$sigma\r\n pred.delta <- sqrt(GS + sig2.est^2)*qt(1-alpha/2,n-d)\r\n df.delta[c(\"lwr.pred\",\"upr.pred\")] <- cbind(pred.input.new - pred.delta,\r\n pred.input.new + pred.delta)\r\n input.df <- data.frame(odometer=input,price=resp)\r\n \r\n #Create plot\r\n p = ggplot(data = df.delta,aes(x=odometer,y=price))+geom_point(data=input.df)+\r\n geom_line(size = 1.5,col=\"green\")+\r\n geom_ribbon(aes(ymin = lwr.conf,ymax = upr.conf,color=\"95% Confidence\"),alpha = 0.2,fill = \"green\")+\r\n geom_ribbon(aes(ymin = lwr.pred,ymax = upr.pred,color=\"95% Prediction\"),alpha = 0.2,fill = \"blue\") +\r\n scale_colour_manual(name=\"\",values=c(\"95% Confidence\"=\"green\",\"95% Prediction\"=\"blue\"))+\r\n labs(title = paste(name, \"prediction plot\"))\r\n \r\n return(list(fit = fit,B.conf = B.ci, pred = df.delta,df = input.df,plot = p))\r\n}\r\n\r\n", "meta": {"hexsha": "4c19c947f5d8dbc26649c645d11cc7b50892a16c", "size": 2606, "ext": "r", "lang": "R", "max_stars_repo_path": "auto/nls_conf.r", "max_stars_repo_name": "acavalos/hyde", "max_stars_repo_head_hexsha": "e5d481155cbc1a63d890060a8c751be1a650f094", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "auto/nls_conf.r", "max_issues_repo_name": "acavalos/hyde", "max_issues_repo_head_hexsha": "e5d481155cbc1a63d890060a8c751be1a650f094", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "auto/nls_conf.r", "max_forks_repo_name": "acavalos/hyde", "max_forks_repo_head_hexsha": "e5d481155cbc1a63d890060a8c751be1a650f094", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 38.8955223881, "max_line_length": 117, "alphanum_fraction": 0.531465848, "num_tokens": 790, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9532750387190132, "lm_q2_score": 0.7905303236047049, "lm_q1q2_score": 0.7535928248428291}} {"text": "## Dale W.R. Rosenthal, 2018\n## You are free to distribute and use this code so long as you attribute\n## it to me or cite the text.\n## The legal disclaimer in _A Quantitative Primer on Investments with R_\n## applies to this code. Use or distribution without these comment lines\n## is forbidden.\n\n## Check residual plots for patterns\nmodel.ibm <- lm(logret.ibm ~ logret.factor1, data=bigdataset)\nres.ibm <- residuals(model.ibm)\nplot(model.ibm$fitted, res.ibm) # plot residuals vs fitted values\nplot(bigdataset$date, res.ibm) # plot residuals versus date\n\n## Test for Autocorrelations\nlibrary{lmtest}\nmodel.ibm <- lm(logret.ibm ~ logret.factor1, data=bigdataset)\nres.ibm <- residuals(model.ibm)\ndwtest(res.ibm ~ 1)\n\n## Test for Cross-Correlations\nmodel.ibm <- lm(logret.ibm ~ logret.factor1, data=bigdataset)\nres.ibm <- residuals(model.ibm)\nmodel.aapl <- lm(logret.aapl ~ logret.factor1, data=bigdataset)\nres.aapl <- residuals(model.aapl)\n# Compute Pearson and Fisher tests\ncor.test(res.ibm, res.aapl, method=\"pearson\")\n\n## Check for Influential Points\nmodel.ibm <- lm(logret.ibm ~ logret.factor1, data=bigdataset)\nres.student.ibm <- rstudent(model.ibm)\nplot(res.student.ibm)\n\ncooks.distances.ibm <- cooks.distance(model.ibm)\nplot(cooks.distances.ibm)\n\n# Compute Pena's sensitivities\np <- length(coef(model.ibm))\nQ <- qr.Q(model.ibm$qr) # the Q of the QR decomposition\nH <- Q %*% t(Q) # the hat matrix\nh <- diag(H)\nS <- H^2 %*% rstudent(model.ibm)^2/(p*h*(1-h))\n\n## Check for Multicollinearity\ncor.coeff <- cov2cor(vcov(model.ibm))\ncor.coeff # coefficient correlation matrix\neigen(cor.coeff) # compute eigenvectors, eigenvalues\ndet(cor.coeff) # determinant\nkappa(cor.coeff, exact=TRUE) # condition number\n", "meta": {"hexsha": "5243546975b111b079941443f8e62efa1774206b", "size": 1757, "ext": "r", "lang": "R", "max_stars_repo_path": "Quantitative Primer/samples/ch10-model-diagnostics.r", "max_stars_repo_name": "bmoretz/Quantitative-Investments", "max_stars_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 7, "max_stars_repo_stars_event_min_datetime": "2020-03-26T05:47:30.000Z", "max_stars_repo_stars_event_max_datetime": "2022-02-18T21:50:54.000Z", "max_issues_repo_path": "Quantitative Primer/samples/ch10-model-diagnostics.r", "max_issues_repo_name": "bmoretz/Quantitative-Investments", "max_issues_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Quantitative Primer/samples/ch10-model-diagnostics.r", "max_forks_repo_name": "bmoretz/Quantitative-Investments", "max_forks_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2020-11-03T09:23:54.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-18T21:50:55.000Z", "avg_line_length": 35.8571428571, "max_line_length": 73, "alphanum_fraction": 0.7154240182, "num_tokens": 461, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9381240177362486, "lm_q2_score": 0.8031737940012418, "lm_q1q2_score": 0.753476626568911}} {"text": "## Dale W.R. Rosenthal, 2018\n## You are free to distribute and use this code so long as you attribute\n## it to me or cite the text.\n## The legal disclaimer in _A Quantitative Primer on Investments with R_\n## applies to this code. Use or distribution without these comment lines\n## is forbidden.\nlibrary(EQL)\n\n# calculate moments to pass to Edgeworth expansion\nmean.obs <- mean(x.obs)\nvar.obs <- var(x.obs)\nskew.obs <- skewness(x.obs, method=\"moment\")*n.obs/(n.obs-2)\nexkurt.obs <- kurtosis(x.obs, method=\"moment\")*n.obs/(n.obs-3)-3\n\n# create the Edgeworth expansion. Since we have moments, we\n# do this for a \"sum\" with 1 term.\nedge.expand <- edgeworth(x, 1, rho3=skew.obs, rho4=exkurt.obs,\n mu=mean.obs, sigma2=var.obs, type=\"sum\")\n\n# without EQL, we would have to do this:\ndedge <- function(x) {\n z <- (x-mean.obs)/sqrt(var.obs)\n dnorm(z)*(1 + skew.obs*(z^3-3*z)/6 + exkurt.obs*(z^4-6*z^2+3)/24\n + skew.obs^2*(z^6-15*z^4+45*z^2-15)/72)/sqrt(var.obs)\n}\n", "meta": {"hexsha": "f90f88bff45d672cfe5c6bd79658cc2994d52785", "size": 998, "ext": "r", "lang": "R", "max_stars_repo_path": "Quantitative Primer/samples/ch8-edgeworth-expansion.r", "max_stars_repo_name": "bmoretz/Quantitative-Investments", "max_stars_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 7, "max_stars_repo_stars_event_min_datetime": "2020-03-26T05:47:30.000Z", "max_stars_repo_stars_event_max_datetime": "2022-02-18T21:50:54.000Z", "max_issues_repo_path": "Quantitative Primer/samples/ch8-edgeworth-expansion.r", "max_issues_repo_name": "bmoretz/Quantitative-Investments", "max_issues_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Quantitative Primer/samples/ch8-edgeworth-expansion.r", "max_forks_repo_name": "bmoretz/Quantitative-Investments", "max_forks_repo_head_hexsha": "25d9a7199f212787dd9ae05f7af9e7407591c5bc", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2020-11-03T09:23:54.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-18T21:50:55.000Z", "avg_line_length": 38.3846153846, "max_line_length": 73, "alphanum_fraction": 0.6583166333, "num_tokens": 316, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.95598134762883, "lm_q2_score": 0.7879312031126512, "lm_q1q2_score": 0.7532475333904377}} {"text": "## Author: Sergio García Prado\n## Title: Statistical Inference - Goodness of Fit - Exercise 01\n\nrm(list = ls())\n\nobserved <- c(6, 18, 32, 35, 17, 10, 2)\n\n(k <- length(observed))\n# 7\n\n(n <- sum(observed))\n# 120\n\nLogLikelihood <- function(lamdba, y, k) {\n (sum(y[1:(k - 1)] * dpois(0:(k - 2), lambda = lamdba, log = TRUE)) +\n y[k] * ppois(k - 2, lambda = lamdba, log = TRUE, lower.tail = FALSE))\n}\n\nNegativeLogLikelihood <- function(...) {\n - LogLikelihood(...)\n}\n\nopt <- optim(1, NegativeLogLikelihood, lower = 10e-4, y = observed, k = k,\n method = \"L-BFGS-B\")\n\n(lambda.hat <- opt$par)\n# 2.65019719097978\n\n(expected <- n * c(dpois(0:(k - 2), lambda = lambda.hat),\n 1 - ppois(k - 1, lambda = lambda.hat)))\n# 8.47647391824289 22.4643273675407 29.7674486433533 26.2965362590832 ...\n\n(Q <- sum((observed - expected) ^ 2 / expected))\n# 4.76208557778011\n\n(pvalue <- 1 - pchisq(Q, df = (k - 1) - 1))\n# 0.445600066398024\n", "meta": {"hexsha": "71a43cb37fc4450661de837afc8563fe9d81e407", "size": 947, "ext": "r", "lang": "R", "max_stars_repo_path": "statistical-inference/goodness-of-fit/exercise-03.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "statistical-inference/goodness-of-fit/exercise-03.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "statistical-inference/goodness-of-fit/exercise-03.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 24.9210526316, "max_line_length": 74, "alphanum_fraction": 0.5966209081, "num_tokens": 353, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9465966762263736, "lm_q2_score": 0.7956580952177051, "lm_q1q2_score": 0.7531673083456871}} {"text": "print (\"first task\")\n\na <- c(-5, 1, 6, -3, 2, -2, 5, 2, 0, -6, 2, 1, 0, -2, -3, 1)\nb <- c(3, -2, 6, -4, -7, 8, -1, 0, 9, -2, 8, 9, -2, 1, 0, -1)\np <- c ( -8, 4, -2, 8, 0, 3, -5, 3, 2, -3, -4, 5, 9, 1, -3, 0)\nfir <- ((5)*a)-(6*b)\nprint (\"first answer\")\nfir\nsec <- ((5)*as.numeric(a%*%p))*b+3*(norm(p, type=\"2\"))*b\nprint (\"second answer\")\nsec\nthr <- (-2)*(norm(p, type=\"2\"))*p+5*as.numeric(a%*%p)*a+3*as.numeric(b%*%p)*b\nprint (\"third answer\")\nthr\n\n2 задание\n\nprint (\"second task\")\nmat <- rbind(c(-4,3,0,-10,8,0,0,0),c(12,-5,0,-1,8,0,0,0),c(-1,6,0,2,8,0,0,0),c(7,0,12,0,0,1,0,-3),c(-7,0,0,0,0,-1,-4,3),c(0,0,0,-3,-8,0,1,-2),c(0,0,0,8,-1,0,-4,-2),c(0,0,0,-6,2,0,-9,1))\nrua <- c(34,44,-6,-44,-4,-61,-13,50)\nX <- solve(mat)%*%rua\nprint (\"Answer for the sec task\")\nX\nmat%*%X\nrua\n\n4 задание\n\nprint (\"fourth task\")\nA <- rbind(c(19, 0, 0, 0, 0 ,0 ,0 ,20),c(0, 7 ,0 ,0 ,7 ,0 ,0 ,0),c(0, 0, 13, 0, 0, 0, 0, 0),c(0 ,0 ,0 ,11, 0, 0, 0, 0),c(0 ,7 ,0 ,0, 17, 0, 0 ,0),c(0, 0, 0, 0, 0 ,5, 0, 0),c(0, 0, 0, 0, 0, 0, 3 ,0),c(0, 0, 0, 0, 0, 0, 0, 1))\nA\noptions(digits=3) # Задать количество значащих цифр для вывода\nprint (\"собственные числа \")\nd <- eigen(A)$values; d # Собственные значения матрицы A\nprint (\"собственные вектора\")\nP <- eigen(A)$vectors; P # Собственные векторы A, стоящие в столбцах матрицы\nP\nprint (\" Проверим ортогональность полученного собственного базиса \")\nsum(P[,1]^2) # Например, длина первого собственного вектора\nP[,1] %*% P[,2] # Например, скалярное произведение (f1, f2)\nsum(P[,2]^2); P[,2] %*% P[,3] # длина 2 собственного вектора и (f2, f3)\nsum(P[,3]^2); P[,3] %*% P[,4] # длина 3 собственного вектора и (f3, f4)\nsum(P[,4]^2); P[,4] %*% P[,5] # длина 4 собственного вектора и (f4, f5)\nsum(P[,5]^2); P[,5] %*% P[,6] # длина 5 собственного вектора и (f5, f6)\nsum(P[,6]^2); P[,6] %*% P[,7] # длина 6 собственного вектора и (f6, f7)\nsum(P[,7]^2); P[,7] %*% P[,8] # длина 7 собственного вектора и (f7, f8)\nsum(P[,8]^2); P[,8] %*% P[,1] # длина 8 собственного вектора и (f8, f1)\nprint (\"Таким образом, получили что полученный базис составляют нормированные и\nортогональные между собой вектора, т.е ортонормированный базис.\nТаким образом, получили что полученный базис составляют нормированные и\nортогональные между собой вектора, т.е ортонормированный базис.\")\n\n6 задание\n\nprint (\"sixth task\")\ninstall.packages(\"lpSolveAPI\") # Загружаем библиотеку\nlibrary(lpSolveAPI) # Активируем библиотеку линейного программирования\nM <- make.lp(ncol= 2) # Объявляем количество неотрицательных переменных в M\nname.lp(M, \"Example\") # Объявляем название \"Example\"для задачи(модели) М\ncolnames(M) <- c(\"X1\", \"X2\") # Объявляем названия переменных в модели М\nlp.control(M, sense = \"min\")$sense# Объявляем задачу на минимум модели М\nset.objfn(M, c(-6, 2)) # Задаем целевую функцию: f = 5*X1 +3*X2 для модели М\nadd.constraint(M, c(5,7), \">=\", 35) # Задаем ограничение:\nadd.constraint(M, c(-3, 9/2), \">=\", -27/2) # Аналогично\nadd.constraint(M, c(1, -3), \">=\", -12) # Аналогично\nadd.constraint(M, c(1, 0), \"<=\", 8) # Аналогично\nrownames(M) <- c(\"A\", \"B\", \"C\", \"D\") # Называем ограничения в модели М\nM\nsolve.lpExtPtr(M)\nget.variables(M) # Оптимальный план\nget.objective(M)\nX1.opt<- get.variables(M)[1]; X1.opt # Оптимальное значение для X1\nX2.opt<- get.variables(M)[2]; X2.opt # Оптимальное значение для X2\nf.max<- get.objective(M); f.max\n", "meta": {"hexsha": "9c51492a50d65bbe59dec4a006728fe8fdf5acc8", "size": 3321, "ext": "r", "lang": "R", "max_stars_repo_path": "Tasks/Task 7/solution.r", "max_stars_repo_name": "Master-sniffer/Doing-some-tasks-with-R", "max_stars_repo_head_hexsha": "629e7add02437ea22c079ecd7a4279e46028b69c", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Tasks/Task 7/solution.r", "max_issues_repo_name": "Master-sniffer/Doing-some-tasks-with-R", "max_issues_repo_head_hexsha": "629e7add02437ea22c079ecd7a4279e46028b69c", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Tasks/Task 7/solution.r", "max_forks_repo_name": "Master-sniffer/Doing-some-tasks-with-R", "max_forks_repo_head_hexsha": "629e7add02437ea22c079ecd7a4279e46028b69c", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 44.28, "max_line_length": 224, "alphanum_fraction": 0.6193917495, "num_tokens": 1694, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9184802373309979, "lm_q2_score": 0.8198933381139645, "lm_q1q2_score": 0.7530558277770182}} {"text": ".overall_f_statistics <- function(X, y){\n n <- dim(X)[1]\n k <- dim(X)[2]\n intercept <- matrix(rep(1, length(y)), ncol=1)\n intecept_only_residual.2 <- sum(residual(intercept, y)^2)\n regression_residual.2 <- sum(residual(X, y)^2)\n f_stat <- (n-k)/k * (intecept_only_residual.2 - regression_residual.2)/regression_residual.2\n return(f_stat)\n} \n\n#' @export\noverall_significance_f_test <- function(X, y){\n n <- dim(X)[1]\n k <- dim(X)[2]\n f_stat <- .overall_f_statistics(X, y)\n\n return(TestResult(test_name = \"Overall Significant F Test\",\n H0_description = \"All coefficients (except intercept) equal 0: β1 = β2 = ... = βk = 0\",\n test_statistic = f_stat,\n distribution = \"f\",\n df1 = k,\n df2 = n-k))\n}", "meta": {"hexsha": "85f7eead08f4e19e949b1c41f2be62468c5b9e8c", "size": 833, "ext": "r", "lang": "R", "max_stars_repo_path": "R/overall_significance_f_test.r", "max_stars_repo_name": "kevinkevin556/econometrics", "max_stars_repo_head_hexsha": "735a25f3eea03d9d1d1d27d90e7c1ef311604c84", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/overall_significance_f_test.r", "max_issues_repo_name": "kevinkevin556/econometrics", "max_issues_repo_head_hexsha": "735a25f3eea03d9d1d1d27d90e7c1ef311604c84", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/overall_significance_f_test.r", "max_forks_repo_name": "kevinkevin556/econometrics", "max_forks_repo_head_hexsha": "735a25f3eea03d9d1d1d27d90e7c1ef311604c84", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 36.2173913043, "max_line_length": 109, "alphanum_fraction": 0.5594237695, "num_tokens": 225, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9653811621568289, "lm_q2_score": 0.7799929053683037, "lm_q1q2_score": 0.7529904574585344}} {"text": "#Example : 2.3b Chapter : 2.3 Pageno : 61\n#Multiplication with Elimination and Permutation matricies\nAb<-matrix(c(1,4,0,2,8,3,2,9,2,1,3,1),ncol=4)\nE21<-matrix(c(1,0,0,-4,1,0,0,0,1),ncol=3,byrow=T)\nP32<-matrix(c(1,0,0,0,0,1,0,1,0),ncol=3,byrow=T)\nE21Ab<-E21%*%Ab\nprint(E21Ab)\nP32E21Ab<-P32%*%E21Ab\nprint(P32E21Ab)\nP32E21<-P32%*%E21\nprint(P32E21)\nP32E21Ab<-P32E21%*%Ab\nprint(P32E21Ab)\n#Solution for this system is\nb<-P32E21Ab[,4]\nP32E21Ab<-P32E21Ab[,-4]\nx<-solve(P32E21Ab,b)\nprint(x)", "meta": {"hexsha": "6dc8d2eedb175c4a20dcbbb07167c4c86d6aa72a", "size": 487, "ext": "r", "lang": "R", "max_stars_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH2/EX2.3.b/Ex2_2.3b.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH2/EX2.3.b/Ex2_2.3b.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH2/EX2.3.b/Ex2_2.3b.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 27.0555555556, "max_line_length": 58, "alphanum_fraction": 0.6919917864, "num_tokens": 261, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9433475762847495, "lm_q2_score": 0.7981867873410141, "lm_q1q2_score": 0.7529675712606565}} {"text": "#Data\r\n\r\nx1 <- 4\r\nx2 <- 9\r\nx3 <- 10\r\n\r\nexpected <- 8.609\r\nvariance <- 3.869\r\n\r\n\r\n#install.packages(\"pracma\", repos=\"http://R-Forge.R-project.org\")\r\nlibrary(pracma)\r\n\r\ndata <- c(x1,x2,x3)\r\n\r\nmomento <- function(x, y, r, centrato = FALSE) {\r\n res <- 0\r\n \r\n if(length(x) != length(y) || r < 0 || r %% 1 != 0 ) {\r\n res <- NaN\r\n }\r\n \r\n if(centrato == FALSE) {\r\n for(i in 1:length(x)) {\r\n res <- res + x[i]^r*y[i]\r\n }\r\n } else {\r\n res <- ifelse(r == 1, 0, \r\n ifelse(r == 2, momento(x, y, 2)-(momento(x, y, 1)^2), \r\n ifelse(r == 3, momento(x, y, 3) - momento(x, y, 1)^3 - \r\n 3*momento(x, y, 1)*momento(x, y, 2, centrato = TRUE),\r\n res <- NaN)))\r\n }\r\n return(res)\r\n}\r\n\r\nmat_original <- matrix(c(data[1], data[2], data[3], expected,\r\n data[1]^2, data[2]^2, data[3]^2, variance+expected^2,\r\n 1, 1, 1, 1), byrow = TRUE, nrow = 3, ncol = 4)\r\n\r\nmat <- rref(mat_original)\r\nprob <- c(mat[10],mat[11],mat[12])\r\n\r\nprint(matrix(c(data[1], data[2], data[3], prob[1], prob[2], prob[3]),\r\n byrow = TRUE, nrow = 2, ncol = 3))\r\n\r\nmnnoncentrato3 <- momento(data, prob, 3)\r\nmncentrato3 <- momento(data, prob, 3, centrato = TRUE)\r\n\r\nprint(mnnoncentrato3)\r\nprint(mncentrato3)", "meta": {"hexsha": "33f1d768176a9a5cfb36b02a602ad8c22d26cf9e", "size": 1302, "ext": "r", "lang": "R", "max_stars_repo_path": "code/Esercizio 31.r", "max_stars_repo_name": "mfranzil/PSUniTN", "max_stars_repo_head_hexsha": "c4baecf5b01fb7cc2cfc66f4881ae47451475dac", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "code/Esercizio 31.r", "max_issues_repo_name": "mfranzil/PSUniTN", "max_issues_repo_head_hexsha": "c4baecf5b01fb7cc2cfc66f4881ae47451475dac", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "code/Esercizio 31.r", "max_forks_repo_name": "mfranzil/PSUniTN", "max_forks_repo_head_hexsha": "c4baecf5b01fb7cc2cfc66f4881ae47451475dac", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 25.5294117647, "max_line_length": 84, "alphanum_fraction": 0.4892473118, "num_tokens": 465, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9372107896491796, "lm_q2_score": 0.8031737869342624, "lm_q1q2_score": 0.752743139078182}} {"text": "# __ _____ _ __ _ \n# <(o )___ | _ |___ ___ ___| |_ ___ ___ | | ___| |_ ___ \n# ( ._> / | __| _| -_|_ -| _| -_|_ -| | |__| .'| . |_ -|\n# `---' |__| |_| |___|___|_| |___|___| |_____|__, |___|___|\n#==============================================================================\n# Nonparametric Smoothing in Regression\n#==============================================================================\n# Title : Nonparametric_regression_kernel.r\n# Description : Nonparametric regression using kernel weights.\n# Author : Isaias V. Prestes \n# Date : 20170604\n# Version : 0.0.1\n# Usage : Run in R 3.4\n# Notes : Reference \n# http://www.stat.cmu.edu/~cshalizi/uADA/12/lectures/ch04.pdf\n# R version : 3.4\n#==============================================================================\n\n# Using Nonparametric Smoothing in Regression\nx = runif(300, 0, 3)\nyf = sin(x)*cos(20*x) + rnorm(length(x), 0, 0.15)\nyg = log(x + 1) + rnorm(length(x), 0, 0.15)\npar(mfcol=c(2, 1))\nplot(x, yf, xlab=\"x\", ylab=expression(f(x) + epsilon))\ncurve(sin(x)*cos(20*x), col=\"grey\", add=TRUE)\nplot(x, yg, xlab=\"x\", ylab=expression(g(x) + eta))\ncurve(log(x + 1), col=\"grey\", add=TRUE)\n\n# Selecting a region \nwindows()\npar(mfcol=c(2,1))\ncolors=ifelse((x<1.7)&(x>1.5),\"black\",\"grey\")\nplot(x,yf,xlab=\"x\",ylab=expression(f(x)+epsilon),col=colors)\ncurve(sin(x)*cos(20*x),col=\"grey\",add=TRUE)\npoints(1.6,mean(yf[(x<1.7)&(x>1.5)]),pch=\"*\",cex=2)\nplot(x,yg,xlab=\"x\",ylab=expression(g(x)+eta),col=colors)\ncurve(log(x+1),col=\"grey\",add=TRUE)\npoints(1.6,mean(yg[(x<1.7)&(x>1.5)]),pch=\"*\",cex=2)\n\n# \nloc_ave_err <- function(h,y,y0) {abs(y0-mean(y[(1.6-h < x) & (1.6+h>x)]))}\nyf0=sin(1.6)*cos(20*1.6)\nyg0=log(1+1.6)\nf.LAE = sapply(0:100/100,loc_ave_err,y=yf,y0=yf0)\ng.LAE = sapply(0:100/100,loc_ave_err,y=yg,y0=yg0)\nplot(0:100/100,f.LAE,xlab=\"Radius of averaging window\",\nylab=\"Absolute value of error\",type=\"l\")\nlines(0:100/100,g.LAE,lty=2)\nabline(h=0.15,col=\"grey\")\n\n# Cross-validation for univariate kernel regression\ncv_bws_npreg <- function(x,y,bandwidths=(1:50)/50, num.folds=10) {\n\trequire(np)\n\tn <- length(x)\n\tstopifnot(n> 1, length(y) == n)\n\tstopifnot(length(bandwidths) > 1)\n\tstopifnot(num.folds > 0, num.folds==trunc(num.folds))\n\tfold_MSEs <- matrix(0,nrow=num.folds,\n\tncol=length(bandwidths))\n\tcolnames(fold_MSEs) = bandwidths\n\tcase.folds <- rep(1:num.folds,length.out=n)\n\tcase.folds <- sample(case.folds)\n\tfor (fold in 1:num.folds) {\n\t\ttrain.rows = which(case.folds==fold)\n\t\tx.train = x[train.rows]\n\t\ty.train = y[train.rows]\n\t\tx.test = x[-train.rows]\n\t\ty.test = y[-train.rows]\n\t\tfor (bw in bandwidths) {\n\t\t\tfit <- npreg(txdat=x.train,tydat=y.train,\n\t\t\texdat=x.test,eydat=y.test,bws=bw)\n\t\t\tfold_MSEs[fold,paste(bw)] <- fit$MSE\n\t\t}\n\t}\n\tCV_MSEs = colMeans(fold_MSEs)\n\tbest.bw = bandwidths[which.min(CV_MSEs)]\n\treturn(list(best.bw=best.bw, CV_MSEs=CV_MSEs, fold_MSEs=fold_MSEs))\n}\n\nfbws <- cv_bws_npreg(x,yf,bandwidths=(1:100)/200)\ngbws <- cv_bws_npreg(x,yg,bandwidths=(1:100)/200)\nplot(1:100/200,sqrt(fbws$CV_MSEs),xlab=\"Bandwidth\", ylab=\"Root CV MSE\",type=\"l\",ylim=c(0,0.6))\nlines(1:100/200,sqrt(gbws$CV_MSEs),lty=2)\nabline(h=0.15,col=\"grey\")\n\nx.ord = order(x)\npar(mfcol = c(2, 1))\nplot(x, yf, xlab = \"x\", ylab = expression(f(x)+epsilon))\nfhat <- npreg(bws = fbws$best.bw, txdat = x, tydat = yf)\nlines(x[x.ord], fitted(fhat)[x.ord], lwd = 4)\ncurve(sin(x)*cos(20*x), col = \"grey\", add = TRUE, lwd = 2)\nplot(x, yg, xlab = \"x\", ylab = expression(g(x)+eta))\nghat <- npreg(bws = fbws$best.bw, txdat = x, tydat = yg)\nlines(x[x.ord], fitted(ghat)[x.ord], lwd = 4)\ncurve(log(x+1), col = \"grey\", add = TRUE, lwd = 2)\n\n# Gaussian kernel regression of the points \nnoise.np <- npreg(y~x1+x2,data=noise)\ny.out <- matrix(0,100,100)\ny.out <- predict(noise.np,newdata=x12grid)\nwireframe(y.out~x12grid$x1*x12grid$x2,scales=list(arrows=FALSE),xlab=expression(x^1),ylab=expression(x^2),zlab=\"y\")\n\n# Average Predictive Comparisons\nnew.frame <- data.frame(x=seq(-3,3,length.out=300),y=median(y.noise))\nplot(new.frame$x,predict(noise.np,newdata=new.frame),\ntype=\"l\",xlab=expression(x^1),ylab=\"y\",ylim=c(0,1.0))\nnew.frame$y <- quantile(y.noise,0.25)\nlines(new.frame$x,predict(noise.np,newdata=new.frame),lty=2)\nnew.frame$y <- quantile(y.noise,0.75)\nlines(new.frame$x,predict(noise.np,newdata=new.frame),lty=3)\n\ncurve(exp(7*x)/(1+exp(7*x)),from=-5,to=5,ylab=\"y\")\n", "meta": {"hexsha": "163edb357e9f5529d5bab276870438f22e3a4f1c", "size": 4462, "ext": "r", "lang": "R", "max_stars_repo_path": "NonParametric_Regression/Nonparametric_regression_kernel.r", "max_stars_repo_name": "isix/R", "max_stars_repo_head_hexsha": "806e2a22e5abd93dc7933d3b9e8c3368562e1eaa", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "NonParametric_Regression/Nonparametric_regression_kernel.r", "max_issues_repo_name": "isix/R", "max_issues_repo_head_hexsha": "806e2a22e5abd93dc7933d3b9e8c3368562e1eaa", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "NonParametric_Regression/Nonparametric_regression_kernel.r", "max_forks_repo_name": "isix/R", "max_forks_repo_head_hexsha": "806e2a22e5abd93dc7933d3b9e8c3368562e1eaa", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 39.4867256637, "max_line_length": 115, "alphanum_fraction": 0.6046615867, "num_tokens": 1654, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8774767938900121, "lm_q2_score": 0.8577681031721324, "lm_q1q2_score": 0.7526716050725998}} {"text": "# define x and z\nlibrary(tidyverse)\nlibrary(dslabs)\ndata(heights)\nindex <- heights$sex==\"Male\"\nx <- heights$height[index]\nz <- scale(x)\n\n# proportion of data below 69.5\nmean(x <= 69.5)\n\n# calculate observed and theoretical quantiles\np <- seq(0.05, 0.95, 0.05)\nobserved_quantiles <- quantile(x, p)\ntheoretical_quantiles <- qnorm(p, mean = mean(x), sd = sd(x))\n\n# make QQ-plot\nplot(theoretical_quantiles, observed_quantiles)\nabline(0,1)\n\n# make QQ-plot with scaled values\nobserved_quantiles <- quantile(z, p)\ntheoretical_quantiles <- qnorm(p) \nplot(theoretical_quantiles, observed_quantiles)\nabline(0,1)\n", "meta": {"hexsha": "20b9702284d4f1d95178de5eb2df2b542bab1e85", "size": 602, "ext": "r", "lang": "R", "max_stars_repo_path": "exploratoryPlots.r", "max_stars_repo_name": "adarshkhare1/DataVisualization", "max_stars_repo_head_hexsha": "5bfb183d2073ac20a2e489f4a3f861338c6e88e8", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "exploratoryPlots.r", "max_issues_repo_name": "adarshkhare1/DataVisualization", "max_issues_repo_head_hexsha": "5bfb183d2073ac20a2e489f4a3f861338c6e88e8", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "exploratoryPlots.r", "max_forks_repo_name": "adarshkhare1/DataVisualization", "max_forks_repo_head_hexsha": "5bfb183d2073ac20a2e489f4a3f861338c6e88e8", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 23.1538461538, "max_line_length": 61, "alphanum_fraction": 0.7358803987, "num_tokens": 184, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9425067276593031, "lm_q2_score": 0.7981867777396211, "lm_q1q2_score": 0.7522964079482938}} {"text": "# Example : 4 Chapter : 4.4 Page No: 233\r\n# Projections of the vector onto line,plane if basis are given as orthonormal vectors\r\nQ<-matrix(c(-1,2,2,2,-1,2,2,2,-1),ncol=3)\r\nQ<-(1/3)*Q\r\nq1<-Q[,1]\r\nq2<-Q[,2]\r\nq3<-Q[,3]\r\nb<-c(0,0,1)\r\np1<-sum(q1*b)*q1\r\np2<-sum(q2*b)*q2\r\np3<-sum(q3*b)*q3\r\nprint(\"Projection of b onto q1\")\r\nprint(p1)\r\nprint(\"Projection of b onto q2\")\r\nprint(p2)\r\nprint(\"Projection of b onto q3\")\r\nprint(p3)\r\nprint(\"Projection of b onto plane of q1 and q2\")\r\nprint(p1+p2)\r\nprint(\"Projection of b onto space of q1,q2, and q3\")\r\nprint(p1+p2+p3) # same as vector b\r\n", "meta": {"hexsha": "6574a53df0595c9dd1608f07865597907b3e5e35", "size": 579, "ext": "r", "lang": "R", "max_stars_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH4/EX4.4.4/Ex4.4_4.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH4/EX4.4.4/Ex4.4_4.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH4/EX4.4.4/Ex4.4_4.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 26.3181818182, "max_line_length": 86, "alphanum_fraction": 0.6373056995, "num_tokens": 230, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9425067179697694, "lm_q2_score": 0.7981867777396212, "lm_q1q2_score": 0.7522964002142362}} {"text": "## Author: Sergio García Prado\n## Title: Statistical Inference - Goodness of Fit - Exercise 09\n\n\nrm(list = ls())\n\nobserved <- c(8, 46, 55, 40, 11)\n\n(k <- length(observed))\n# 5\n\n(n <- sum(observed))\n# 160\n\n(p.hat <- sum(observed * 0:(k-1)) / (n * (k - 1)))\n# 0.5\n\n(expected <- n * dbinom(0:(k - 1), size = k - 1, prob = p.hat))\n# 10 40 60 40 10\n\n(Q <- sum((observed - expected ) ^ 2 / expected))\n# 1.81666666666666\n\n(pvalue <- 1 - pchisq(Q, df = (k - 1) - 1))\n# 0.611314815940897\n", "meta": {"hexsha": "0348c1808c77cde37447ea041dd48c4220e05e67", "size": 479, "ext": "r", "lang": "R", "max_stars_repo_path": "statistical-inference/goodness-of-fit/exercise-09.r", "max_stars_repo_name": "garciparedes/r-examples", "max_stars_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-15T19:56:31.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-15T19:56:31.000Z", "max_issues_repo_path": "statistical-inference/goodness-of-fit/exercise-09.r", "max_issues_repo_name": "garciparedes/r-examples", "max_issues_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2018-03-23T09:34:55.000Z", "max_issues_repo_issues_event_max_datetime": "2019-01-09T14:13:32.000Z", "max_forks_repo_path": "statistical-inference/goodness-of-fit/exercise-09.r", "max_forks_repo_name": "garciparedes/r-examples", "max_forks_repo_head_hexsha": "0e0e18439ad859f97eafb27c5e7f77d33da28bc6", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 18.4230769231, "max_line_length": 63, "alphanum_fraction": 0.5678496868, "num_tokens": 198, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9711290963960277, "lm_q2_score": 0.7745833789613196, "lm_q1q2_score": 0.7522204568940882}} {"text": "##### Importing the necessary libraries\r\n\r\nlibrary(readr)\r\nlibrary(dplyr)\r\nlibrary(tidyr)\r\nlibrary(knitr)\r\nlibrary(TSA)\r\nlibrary(tseries)\r\nlibrary(car)\r\nlibrary(dynlm)\r\nlibrary(Hmisc)\r\nlibrary(forecast)\r\nlibrary(xts)\r\nlibrary(ggplot2)\r\nlibrary(AER)\r\nlibrary(x12)\r\nlibrary(dLagM)\r\nlibrary(kableExtra)\r\n\r\n\r\n##### Function Definations \r\n\r\n# Descriptive Analysis function\r\ndescriptive_analysis <- function(ts, object)\r\n{\r\n plot(ts,\r\n ylab = c(paste0(toString(object))),\r\n main = c(paste0(\"Time Series Plot of \",toString(object))),\r\n type=\"o\")\r\n points(y=ts,x=time(ts), pch=as.vector(season(ts)))\r\n \r\n acf(ts,\r\n lag.max = 48,\r\n main = c(paste0(\"ACF plot of \",toString(object))))\r\n \r\n print(adf.test(ts))\r\n}\r\n\r\n\r\n# Function for Decomposition\r\ndecom <- function(ts, ts_series)\r\n{\r\n decom.x12 = x12(ts)\r\n plot(decom.x12 , sa=TRUE , trend=TRUE,\r\n main = c(paste0(\"Monthly \", toString(ts_series)), \" X12 Decomposed Series\"))\r\n \r\n plotSeasFac(decom.x12)\r\n \r\n \r\n decomposition <- stl(ts, t.window=15, s.window=\"periodic\", robust=TRUE)\r\n plot(decomposition,\r\n main = c(paste0(\"Monthly \", toString(ts_series)), \" STL Decomposed Series\"))\r\n}\r\n\r\n\r\n# Function for Summary and Residual Analysis\r\nsummary_residual_analysis <- function(m)\r\n{\r\n summary(m, diagnostics = TRUE)\r\n checkresiduals(m$model)\r\n print(bgtest(m$model))\r\n print(vif(m$model))\r\n print(shapiro.test(m$model$residuals))\r\n}\r\n\r\n\r\n# Task-1 : Analysis and Prediction of Monthly Average Solar Radiation\r\n\r\n## Data Preparation\r\n{r, message=FALSE}\r\ntask_1 <- read_csv(\"data.x.csv\")\r\nsolar_radiation <- read_csv(\"data1.csv\")\r\n\r\nhead(solar_radiation)\r\nclass(solar_radiation)\r\n\r\nAfter importing necessary libraries and dataset, We must convert each variable into time-series object for Time Series Analysis.\r\n\r\n\r\nsolar_radiation_TS <- ts(solar_radiation, start = c(1960,1), frequency = 12)\r\nsolar_TS <- ts(solar_radiation$solar, start = c(1960,1), frequency = 12)\r\nppt_TS <- ts(solar_radiation$ppt, start = c(1960,1), frequency = 12)\r\n\r\nsolar_radiation_TS %>% head()\r\nclass(solar_radiation_TS)\r\n\r\n##### 1. Solar Radiation\r\n\r\nhead(solar_TS)\r\nclass(solar_TS)\r\n\r\n##### 2. Precipitation\r\n\r\nhead(ppt_TS)\r\nclass(ppt_TS)\r\n\r\n\r\n## Descriptive Analysis\r\n\r\n#### 1. Solar Radiation\r\ndescriptive_analysis(solar_TS, \"Monthly Average Solar Radiation\")\r\n\r\n\r\n#### 2. Precipitation\r\ndescriptive_analysis(ppt_TS, \"Monthly Precipitation\")\r\n\r\n\r\n#### 3. Combined Scaled Time Series Plot\r\ncombined <- scale(solar_radiation_TS)\r\n\r\nplot(combined, \r\n plot.type=\"s\", \r\n col = c(\"#05386b\",\"#f01b1d\"), \r\n main = \"Scaled Time Series Plot of Solar Radiation and Precipitation\")\r\n\r\nlegend(\"topleft\", \r\n lty=1, \r\n col = c(\"#05386b\",\"#f01b1d\"), \r\n c(\"Solar Radiation\", \"Precipitation\"))\r\n\r\n\r\n#Correlation\r\n \r\ncor(solar_TS, ppt_TS) %>% round(3)\r\n\r\n\r\n## Decomposition\r\n\r\n#### 1. Solar Radiation\r\ndecom(solar_TS, \"Average Solar Radiatoin\")\r\n\r\n\r\n#### 2. Precipitation\r\ndecom(ppt_TS, \"Precipitation\")\r\n\r\n\r\n### Finite Distributed Lag Model\r\nfor (i in 1:12)\r\n{\r\n model_dlm <- dlm(formula = solar ~ ppt, data = data.frame(solar_radiation), q = i)\r\n cat(\"q = \", i, \r\n \"AIC = \", AIC(model_dlm$model), \r\n \"BIC = \", BIC(model_dlm$model), \r\n \"MASE = \", MASE(model_dlm)$MASE, \"\\n\")\r\n}\r\n\r\n\r\nmodel1 <- dlm(formula = solar ~ ppt, \r\n data = data.frame(solar_radiation), \r\n q = 12)\r\n\r\nsummary_residual_analysis(model1)\r\n\r\n\r\n\r\n### PolyNomial Distributed Lag Model\r\nmodel2 = polyDlm(x = as.vector(solar_radiation$ppt), \r\n y = as.vector(solar_radiation$solar), \r\n q = 12, \r\n k = 2, \r\n show.beta = TRUE)\r\n\r\nsummary_residual_analysis(model2)\r\n\r\n\r\n### Koyck Distributed Lag Model\r\nmodel3 = koyckDlm(x = as.vector(solar_radiation$ppt), \r\n y = as.vector(solar_radiation$solar))\r\nsummary_residual_analysis(model3)\r\n\r\n\r\n### Autoregressive Distributed Lag Model\r\nfor (i in 1:5)\r\n{\r\n for(j in 1:5)\r\n { \r\n model_ardlm <- ardlDlm(formula = solar ~ ppt, \r\n data = data.frame(solar_radiation), \r\n p = i,\r\n q = j)\r\n cat(\"p =\", i, \r\n \"q =\" , j,\r\n \"AIC =\", AIC(model_ardlm$model), \r\n \"BIC =\", BIC(model_ardlm$model),\r\n \"MASE =\", MASE(model_ardlm)$MASE, \"\\n\")\r\n }\r\n}\r\n\r\n\r\n#ardlDLM(3,5)\r\nmodel4_1 = ardlDlm(formula = solar ~ ppt, \r\n data = data.frame(solar_radiation), \r\n p = 3,\r\n q = 5)\r\n \r\nsummary_residual_analysis(model4_1)\r\n\r\n#ardlDLM(4,5)\r\nmodel4_2 = ardlDlm(formula = solar ~ ppt, \r\n data = data.frame(solar_radiation), \r\n p = 4,\r\n q = 5)\r\n \r\nsummary_residual_analysis(model4_2)\r\n\r\n#ardlDLM(5,5)\r\nmodel4_3 = ardlDlm(formula = solar ~ ppt, \r\n data = data.frame(solar_radiation), \r\n p = 5,\r\n q = 5)\r\n \r\nsummary_residual_analysis(model4_3)\r\n\r\n\r\n### Dynamic Models\r\n\r\n#model5_1\r\nmodel5_1 = dynlm(solar_TS ~ L(solar_TS , k = 1 ) + season(solar_TS))\r\nsummary(model5_1)\r\ncheckresiduals(model5_1)\r\n\r\n#model5_2\r\nmodel5_2 = dynlm(solar_TS ~ L(solar_TS , k = 1 ) + trend(solar_TS) + season(solar_TS))\r\nsummary(model5_2)\r\ncheckresiduals(model5_2)\r\n\r\n#model5_3\r\nmodel5_3 = dynlm(solar_TS ~ L(solar_TS , k = 1 ) + L(solar_TS , k = 2 ) + trend(solar_TS) + season(solar_TS))\r\nsummary(model5_3)\r\ncheckresiduals(model5_3)\r\n\r\n#model5_4\r\nmodel5_4 = dynlm(solar_TS ~ L(solar_TS , k = 1 ) + L(solar_TS , k = 2 ) + L(solar_TS , k = 3 ) + season(solar_TS))\r\nsummary(model5_4)\r\ncheckresiduals(model5_4)\r\n\r\n#model5_5\r\nmodel5_5 = dynlm(solar_TS ~ L(solar_TS , k = 1 ) + L(solar_TS , k = 2 ) + L(solar_TS , k = 3 ) + trend(solar_TS) + season(solar_TS))\r\nsummary(model5_5)\r\ncheckresiduals(model5_5)\r\n\r\n\r\n#Model Comparison\r\n#The following table display the each fitted Time-series regression models with `MASE()`, `AIC()` and `BIC()`. \r\n\r\n\r\nattr(model3$model,\"class\") = \"lm\"\r\nmodels <- c(\"Finite DLM\", \"Poly DLM\", \"Koyck\", \"ARDL_3_5\", \"ARDL_4_5\", \"ARDL_5_5\", \"dynlm_1\", \"dynlm_2\", \"dynlm_3\", \"dynlm_4\", \"dynlm_5\")\r\n\r\naic <- AIC(model1$model, model2$model, model3$model, model4_1$model, model4_2$model, model4_3$model, model5_1,model5_2,model5_3, model5_4, model5_5)$AIC\r\n\r\nbic <- BIC(model1$model, model2$model, model3$model, model4_1$model, model4_2$model, model4_3$model, model5_1,model5_2,model5_3, model5_4, model5_5)$BIC\r\n\r\nmase <- MASE(model1$model, model2$model, model3$model, model4_1, model4_2, model4_3, lm(model5_1), lm(model5_2), lm(model5_3), lm(model5_4), lm(model5_5))$MASE\r\n\r\nModel_Comparison <- data.frame(models, mase, aic, bic)\r\ncolnames(Model_Comparison) <- c(\"Model\",\"MASE\",\"AIC\", \"BIC\")\r\n\r\n\r\n\r\n## Exponential smoothing methods\r\nHW_models = c(\"Holt_Winter additive method\",\r\n \"Holt_Winter multiplicative method with exponential trend\",\r\n \"Holt_Winter multiplicative method\",\r\n \"Holt_Winter additive method\",\r\n \"Holt_Winter multiplicative method with exponential trend\",\r\n \"Holt_Winter multiplicative method\")\r\n\r\nexponential = c(TRUE,FALSE)\r\nseasonality = c(\"additive\",\"multiplicative\")\r\ndamped = c(TRUE,FALSE)\r\nexponential_models <- expand.grid(exponential, seasonality, damped)\r\nexponential_models <- exponential_models[-c(1,5),]\r\n\r\nHW_AIC <- array(NA, 6)\r\nHW_BIC <- array(NA, 6)\r\nHW_MASE <- array(NA, 6)\r\nlevels <- array(NA, dim=c(6,3))\r\n\r\nfor (i in 1:6)\r\n{\r\n HW_model <- hw(solar_TS,\r\n exponential = exponential_models[i,1],\r\n seasonal = toString(exponential_models[i,2],\r\n damped = exponential_models[i,3]))\r\n HW_AIC[i] <- HW_model$model$aic\r\n HW_BIC[i] <- HW_model$model$bic\r\n HW_MASE[i] <- accuracy(HW_model)[6]\r\n levels[i,1] <- exponential_models[i,1]\r\n levels[i,2] <- toString(exponential_models[i,2])\r\n levels[i,3] <- exponential_models[i,3]\r\n summary(HW_model)\r\n checkresiduals(HW_model)\r\n print(shapiro.test(HW_model$model$residuals))\r\n}\r\n\r\nresults_HW = data.frame(HW_models, levels, HW_MASE, HW_AIC, HW_BIC)\r\ncolnames(results_HW) = c(\"Model\", \"Exponential\",\"Seasonality\",\"Damped\",\"MASE\",\"AIC\", \"BIC\")\r\n\r\nkbl(results_HW) %>% kable_paper()\r\n\r\n\r\n## State-space Models\r\nets_models = c(\"AAA\", \"MAA\", \"MAM\", \"MMM\")\r\ndamped = c(TRUE,FALSE)\r\nETS_models <- expand.grid(ets_models, damped)\r\n\r\nETS_AIC <- array(NA, 8)\r\nETS_BIC <- array(NA, 8)\r\nETS_MASE <- array(NA, 8)\r\nlevels <- array(NA, dim=c(8,2))\r\n\r\nfor (i in 1:8)\r\n{\r\n ETS <- ets(solar_TS,\r\n model = toString(ETS_models[i, 1]), damped = ETS_models[i,2])\r\n ETS_AIC[i] <- ETS$aic\r\n ETS_BIC[i] <- ETS$bic\r\n ETS_MASE[i] <- accuracy(ETS)[6]\r\n levels[i,1] <- toString(ETS_models[i,1])\r\n levels[i,2] <- ETS_models[i,2]\r\n summary(ETS)\r\n checkresiduals(ETS)\r\n print(shapiro.test(ETS$residuals))\r\n}\r\n\r\nresults_ETS = data.frame(levels, ETS_MASE, ETS_AIC, ETS_BIC)\r\ncolnames(results_ETS) = c(\"Model\",\"Damped\",\"MASE\",\"AIC\", \"BIC\")\r\n\r\nkbl(results_ETS) %>% kable_paper()\r\n\r\n\r\n### Auto-Fit State-Space Model\r\nETS_auto_model = ets(solar_TS,model=\"ZZZ\")\r\nETS_auto_model$method\r\n\r\n\r\n## Model Comparison\r\nFormating results_ETS table \r\n\r\n\r\nresults_ETS$Damped <- factor(results_ETS$Damped,\r\n levels = c(TRUE, FALSE),\r\n labels = c(\"Dumped\",\" \"))\r\n\r\nresults_ETS <- unite(results_ETS,\r\n \"Model\", c(\"Model\",\"Damped\"), sep = \"_\")\r\n\r\nkbl(results_ETS) %>% kable_paper()\r\n\r\nFormating results_HW table \r\n\r\n\r\nresults_HW$Damped <- factor(results_HW$Damped,\r\n levels = c(TRUE, FALSE),\r\n labels = c(\"Dumped\",\" \"))\r\n\r\nresults_HW <- unite(results_HW,\r\n \"Model\", c(\"Model\",\"Damped\"), sep = \"_\")\r\n\r\nresults_HW <- results_HW[,-c(2,3)]\r\nkbl(results_HW) %>% kable_paper()\r\n\r\n#Merge Model Comparison Table\r\nModel_Comparison <- rbind(Model_Comparison, results_ETS, results_HW)\r\n\r\nsorted_MASE <- Model_Comparison %>% arrange(MASE)\r\nkbl(sorted_MASE) %>%\r\n kable_paper()\r\n\r\n\r\n\r\n## Forecasting\r\nprediction_1 <- hw(solar_TS,\r\n seasonal = \"multiplicative\",\r\n dumped = TRUE,\r\n h = 2*frequency(solar_TS))\r\n\r\nprediction_2 <- hw(solar_TS,\r\n seasonal = \"multiplicative\",\r\n dumped = TRUE,\r\n exponential = TRUE,\r\n h = 2*frequency(solar_TS))\r\n\r\n\r\nprediction_3 <- ets(solar_TS,\r\n model=\"AAA\",\r\n damped = T)\r\nprediction_3 <- forecast(prediction_3)\r\n\r\nplot(prediction_3,\r\n main = \"Next Two years Forecast of Solar Radiation)\",\r\n ylab = \"Solar Radiation\",\r\n fcol = \"#e8d31d\")\r\n\r\nlines(fitted(prediction_3), col = \"#e8d31d\")\r\n\r\nlines(fitted(prediction_2), col = \"#039fbe\")\r\nlines(prediction_2$mean, col = \"#039fbe\", lwd = 2)\r\n\r\nlines(fitted(prediction_1), col = \"#b20238\")\r\nlines(prediction_1$mean, col = \"#b20238\", lwd = 2)\r\n\r\n\r\nlegend(\"bottomleft\",\r\n lty = 1,\r\n col = c(\"black\", \"#b20238\", \"#039fbe\", \"#e8d31d\"),\r\n c(\"Data\", \"Holt-Winters' Multiplicative_Damped\", \"Holt-Winters' Multiplicative Exponential_Damped\", \"ETS(A,Ad,A)\"))\r\n\r\n\r\n# final prediction\r\nplot(prediction_1, fcol = \"#b20238\", \r\n main = \"Forecasting of Solar Radiation in 2015 and 2106\",\r\n ylab = \"Radiation\")\r\nlines(fitted(prediction_1), col = \"#b20238\")\r\n\r\nlegend(\"topleft\", \r\n lty = 1, \r\n col = c(\"black\", \"#b20238\"), \r\n c(\"Data\", \"Prediction\"))\r\n\r\n\r\n\r\n\r\n# confidence interval\r\nkbl(prediction_1) %>% kable_paper()\r\n\r\n\r\n\r\n# Task - 2 : Demonstrate whether correlation between Residential PPI and Population Change is Spurious or not.\r\n\r\n# data reading\r\ntask_2 <- read_csv(\"data2.csv\")\r\n\r\nhead(task_2)\r\nclass(task_2)\r\n\r\n\r\n## Data Preparation\r\n\r\n# time series object\r\ntask_2_TS <- ts(task_2[,2:3], start = c(2003,3), frequency = 4)\r\nprice_TS <- ts(task_2$price, start = c(2003,3), frequency = 4)\r\nchange_TS <- ts(task_2$change, start = c(2003,3), frequency = 4)\r\n\r\n\r\ntask_2_TS %>% head()\r\nclass(task_2_TS)\r\n\r\n##### 1. Residential Property Price Index\r\n\r\nhead(price_TS)\r\nclass(price_TS)\r\n\r\n##### 2. Population Change\r\n\r\nhead(change_TS)\r\nclass(change_TS)\r\n\r\n\r\n## Descriptive Analysis\r\nplot(task_2_TS,\r\n main = \"Time Series plot Residential PPI and Population Change\",\r\n yax.flip = TRUE, \r\n type = 'o')\r\n\r\n\r\n## Cross-Covariance Function\r\nccf(as.vector(price_TS), \r\n as.vector(change_TS), \r\n ylab = \"Cross-Covariance Function\", \r\n main = \"CCF plot of Residential PPI and Population Change\")\r\n\r\n\r\n## Cheking the Stationarity\r\n\r\n#### 1. Residential Property Price Index(PPI)\r\ndescriptive_analysis(price_TS, \"Residential Property Price Index\")\r\n\r\n\r\n#### 2. Population Change\r\ndescriptive_analysis(change_TS, \"Population Change\")\r\n\r\n\r\n## Transformation to Stationary Series\r\n\r\n#### 1. Residential Property Price Index(Differenced)\r\n\r\nprice_TS_diff <- diff(diff(price_TS),4)\r\ndescriptive_analysis(price_TS_diff, \"Residential PPI (Differenced)\")\r\n\r\n\r\n#### 2. Population Change(Differenced)\r\n\r\nchange_TS_diff <- diff(diff(change_TS),4)\r\ndescriptive_analysis(change_TS_diff, \"Population Change(Differenced)\")\r\n\r\n\r\n## Prewhitening\r\nprewhiten(as.vector(price_TS_diff), \r\n as.vector(change_TS_diff), \r\n ylab='Cross-Covariance Function', \r\n main = \"CCF plot of Residential PPI and Population Change after prewhitening\")", "meta": {"hexsha": "e8565fcb3e4ce6c5127864e746b74c26cb70e72d", "size": 13326, "ext": "r", "lang": "R", "max_stars_repo_path": "forecasting_assignment2.r", "max_stars_repo_name": "modihill/solar_radiation_and_spurious_relationship_forecasting2", "max_stars_repo_head_hexsha": "491b80915035cc8669d3f2cbc0e846ee623ba253", "max_stars_repo_licenses": ["Unlicense"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "forecasting_assignment2.r", "max_issues_repo_name": "modihill/solar_radiation_and_spurious_relationship_forecasting2", "max_issues_repo_head_hexsha": "491b80915035cc8669d3f2cbc0e846ee623ba253", "max_issues_repo_licenses": ["Unlicense"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "forecasting_assignment2.r", "max_forks_repo_name": "modihill/solar_radiation_and_spurious_relationship_forecasting2", "max_forks_repo_head_hexsha": "491b80915035cc8669d3f2cbc0e846ee623ba253", "max_forks_repo_licenses": ["Unlicense"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.4930417495, "max_line_length": 160, "alphanum_fraction": 0.629070989, "num_tokens": 3812, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9252299653388752, "lm_q2_score": 0.8128673201042492, "lm_q1q2_score": 0.752089202405159}} {"text": "\n# Simulacion estocastica para interaciones competitivas \n#\nSTO_interact <- function(x,pars,times)\n{\n # Setup an array to store results: time, N\n #\n ltimes<-length(times)\n output <- array(dim=c(ltimes,3),dimnames=list(NULL,names(x)))\n t <- x[1]\n stopifnot(t<=times[1])\n \n # loop until either k > maxstep or\n #\n output[1,] <-x\n k <- 2\n while (k <= ltimes) {\n while (t < times[k]) {\n x <- interact_onestep(x,pars) \n t <- x[1]\n }\n while (t >= times[k] && k <= ltimes) {\n output[k,] <- x\n k <- k+1\n }\n }\n as.data.frame(output)\n}\n\n# interaciones competitivas - Simulacion de Eventos \n#\ninteract_onestep<- function(x,pars){\n p<-as.list(pars)\n # 2nd element is the population \n #\n N1<-x[2]\n N2<-x[3]\n B1<-N1*p$r1+p$im\n B2<-N2*p$r2+p$im\n D1<- N1*(N1*p$d11+N2*p$d12)\n D2<- N2*(N1*p$d21+N2*p$d22)\n R <- B1+B2+D1+D2\n if(R>0) {\n Y1 <- runif(1)\n \n if(Y1 <=B1/R){\n if(N1>0) N1<-N1+1\n } else if(Y1 <= (B1+D1)/R) {\n N1<-N1-1\n } else if(Y1 <= (B1+D1+B2)/R) {\n if(N2>0) N2<-N2+1\n } else {\n N2<-N2-1\n }\n # Exponential random number\n tau<-rexp(n=1,rate=R)\n \n } else tau<-1\n \n c(x[1]+tau,N1,N2)\n}\n\n\n#\nDET_interact<-function(t,State,Pars){\n with(as.list(c(State, Pars)), {\n \n dN1 <- N1*(r1-d11*N1-d12*N2)+im \n dN2 <- N2*(r2-d21*N1-d22*N2)+im \n return(list(c(dN1,dN2)))\n })\n}\n", "meta": {"hexsha": "dada13714bd8100fceabcc503d3a4bd64102f8c3", "size": 1380, "ext": "r", "lang": "R", "max_stars_repo_path": "Simul_fun.r", "max_stars_repo_name": "lsaravia/StochasticCompetition", "max_stars_repo_head_hexsha": "17ab84b097176fd33fa7b51bfee4705f1bc003d0", "max_stars_repo_licenses": ["Unlicense", "MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2016-12-22T06:03:59.000Z", "max_stars_repo_stars_event_max_datetime": "2016-12-22T06:03:59.000Z", "max_issues_repo_path": "Simul_fun.r", "max_issues_repo_name": "lsaravia/StochasticCompetition", "max_issues_repo_head_hexsha": "17ab84b097176fd33fa7b51bfee4705f1bc003d0", "max_issues_repo_licenses": ["Unlicense", "MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Simul_fun.r", "max_forks_repo_name": "lsaravia/StochasticCompetition", "max_forks_repo_head_hexsha": "17ab84b097176fd33fa7b51bfee4705f1bc003d0", "max_forks_repo_licenses": ["Unlicense", "MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 18.904109589, "max_line_length": 63, "alphanum_fraction": 0.5355072464, "num_tokens": 568, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9334308110294983, "lm_q2_score": 0.805632181981183, "lm_q1q2_score": 0.75200190101816}} {"text": "# https://www.hackerrank.com/challenges/s10-geometric-distribution-1/problem\n# The probability that a machine produces a defective product is 1/3 . What is the probability that the 1st defect is found during the 5th inspection?\nlibrary(magrittr)\nn <- 100000\npr <- 1/3\ntestval <- 5\n\ntrials <- rnbinom(n = n, prob = pr, size = 1) + 1 #+1 b/c this actually gives the number of trials b4 1 success (size = 1), so +1 gives the trial number of the first sucess\ngeotrials <- rgeom(n = n, prob = pr) + 1 #geometric distr - special case of neg binomial dist with size = 1 (ie continues until the first success)\n#size is number of sucesses b4 stopping (success has probability = 1/3)\nfifth <- ifelse(trials == 5, 1, 0)#true (1) iff stopped in the fifth trial\nfifthgeo <- (geotrials == 5) %>% ifelse(1,0)\nans <- sum(fifth)/n\nansgeo <- sum(fifthgeo)/n\n#round(ans, digits = 3)#sprintf rounds? \nround(ansgeo, digits = 3) %>% cat\ncat(sprintf(\"%.3f\\n\", ans))\n#remeber \"sucess\" means found a failing part!\n\n\n#analytical solution:\n(1-pr)^4 * pr", "meta": {"hexsha": "11a33e11d9cf0ed8112b8b16166b4df062fa4d0a", "size": 1026, "ext": "r", "lang": "R", "max_stars_repo_path": "HackerRankGeometricDistribution1.r", "max_stars_repo_name": "DU-ds/MiscRScripts", "max_stars_repo_head_hexsha": "012fb6ecb60414f8952e3884271dba7add9f4d33", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "HackerRankGeometricDistribution1.r", "max_issues_repo_name": "DU-ds/MiscRScripts", "max_issues_repo_head_hexsha": "012fb6ecb60414f8952e3884271dba7add9f4d33", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "HackerRankGeometricDistribution1.r", "max_forks_repo_name": "DU-ds/MiscRScripts", "max_forks_repo_head_hexsha": "012fb6ecb60414f8952e3884271dba7add9f4d33", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 46.6363636364, "max_line_length": 172, "alphanum_fraction": 0.7056530214, "num_tokens": 330, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9273633016692236, "lm_q2_score": 0.8104789178257654, "lm_q1q2_score": 0.7516084051682013}} {"text": "########################\n# R Script for Class 5 #\n########################\n\nx <- seq(-4, 4, length=100)\nhx <- dnorm(x)\nhx2 = dt(x, df=99)\nplot(x, hx2, type='l', xlab=\"t\", ylab=\"density\", col=\"black\", lwd=2, yaxs=\"i\")\nabline(v=-2)\n\ncord.x <- c(-4,seq(-4,-2,0.01),-2) \ncord.y <- c(0,dt(seq(-4,-2,0.01), df=99),0)\npolygon(cord.x,cord.y,col='#fdae61')\n\ncord.x <- c(2,seq(2,4,0.01),4) \ncord.y <- c(0,dt(seq(2,4,0.01), df=99),0)\npolygon(cord.x,cord.y,col='#fdae61')\n\n\nhelp(pt)\n\n\n\nsetwd(\"~/Google Drive File Stream/My Drive/upf_courses/GSRM/2018/slides/global_studies_research_methods_2018\")\nD = read.csv('shoesize.csv')\nD\n\n# exploring height\nD$Height\nmean(D$Height)\nsd(D$Height)\nquantile(D$Height)\nhist(D$Height)\nplot(density(D$Height))\n\nsd(D$Height)/sqrt(408)\n\n# Assumming this data is a random sample of the full school populatio, what is our best estimate of the mean height of all students at this university? Provide a point estimate and 95% confidence interval.\n\n\n2*(pt(-2, df=99))\n1-pnorm(2)\n\n\n# Assumming this data is a random sample of the full school populatio, what is our best estimate of the mean shoe sizeght of all students at this university? Provide a point estimate and 95% confidence interval.\n\nhist(D$Size)\nmean(D$Size)\nsd(D$Size)\n\nmean(D$Size)+(2*(sd(D$Size)/sqrt(408)))\nmean(D$Size)-(2*(sd(D$Size)/sqrt(408)))\n\n\n# What is the relationship between height and shoe size?\n\nplot(D$Height, D$Size, pch=20, xlab=\"height (inches)\", ylab=\"shoe size\")\nM = lm(D$Size~D$Height)\ncurve(coef(M)[1] + coef(M)[2]*x, add=TRUE, lwd=2, col=\"#d7191c\")\n\n\ncor(D$Height, D$Size)\n\n\nM = lm(D$Height~D$Size)\nsummary(M)\n\nM = lm(D$Height~D$Size+D$Gender)\nsummary(M)\n\nM = lm(D$Height~D$Size+D$Gender + D$Size*D$Gender )\nsummary(M)\n\n# family planning data\nlibrary(foreign)\nlibrary(calibrate)\n\nD = read.dta('effort.dta')\nhead(D)\n\nplot(change~effort, data=D, ylab=\"CBR change\", xlab=\"program effort\", pch=20, col=\"#000099dd\", cex=2)\n\nM = lm(change~effort, data=D)\nsummary(M)\n\nM = lm(change~effort+setting, data=D)\nsummary(M)", "meta": {"hexsha": "11a0431a51829d128fffff373c472edfc4a9a03d", "size": 2008, "ext": "r", "lang": "R", "max_stars_repo_path": "r_demo_class6_old.r", "max_stars_repo_name": "JohnPalmer/GSRM2018-Slides", "max_stars_repo_head_hexsha": "a8d0d3e36867e42592cb5efd08ffe63695c42366", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "r_demo_class6_old.r", "max_issues_repo_name": "JohnPalmer/GSRM2018-Slides", "max_issues_repo_head_hexsha": "a8d0d3e36867e42592cb5efd08ffe63695c42366", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "r_demo_class6_old.r", "max_forks_repo_name": "JohnPalmer/GSRM2018-Slides", "max_forks_repo_head_hexsha": "a8d0d3e36867e42592cb5efd08ffe63695c42366", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 23.0804597701, "max_line_length": 211, "alphanum_fraction": 0.6658366534, "num_tokens": 685, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9273632876167044, "lm_q2_score": 0.8104789109591832, "lm_q1q2_score": 0.7516083874111144}} {"text": "# indep.t.test.unequal.var.r\r\n x <- c(21.6,20.8,17.6,20.1,20.1,21.9,20.6,19.4,21.5,26.1) \r\n y <- c(20.6,20.4,20.2,20.2,18.0,19.8,20.9,19.7,20.3,19.7,22.7)\r\n mx <- mean(x); my <- mean(y)\r\n sdx <- sd(x); sdy <- sd(y)\r\n\r\n t0 <- (mx-my)/sqrt(sdx^2/10+sdy^2/11)\r\n t0\r\n sw.df <- (sdx^2/10+sdy^2/11)^2/((sdx^2/10)^2/9 + (sdy^2/11)^2/10)\r\n 1-pt(t0, sw.df)\r\n lbd <- (mx-my) - qt(0.995, sw.df)*sqrt(sdx^2/10+sdy^2/11)\r\n lbd\r\n ubd <- (mx-my) + qt(0.995, sw.df)*sqrt(sdx^2/10+sdy^2/11)\r\n ubd\r\n", "meta": {"hexsha": "552f9f60efd5a102008fa14da4e872f567664dc6", "size": 493, "ext": "r", "lang": "R", "max_stars_repo_path": "R.2019.2/advanced.R/Rcode/Chap3/indep.t.test.unequal.var.r", "max_stars_repo_name": "tolkien/misc", "max_stars_repo_head_hexsha": "84651346a3a0053b6a2af31db26c227a34da33c8", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R.2019.2/advanced.R/Rcode/Chap3/indep.t.test.unequal.var.r", "max_issues_repo_name": "tolkien/misc", "max_issues_repo_head_hexsha": "84651346a3a0053b6a2af31db26c227a34da33c8", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R.2019.2/advanced.R/Rcode/Chap3/indep.t.test.unequal.var.r", "max_forks_repo_name": "tolkien/misc", "max_forks_repo_head_hexsha": "84651346a3a0053b6a2af31db26c227a34da33c8", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 32.8666666667, "max_line_length": 68, "alphanum_fraction": 0.5131845842, "num_tokens": 282, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9504109798251321, "lm_q2_score": 0.7905303285397349, "lm_q1q2_score": 0.751328704128933}} {"text": "library(nloptr)\n\nget_expected = function(beta, gamma, tau, N0, A0) {\n \"\n Calculates expected new case counts for each step in the time series.\n \n Parameters\n ----------\n N0 : numeric\n Initial number of contagious patients.\n A0 : numeric\n Initial number of asymptomatic patients.\n beta : numeric vector\n Expected number of cases stemming from a single person in a single day.\n Lagged one step (beta[1] = beta(0) in our notation).\n gamma : numeric\n Probability that an asymptomatic patient will turn contagious in the next\n time step.\n tau : numeric\n (1 / mean) number of days an individual will continue to be infectious.\n \n Returns\n -------\n expected : list\n Daily expected number of infectious (N), new asymptomatic (A), and new\n infectious (I) patients.\n \"\n steps = length(beta)\n expected_I = rep(0, steps)\n expected_N = rep(0, steps)\n expected_A = rep(0, steps)\n N_previous = N0\n A_previous = A0\n for(t in 1:steps) {\n expected_I[t] = gamma * (A_previous + (beta[t] * N_previous))\n expected_N[t] = N_previous * pexp(1, rate=tau, lower.tail=FALSE) + expected_I[t]\n expected_A[t] = (1 - gamma) * (A_previous + (beta[t] * N_previous))\n N_previous = expected_N[t]\n A_previous = expected_A[t]\n }\n return(list(\"N\"=c(N0, expected_N), \"A\"=c(A0, expected_A), \"I\"=expected_I))\n}\n\nfit = function(observed_I, beta0, beta_min, beta_max, gamma0, gamma_min,\n gamma_max, tau0, tau_min, tau_max, N00, N0_min, N0_max, A00,\n A0_min, A0_max, lambda, ignore_beta_diff) {\n \"\n Fits the model to observed daily new case counts.\n \n Parameters\n ----------\n observed_I : numeric vector\n Daily observed number of new cases.\n beta0 : numeric vector\n Initial value for beta; the expected number of cases stemming from a single\n person in a single day.\n beta_min : numeric\n Beta lower bound.\n beta_max : numeric\n Beta upper bound.\n ignore_beta_diff : numeric vector\n List of beta indices for which differences should be ignored while\n calculating the loss function. This amounts to moments in time in which we\n allow the beta series to be discontinuous.\n \n Returns\n -------\n beta : numeric vector\n Expected number of cases stemming from a single person in a single day.\n \"\n # concatenate initial parameters into a single vector for optimization\n x0 = c(beta0, gamma0, tau0, N00, A00)\n steps = length(observed_I)\n lb = c(rep(beta_min, steps), gamma_min, tau_min, N0_min, A0_min)\n ub = c(rep(beta_max, steps), gamma_max, tau_max, N0_max, A0_max)\n # set optimization parameters\n opts = list(\"algorithm\" = \"NLOPT_LN_BOBYQA\", \"xtol_rel\" = 1.0e-7, \"maxeval\" = 10000000)\n # define loss function\n loss = function(x) {\n # unpack values\n beta = x[1:steps]\n gamma = x[steps + 1]\n tau = x[steps + 2]\n N0 = x[steps + 3]\n A0 = x[steps + 4]\n # calculate loss\n expected = get_expected(beta, gamma, tau, N0, A0)\n regularization = (diff(beta) / beta[1:(steps - 1)]) ^ 2\n regularization = regularization[!1:length(regularization) %in% ignore_beta_diff]\n observed_I = round(observed_I, 0)\n factSum = function(x) {\n return(sum(log(1:round(x, 0))))\n }\n loglikelihood = observed_I*log(expected$I)-expected$I-sapply(as.matrix(observed_I), FUN=factSum)\n loglikelihood[observed_I==0] = -expected$I[observed_I==0]\n return(-mean(loglikelihood) + lambda*mean(regularization))\n }\n result = nloptr(x0=x0, eval_f=loss, lb=lb, ub=ub, opts=opts)\n model = list(\n \"beta\" = result$solution[1:steps],\n \"gamma\" = result$solution[steps + 1],\n \"tau\" = result$solution[steps + 2],\n \"N0\" = result$solution[steps + 3],\n \"A0\" = result$solution[steps + 4],\n \"loss\" = result$objective\n )\n regularization = (diff(model$beta) / model$beta[1:(steps - 1)]) ^ 2\n regularization = regularization[!1:(steps - 1) %in% ignore_beta_diff]\n model$likelihood = (model$loss - lambda * mean(regularization)) * steps\n return(model)\n}", "meta": {"hexsha": "8f97bff82b49d28848eeac57d19bedbb6da194b1", "size": 3967, "ext": "r", "lang": "R", "max_stars_repo_path": "likelihood_incubation/model_fitting.r", "max_stars_repo_name": "secg95/INS_COVID", "max_stars_repo_head_hexsha": "d3e1e9b2d83de9bbfb246c9be93624ffb4df88a1", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "likelihood_incubation/model_fitting.r", "max_issues_repo_name": "secg95/INS_COVID", "max_issues_repo_head_hexsha": "d3e1e9b2d83de9bbfb246c9be93624ffb4df88a1", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "likelihood_incubation/model_fitting.r", "max_forks_repo_name": "secg95/INS_COVID", "max_forks_repo_head_hexsha": "d3e1e9b2d83de9bbfb246c9be93624ffb4df88a1", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 35.7387387387, "max_line_length": 100, "alphanum_fraction": 0.6692714898, "num_tokens": 1155, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.913676530465412, "lm_q2_score": 0.822189134878876, "lm_q1q2_score": 0.75121491614249}} {"text": "#\n# Exemplo 3\n#\n\n# Serie de Taylor mais generica\n# quantidade de termos\nn <- 100\n# em torno do ponto\na <- 2\n# função\nf <- exp(a)\n# valor de x\nx <- -1\n# valor inicial da soma\ntaylor <- 0\n# percorre k de 0 até n\nfor (k in 0:n) {\n # define o termo\n termo <- (f * ((x - a)^k)) / factorial(k)\n # soma-se o termo ao valor anterior\n taylor <- taylor + termo\n}\n\ntaylor\n# valor original\nexp(x)", "meta": {"hexsha": "2c0d283d7c03b20632372534f39f9ddfb7aa494f", "size": 396, "ext": "r", "lang": "R", "max_stars_repo_path": "src/r/aula4/exemplo3.r", "max_stars_repo_name": "EduardoJM/anotacoes-matematica-aplicada", "max_stars_repo_head_hexsha": "75eaa8548ec01cc596e40dc4699fbef06001f20d", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "src/r/aula4/exemplo3.r", "max_issues_repo_name": "EduardoJM/anotacoes-matematica-aplicada", "max_issues_repo_head_hexsha": "75eaa8548ec01cc596e40dc4699fbef06001f20d", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "src/r/aula4/exemplo3.r", "max_forks_repo_name": "EduardoJM/anotacoes-matematica-aplicada", "max_forks_repo_head_hexsha": "75eaa8548ec01cc596e40dc4699fbef06001f20d", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 15.2307692308, "max_line_length": 45, "alphanum_fraction": 0.6035353535, "num_tokens": 146, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9324533088603709, "lm_q2_score": 0.8056321796478255, "lm_q1q2_score": 0.7512143916370077}} {"text": "#' Generate a noisy power law power spectrum.\n#'\n#' \\deqn{PSD(f) = f^{-\\beta}}\n#'\n#' @param N Number of frequencies (must be even).\n#' @param freq.max Value of largest frequency.\n#' @param beta Value of power.\n#' @param sd Standard deviation.\n#'\n#' @return Frequencies and power spectral density.\n#'\n#' @examples\n#' power.law(100) # 100 samples with default options\n#' power.law(100, freq.max = 50) # provide maximum frequency\n#' power.law(100, sd = 2.0) # provide standard deviation\n#' power.law(100, beta = 0.0) # white noise\n#' power.law(100, beta = 1.0) # 1/f noise\n#' power.law(100, beta = 2.0) # brown noise\n#'\n#' @export\npower.law <- function(N, freq.max = 1/(2*pi),\n beta = 0.0, sd = 1.0) {\n f <- freq(N, freq.max = freq.max)\n freq.pos <- f$freq.pos\n freq <- f$freq\n\n # compute the mean values of the power spectrum's absolute value\n mean.power <- freq.pos^(0.5*beta)\n\n # generate a noisy power spectrum in complex form\n power <- noisy.power.spectrum(mean.power, sd = sd)\n # include negative frequencies in the final spectrum, with opposite phase\n power <- mirror.complex(power)\n\n data.frame(freq, power)\n}\n", "meta": {"hexsha": "9958335fa181f49ecb8ce692391a63a1e031be56", "size": 1199, "ext": "r", "lang": "R", "max_stars_repo_path": "R/power.law.r", "max_stars_repo_name": "dwysocki/random-noise-generation", "max_stars_repo_head_hexsha": "97bb8392faa4c25399b44b52bc471a95cb44ec7d", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-02-24T05:46:19.000Z", "max_stars_repo_stars_event_max_datetime": "2018-02-24T05:46:19.000Z", "max_issues_repo_path": "R/power.law.r", "max_issues_repo_name": "dwysocki/random-noise-generation", "max_issues_repo_head_hexsha": "97bb8392faa4c25399b44b52bc471a95cb44ec7d", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/power.law.r", "max_forks_repo_name": "dwysocki/random-noise-generation", "max_forks_repo_head_hexsha": "97bb8392faa4c25399b44b52bc471a95cb44ec7d", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 32.4054054054, "max_line_length": 77, "alphanum_fraction": 0.6255212677, "num_tokens": 345, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9324533032291501, "lm_q2_score": 0.8056321843145404, "lm_q1q2_score": 0.7512143914518087}} {"text": "#' Fisher's Linear Discriminant\n#' \n#' Compute the 2-class Fisher's linear discriminant either in \n#' serial or parallel.\n#' \n#' @param x\n#' The data in the form of a matrix or ddmatrix.\n#' @param g\n#' The group variable in the form of a matrix/vector or a ddmatrix.\n#' The values should be 0 and 1 exclusively.\n#' \n#' @return\n#' A list of class 'fld' containing the prior probabilities, group means, \n#' w vector, and c scalar. In the distributed case, the priors and c scalar\n#' are both global, while the other values are distributed.\n#' \n#' @references\n#' Duda, R. O., Hart, P. E., & Stork, D. G. (2012). Pattern classification,\n#' chapter 5. John Wiley & Sons.\n#' \n#' @author\n#' Drew Schmidt\n#' \n#' @examples\n#' \\dontrun{\n#' x <- matrix(rnorm(30), 10)\n#' g <- sample(0:1, size=10, replace=TRUE)\n#' \n#' fld(x, g)\n#' }\n#' \n#' @name fld\n#' @rdname fld\n#' @export\nfld <- function(x, g)\n{\n if (!is.ddmatrix(x))\n x <- as.matrix(x)\n \n # if (!all.sametype(x, g))\n # comm.stop(\"arguments 'x' and 'g' must either both be of type 'matrix', or both of type 'ddmatrix'\")\n \n n <- NROW(x)\n if (n != NROW(g))\n comm.stop(\"argument 'g' must be the same length as 'x'\")\n \n if (!comm.all(check_groupvar(g)))\n comm.stop(\"argument 'g' must be a vector of only 0's and 1's\")\n \n \n ### Get group indices/priors\n if (is.ddmatrix(g))\n g <- as.vector(g) ### FIXME\n \n ind0 <- which(submatrix(g) == 0)\n ind1 <- setdiff(1:n, ind0)\n \n prior0 <- length(ind0)/n\n prior1 <- length(ind1)/n\n \n ### Get group covariances and means\n x0 <- x[ind0, , drop=FALSE]\n x1 <- x[ind1, , drop=FALSE]\n \n cov0 <- cov(x0)\n cov1 <- cov(x1)\n \n mu0 <- colMeans(x0)\n mu1 <- colMeans(x1)\n \n ### fld\n mu_sum <- mu0 + mu1\n if (is.ddmatrix(mu_sum))\n mu_sum <- t(mu_sum)\n \n w <- solve(cov0 + cov1, mu_sum)\n c <- as.vector(0.5 * crossprod(w, mu_sum))\n \n ### wrangle return\n means <- list(mu0=mu0, mu1=mu1)\n prior <- c(\"0\"=prior0, \"1\"=prior1)\n \n ret <- list(prior=prior, means=means, w=w, c=c)\n class(ret) <- \"fld\"\n \n return(ret)\n}\n\n\n\n#' @method print fld\n#' @export\nprint.fld <- function(x, ...)\n{\n comm.cat(\"Prior probabilities of groups:\\n\", quiet=TRUE)\n comm.print(x$prior, quiet=TRUE)\n \n comm.cat(\"\\nc =\", x$c, \"\\n\", quiet=TRUE)\n}\n", "meta": {"hexsha": "0e10b27b5cc359d9b2af102642951c827d8c27a7", "size": 2245, "ext": "r", "lang": "R", "max_stars_repo_path": "R/fld.r", "max_stars_repo_name": "wrathematics/pbdML", "max_stars_repo_head_hexsha": "cac079480be8622b8ac781def5f81fe9932614bb", "max_stars_repo_licenses": ["BSD-2-Clause"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/fld.r", "max_issues_repo_name": "wrathematics/pbdML", "max_issues_repo_head_hexsha": "cac079480be8622b8ac781def5f81fe9932614bb", "max_issues_repo_licenses": ["BSD-2-Clause"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2015-09-22T22:36:57.000Z", "max_issues_repo_issues_event_max_datetime": "2015-09-22T22:45:14.000Z", "max_forks_repo_path": "R/fld.r", "max_forks_repo_name": "wrathematics/pbdML", "max_forks_repo_head_hexsha": "cac079480be8622b8ac781def5f81fe9932614bb", "max_forks_repo_licenses": ["BSD-2-Clause"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.45, "max_line_length": 105, "alphanum_fraction": 0.6004454343, "num_tokens": 743, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8991213799730774, "lm_q2_score": 0.8354835309589073, "lm_q1q2_score": 0.7512011053005521}} {"text": "## https://israeldi.github.io/bookdown/_book/monte-carlo-simulation-of-stock-portfolio-in-r-matlab-and-python.html\n\nsource('/home/dlhjel/GitHub_repos/R-setup/setup.r')\n\ndata <- '\n Date AAPL_Adj_Close GOOG_Adj_Close FB_Adj_Close\n11/15/17 166.5791 1020.91 177.95\n11/16/17 168.5693 1032.50 179.59\n11/17/17 167.6333 1019.09 179.00\n11/20/17 167.4658 1018.38 178.74\n11/21/17 170.5791 1034.49 181.86\n11/22/17 172.3721 1035.96 180.87\n11/24/17 172.3820 1040.61 182.78\n11/27/17 171.5150 1054.21 183.03\n11/28/17 170.5101 1047.41 182.42\n11/29/17 166.9732 1021.66 175.13\n'\nstock_Data = readall(data)\nstock_Price = as.matrix( stock_Data[ , 2:4] )\n\nmc_rep = 10 # Number of Monte Carlo Simulations\ntraining_days = 5\n\n# This function returns the first differences of a t x q matrix of data\nreturns = function(Y){\n len = nrow(Y)\n yDif = Y[2:len, ] / Y[1:len-1, ] - 1\n}\n\n# Get the Stock Returns\nstock_Returns = returns(stock_Price)\n\n# Suppose we invest our money evenly among all three assets \n# We use today's Price 11/14/2018 to find the number of shares each stock \n# that we buy\nportfolio_Weights = t(as.matrix(rep(1/ncol(stock_Returns), ncol(stock_Returns))))\nprint(portfolio_Weights)\n\n# Get the Variance Covariance Matrix of Stock Returns\npairs(stock_Returns)\ncoVarMat = cov(stock_Returns)\n\n# calculate meaan return for each stock\nmiu = colMeans(stock_Returns)\n# Extend the vector to a matrix\nMiu = matrix(rep(miu, training_days), nrow = 3)\n\n# Initializing simulated 30 day portfolio returns\nportfolio_Returns_30_m = matrix(0, training_days, mc_rep)\n\nset.seed(200)\nfor (i in 1:mc_rep) {\n Z = matrix ( rnorm( dim(stock_Returns)[2] * training_days ), ncol = training_days )\n # Lower Triangular Matrix from our Choleski Factorization\n L = t( chol(coVarMat) )\n # Calculate stock returns for each day\n daily_Returns = Miu + L %*% Z \n # Calculate portfolio returns for 30 days\n portfolio_Returns_30 = cumprod( portfolio_Weights %*% daily_Returns + 1 )\n # Add it to the monte-carlo matrix\n portfolio_Returns_30_m[,i] = portfolio_Returns_30;\n}\n\n# Visualising result\nx_axis = rep(1:training_days, mc_rep)\ny_axis = as.vector(portfolio_Returns_30_m-1)\nplot_data = data.frame(x_axis, y_axis)\nggplot(data = plot_data, aes(x = x_axis, y = y_axis)) + geom_path(col = 'red', size = 0.1) +\n xlab('Days') + ylab('Portfolio Returns') + \n ggtitle('Simulated Portfolio Returns in 30 days')+\n theme_bw() +\n theme(plot.title = element_text(hjust = 0.5))\n\n# Porfolio Returns statistics on the 30th day.\nAvg_Portfolio_Returns = mean(portfolio_Returns_30_m[30,]-1)\nSD_Portfolio_Returns = sd(portfolio_Returns_30_m[30,]-1)\nMedian_Portfolio_Returns = median(portfolio_Returns_30_m[30,]-1)\nprint(c(Avg_Portfolio_Returns,SD_Portfolio_Returns,Median_Portfolio_Returns))\n\n# Construct a 95% Confidential Interval for average returns\nAvg_CI = quantile(portfolio_Returns_30_m[30,]-1, c(0.025, 0.975))\nprint(Avg_CI)\n", "meta": {"hexsha": "fb75056b3202e9e2e2a02f64607b5cc6a7c98a89", "size": 3078, "ext": "r", "lang": "R", "max_stars_repo_path": "portfolio_return_v00.r", "max_stars_repo_name": "dhjelmar/Retirement", "max_stars_repo_head_hexsha": "2f844025e72d89c241aac5a6bd14780c48bb8dbb", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "portfolio_return_v00.r", "max_issues_repo_name": "dhjelmar/Retirement", "max_issues_repo_head_hexsha": "2f844025e72d89c241aac5a6bd14780c48bb8dbb", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "portfolio_return_v00.r", "max_forks_repo_name": "dhjelmar/Retirement", "max_forks_repo_head_hexsha": "2f844025e72d89c241aac5a6bd14780c48bb8dbb", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 37.0843373494, "max_line_length": 114, "alphanum_fraction": 0.7011046134, "num_tokens": 990, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9086178969328287, "lm_q2_score": 0.8267117983401363, "lm_q1q2_score": 0.7511651355773714}} {"text": "library(pomp)\n\n\nset.seed(1111)\n\n# Function to simulate one time step \nstep_fun_R <- function(x, t, params, delta.t, ...){\n S <- x[1]\n I <- x[2] \n R <- x[3]\n N <- S + I + R \n logbeta <- x[4]\n beta <- exp(logbeta)\n\n gamma = params[1] \n sigma = params[2] \n alpha = params[3]\n\n newinf <- beta * S * I * delta.t/N\n newdeath <- gamma * I *delta.t \n S <- max(0, S - newinf )\n I <- max(0, I + newinf - newdeath )\n R <- max(0, R + newdeath )\n logbeta <- logbeta + rnorm(1, -alpha * I * delta.t, sd = sigma * sqrt(delta.t) )\n c( S = unname(S) , I = unname(I), R = unname(R), logbeta = unname( logbeta ))\n}\n\n# Defines pomp object that could be used for simulation or inference \nspsir_pomp_R <- pomp ( rprocess = euler.sim( step.fun = step_fun_R, delta.t = .001)\n , t0 = 0\n , statenames = c( 'S', 'I', 'R', 'logbeta')\n , paramnames = c('gamma', 'sigma', 'alpha')\n , data = data.frame( time = seq(0, 10, by=.01), S = NA, I = NA, R = NA, logbeta = NA)\n , time = 'time'\n , initializer = function(params, t0, ... ) c( S = 50, I = 1, R = 0, logbeta = log(3) )\n , rmeasure = function( x, t, params, ... ) x \n)\n\nspsir_pomp_R_sol <- simulate(spsir_pomp_R, params = c( gamma = 1, sigma = 1, alpha = 0.1) )\n\nplot( spsir_pomp_R_sol )\n", "meta": {"hexsha": "e61869b4633685414eec375bc3227bccb6f2a095", "size": 1262, "ext": "r", "lang": "R", "max_stars_repo_path": "models/time_varying_parameters/semiparametric_sir.r", "max_stars_repo_name": "epimodels/epicookbook", "max_stars_repo_head_hexsha": "496088ddc8fc913505d92877e0a687c81976c8f2", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "models/time_varying_parameters/semiparametric_sir.r", "max_issues_repo_name": "epimodels/epicookbook", "max_issues_repo_head_hexsha": "496088ddc8fc913505d92877e0a687c81976c8f2", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "models/time_varying_parameters/semiparametric_sir.r", "max_forks_repo_name": "epimodels/epicookbook", "max_forks_repo_head_hexsha": "496088ddc8fc913505d92877e0a687c81976c8f2", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2020-10-10T12:46:31.000Z", "max_forks_repo_forks_event_max_datetime": "2020-10-10T12:46:31.000Z", "avg_line_length": 30.0476190476, "max_line_length": 92, "alphanum_fraction": 0.557844691, "num_tokens": 455, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9381240142763573, "lm_q2_score": 0.8006920044739461, "lm_q1q2_score": 0.7511483974360813}} {"text": "cities<-c(\"c1\",\"c2\",\"c3\",\"c4\",\"c5\",\"c6\",\"c7\",\"c8\",\"c9\",\"c10\")\r\n# All possible samples are\r\nt(combn(cities, 2)) \r\ntotal_pairs<-nrow(t(combn(cities, 2)))\r\n# the probability associated with each sample in a random sample of 2 cities selected from the population\r\nprobability_selecting2cities<-1/total_pairs\r\nprint(probability_selecting2cities)", "meta": {"hexsha": "22917d25110f5f4ba3ffed790d285efaba436a5a", "size": 340, "ext": "r", "lang": "R", "max_stars_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH4/EX4.20/Ex4_20.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH4/EX4.20/Ex4_20.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "An_Introduction_To_Statistical_Methods_And_Data_Analysis_by_R_Lyman_Ott_And_Michael_Longnecker/CH4/EX4.20/Ex4_20.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 48.5714285714, "max_line_length": 106, "alphanum_fraction": 0.7352941176, "num_tokens": 103, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9294403999037784, "lm_q2_score": 0.8080672043084051, "lm_q1q2_score": 0.7510503055215322}} {"text": "library(modreg)\n\npostscript(\"Plots/plot-06-01.ps\")\nn <- 100\nx <- rnorm(n);y <- rnorm(n)\nlambda <- seq(0.05,1,len=50)\ndf <- sapply(lambda,function(l) if(l==0) return(n) else return(sum(loess(y~x,span=l)$trace.hat)))\npar(mfrow=c(1,2))\nplot(lambda,df,main=\"Loess\",type=\"l\")\nlambda <- seq(0.01,2,len=100)\ndf <- sapply(lambda,function(l) smooth.spline(x,y,spar=l,all.k=T)$df)\nplot(lambda,df,main=\"Smoothing spline\",type=\"l\")\ndev.off()\n\n###different definitions of degrees of freedom\npostscript(\"Plots/plot-06-02.ps\")\nn <- 100\nx <- sort(runif(n,0,1))\nY <- diag(n)\nlambda <- seq(.02,1,len=10)\ndf <- matrix(0,length(lambda),3)\nfor(i in 1:length(lambda)){\n l <- lambda[i]\n S <- apply(Y,1,function(yy) loess(yy~x,span=l)$fitted)\n aux1 <- sum(diag(S));aux2 <- sum(diag(S%*%t(S)))\n df[i,] <- c(aux1,aux2,2*aux1-aux2)\n}\npar(mfrow=c(1,1))\nplot(lambda,df[,1],ylim=range(df),type=\"l\",ylab=\"df\",log=\"y\")\nlines(lambda,df[,2],lty=2)\nlines(lambda,df[,3],lty=3)\nlegend(.7,range(df)[2]*.95,c(\"tr(S)\",\"tr(SS')\",\"2tr(S)-tr(SS')\"),lty=c(1,2,3))\ndev.off()\n\n\n###might as well draw the columns of the smoothing spline\npostscript(\"Plots/plot-06-03.ps\")\nn <- 101\nx <- sort(runif(n,0,1))\nY <- diag(n)\nS <- apply(Y,1,function(yy) smooth.spline(x,yy,spar=.8,all.knots=T)$y)\npar(mfrow=c(3,2))\nfor(i in seq(1,101,len=6))\n plot(x,S[i,],ylab=paste(i,\"th row of S\",sep=\"\"),type=\"b\")\ndev.off()\n\n\n\n\nn <- 30\nx <- sort(runif(n,0,1))\n##first linear to show example\nX <- cbind(1,x)\nS <- X%*%solve(t(X)%*%X)%*%t(X)\naux <- eigen(S,symmetric=T)\nU <- aux$vector; D <- diag(aux$values) ###S should be UDU'\n\npostscript(\"Plots/plot-06-04.ps\")\npar(mfrow=c(1,2),oma=c(0,0,2,0))\nplot(diag(D),xlab=\"\",ylab=\"Eigenvalues\")\npar(mfrow=c(2,2))\npar(mfg=c(1,2))\nplot(x,U[,1],xlab=\"x\",ylab=\"First Eigenvector\")\npar(mfg=c(2,2))\nplot(x,U[,2],xlab=\"x\",ylab=\"Second Eigenvector\")\nmtext(\"Simple linear regression\",outer=T,side=3,line=0,cex=1.5)\ndev.off()\n \n###NOW for smoothing splines\nn <- 30\nx <- sort(runif(n,0,1))\npostscript(\"Plots/plot-06-05.ps\")\nY <- diag(n)\nS <- apply(Y,1,function(yy) smooth.spline(x,yy,spar=.6,all.knots=T)$y)\naux <- eigen(S,symmetric=T)\nU <- aux$vector; D <- diag(aux$values) ###S should be UDU'\npar(mfrow=c(1,1))\nplot(diag(D),xlab=\"\",ylab=\"Eigenvalues\")\ndev.off()\n\npostscript(\"Plots/plot-06-06.ps\")\npar(mfcol=c(5,2),mai=c(.3,.5,.1,.3),oma=c(0,0,2,0))\nfor(i in 1:10)\n plot(x,U[,i],xlab=\"x\",ylab=paste(i,\"th Eigenvector\",sep=\"\"),type=\"l\")\nmtext(\"Smoothing spline\",outer=T,side=3,line=0,cex=1.5)\ndev.off()\n\npostscript(\"Plots/plot-06-07.ps\")\npar(mfcol=c(5,2),mai=c(.3,.5,.1,.3),oma=c(0,0,2,0))\nfor(i in 11:20)\n plot(x,U[,i],xlab=\"x\",ylab=paste(i,\"th Eigenvector\",sep=\"\"),type=\"l\")\nmtext(\"Smoothing spline\",outer=T,side=3,line=0,cex=1.5)\ndev.off()\n\n\npostscript(\"Plots/plot-06-08.ps\")\npar(mfcol=c(5,2),mai=c(.3,.5,.1,.3),oma=c(0,0,2,0))\nfor(i in 21:30)\n plot(x,U[,i],xlab=\"x\",ylab=paste(i,\"th Eigenvector\",sep=\"\"),type=\"l\")\nmtext(\"Smoothing spline\",outer=T,side=3,line=0,cex=1.5)\ndev.off()\n\n\n###REACT STUFF\nn <- 48\nx <- (1:n)/n\ny <- scan(\"Data/mouse-bt.dat\")\nU <- cbind(rep(1/sqrt(n),n),\n sapply(1:(n/2-1),function(k) sqrt(2/n)*cos(2*pi*k*x)),\n sapply(1:(n/2-1),function(k) sqrt(2/n)*sin(2*pi*k*x)),\n 1/sqrt(n)*cos(pi*n*x))\n\n\npostscript(\"Plots/plot-06-09.ps\")\npar(mfrow=c(5,2),mai=c(.3,.5,.1,.3),oma=c(0,0,2,0))\nfor(i in 1:5){\n plot(x,U[,i+1],xlab=\"x\",ylab=paste(i,\"th FFT row\",sep=\"\"),type=\"l\")\n plot(x,U[,n/2+i],xlab=\"x\",ylab=paste(i,\"th FFT row\",sep=\"\"),type=\"l\")\n}\ndev.off()\n\n\n\n##fft of data\naux <- fft(y)/sqrt(n)\nz <- c(Re(aux[1]),\n as.vector(t(matrix(c(Re(aux[2:(n/2)]),Im(aux[2:(n/2)])),ncol=2))),\n Re(aux[n/2+1]))\n##this functions recieves a fft and returns an estimate of f\nifft <- function(z){\n n <- length(z)\n aux <- complex(real=z[seq(2,n-1,2)],im=z[seq(3,n-1,2)])\n yhat <-Re(fft(c(z[1],aux,z[n],rev(Conj(aux))),inv=T)/sqrt(n))\n}\n\npostscript(\"Plots/plot-06-10.ps\")\npar(mfrow=c(2,2))\nfor(m in c(1,4,8,23)){\n plot(x,y,main=paste(m,\"non zero\"))\n zhat <- z*c(rep(1,1+2*m),rep(0,n-2*m-1))\n lines(x,ifft(zhat))\n}\ndev.off()\n\n\n###We need to define the average and PAV functions\naverage_function(y, wt = rep(1, length(y)))\n{\n# compute a weighted average of a vector, y\n if(any(is.na(wt))) stop(\"NA's not allowed for wt\")\n if(any(wt < 0))\n stop(\"wt must be a vector of NON-NEGATIVE weights\")\n if(length(wt) != length(y)) stop(\n \"y and wt must be vectors of the same length\")\n# if any observations have Infinite weight, return the simple\n# (unweighted) average of only those observations (giving no\n# weight to observations with finite weight)\n if(any(wt == Inf)) {\n wt[wt < Inf] <- 0\n wt[wt == Inf] <- 1\n }\n# if all weights are zero, return the simple (unweighted)\n# average of y\n if(sum(wt) == 0)\n wt <- rep(1, length(wt))\n return(sum((y * wt)/sum(wt)))\n}\n\n\nPAV_function(y, wt = rep(1,p))\n{\n### This is a modification of Derick's PAV program\n### (Weighted) Pool-Adjacent-Violators (PAV) algorithm\n### for non-parametric monotonic (decreasing) regression of y on x\n n <- length(y)\n if(n != length(wt))\n stop(\"y, and wt must be vectors of equal length\")\n yhat <- y # initialize while loop\n j <- count <- 1\n k <- 2\n support <- vector(\"numeric\", n)\n support[count] <- j\n while(k <= n) {\n while(yhat[j] < yhat[k]) {\n yhat[j:k] <- average(y[j:k], wt[j:k])\n if(yhat[support[count]] < yhat[k]) {\n j <- support[count]\n if(count > 1)\n count <- count - 1\n }\n else {\n k <- ifelse(k == n, k, k + 1)\n }\n }\n count <- count + 1\n support[count] <- j\n j <- k\n k <- k + 1\n }\n return(y = yhat, wt)\n}\npostscript(\"Plots/plot-06-11.ps\")\npar(mfrow=c(2,2))\nplot(x,y,xlab=\"Time\",ylab=\"Temperature\",type=\"n\",main=\"Harmonic Model\")\npoints(x,y,col=4)\nm <- 4\nyhat <- z*c(rep(1,1+2*m),rep(0,n-2*m-1))\nlines(x,ifft(yhat),col=9)\nplot(2:48,abs(z[-1]),xlab=\"coefficient of z\",ylab=\"Absolute value\",type=\"h\")\npoints(2:(1+2*m),abs(z[2:(1+2*m)]),col=3)\npoints((2+2*m):n,abs(z[(2+2*m):n]),col=4,pch=4)\nabline(h=0)\nplot(x,y,xlab=\"Time\",ylab=\"Temperature\",type=\"n\",main=\"REACT\")\npoints(x,y,col=4)\nsigma2 <- .1520197 ##we got this from somewhere else\ng <- 1 - sigma2/z^2\nfhat <- PAV(g, z^2)$y\nfhat <- sapply(fhat, function(x) max(x, 0))\nfit1 <- ifft(z*fhat)\nlines(x,fit1,col=9)\nplot(2:48,abs(z[-1]),xlab=\"coefficient of z\",ylab=\"Absolute value\",type=\"h\")\npoints(2:n,abs(z[2:n]),col=3)\npoints(2:n,abs(z*fhat)[-1],col=4,pch=4)\nabline(h=0)\ndev.off()\n\n\npostscript(\"Plots/plot-06-12.ps\")\nY <- matrix(scan(\"Data/all-mouse-bt.dat\"),48,12,byrow=T)\nY <- sweep(Y,2,apply(Y,2,mean))\npar(mfrow=c(1,1))\nplot(rep(x,12),as.vector(Y),xlab=\"Time\",ylab=\"Temperature\")\n\nlines(x,apply(Y,1,mean),lwd=3)\nlines(x,fit1-mean(fit1),col=3,lty=2,lwd=3)\nlines(x,ifft(yhat)-mean(ifft(yhat)),col=4,lty=3,lwd=3)\nlegend(0.05,1.5,c(\"Average\",\"REACT\",\"Harmonic\"),lty=c(1,2,3),col=c(1,3,4))\ndev.off()\n\n##the rest is code-06.s... becuase of the wavelet module\n\n", "meta": {"hexsha": "764c099c8d019d240dd25f34bae7bd77388f1876", "size": 7013, "ext": "r", "lang": "R", "max_stars_repo_path": "pages/754/code-06.r", "max_stars_repo_name": "igrabski/rafalab.github.io", "max_stars_repo_head_hexsha": "2f27ea0d9e0b8a2342bb851ae7415ba3268fd00f", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 50, "max_stars_repo_stars_event_min_datetime": "2016-08-17T23:04:04.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-31T19:21:02.000Z", "max_issues_repo_path": "pages/754/code-06.r", "max_issues_repo_name": "igrabski/rafalab.github.io", "max_issues_repo_head_hexsha": "2f27ea0d9e0b8a2342bb851ae7415ba3268fd00f", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 6, "max_issues_repo_issues_event_min_datetime": "2016-08-18T00:41:36.000Z", "max_issues_repo_issues_event_max_datetime": "2021-01-21T22:35:40.000Z", "max_forks_repo_path": "pages/754/code-06.r", "max_forks_repo_name": "igrabski/rafalab.github.io", "max_forks_repo_head_hexsha": "2f27ea0d9e0b8a2342bb851ae7415ba3268fd00f", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 38, "max_forks_repo_forks_event_min_datetime": "2016-08-17T22:17:30.000Z", "max_forks_repo_forks_event_max_datetime": "2021-11-20T12:17:08.000Z", "avg_line_length": 28.979338843, "max_line_length": 97, "alphanum_fraction": 0.603308142, "num_tokens": 2700, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8774767906859265, "lm_q2_score": 0.855851143290548, "lm_q1q2_score": 0.7509895145194712}} {"text": "# Group members (Name, Student ID, E-Mail):\n# 1. Baldomero Valdez, Valenzuela, 2905175, baldmer.w@gmail.com\n# 2. Omar Trinidad Gutierrez Mendez, 2850441, omar.vpa@gmail.com\n# 3. Shinho Kang, 2890169, wis.shinho.kang@gmail.com\n\n\n# import package nnet to implement multinomial logistic regression\nlibrary(nnet)\n\n# 1. Fit a logistic regression model on iris dataset\n# Multinomial logistic regression with nnet package\ndata(iris)\n\n# shuffle the dataset and get training and test dataset\nshuffled.iris <- iris[sample(1:nrow(iris)), ]\ntest.ds <- shuffled.iris[1:30,]\ntraining.ds <- shuffled.iris[31:150,]\n\nformula <- Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width\nmultinomial.model <- multinom(formula, training.ds)\nprint(multinomial.model)\n\n#Call:\n#multinom(formula = formula, data = training.ds)\n#\n#Coefficients:\n# (Intercept) Sepal.Length Sepal.Width Petal.Length Petal.Width\n#versicolor 15.78584 -5.753264 -6.333713 12.78611 -2.309163\n#virginica -22.61359 -8.586707 -12.026601 22.15053 13.246169\n#\n#Residual Deviance: 11.38084\n#AIC: 31.38084\n\ne = predict(multinomial.model)\n\n# Binomial logistic regression using `glm` function\n\n# for setosa\nsetosa.ds = shuffled.iris\ntraining.setosa <- setosa.ds[31:150,]\nnewcol <- data.frame(isSetosa=(training.setosa$Species == 'setosa'))\ntraining.setosa <- cbind(training.setosa, newcol)\n\nformula <- isSetosa ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width\nmodel.setosa <- glm(formula, data=training.setosa, family='binomial')\nprint(model.setosa)\n#Call: glm(formula = formula, family = \"binomial\", data = training.setosa)\n#\n#Coefficients:\n# (Intercept) Sepal.Length Sepal.Width Petal.Length Petal.Width\n# 8.083 4.034 11.240 -22.097 -4.758\n#\n#Degrees of Freedom: 119 Total (i.e. Null); 115 Residual\n#Null Deviance: 152.8\n#Residual Deviance: 2.285e-09 AIC: 10\ne = predict(model.setosa, newdata=test.ds, type='response')\n\n# for versicolor\nversicolor.ds = shuffled.iris\ntraining.versicolor <- versicolor.ds[31:150,]\nnewcol <- data.frame(isVersicolor=(training.versicolor$Species == 'versicolor'))\ntraining.versicolor <- cbind(training.versicolor, newcol)\n\nformula <- isVersicolor ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width\nmodel.versicolor <- glm(formula, data=training.versicolor, family='binomial')\nprint(model.versicolor)\n#Call: glm(formula = formula, family = \"binomial\", data = training.versicolor)\n#\n#Coefficients:\n# (Intercept) Sepal.Length Sepal.Width Petal.Length Petal.Width\n# 7.7785 -0.3307 -2.7866 1.2605 -2.5890\n#\n#Degrees of Freedom: 119 Total (i.e. Null); 115 Residual\n#Null Deviance: 152.8\n#Residual Deviance: 115.4 AIC: 125.4\ne = predict(model.versicolor, newdata=test.ds, type='response')\n\n# for virginica\nvirginica.ds = shuffled.iris\ntraining.virginica <- virginica.ds[31:150,]\nnewcol <- data.frame(isVirginica=(training.virginica$Species == 'virginica'))\ntraining.virginica <- cbind(training.virginica, newcol)\n\nformula <- isVirginica ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width\nmodel.virginica <- glm(formula, data=training.virginica, family='binomial')\nprint(model.virginica)\n\n#Call: glm(formula = formula, family = \"binomial\", data = training.virginica)\n#\n#Coefficients:\n# (Intercept) Sepal.Length Sepal.Width Petal.Length Petal.Width\n# -38.802 -2.830 -5.672 9.420 15.584\n#\n#Degrees of Freedom: 119 Total (i.e. Null); 115 Residual\n#Null Deviance: 152.8\n#Residual Deviance: 11.38 AIC: 21.38\ne = predict(model.virginica, newdata=test.ds, type='response')\n\n", "meta": {"hexsha": "b6ce0a93eaffac0f0d9081e1996cc7946cdbee9e", "size": 3656, "ext": "r", "lang": "R", "max_stars_repo_path": "Ex5/ex5_2.r", "max_stars_repo_name": "omartrinidad/ml_bioinformatics", "max_stars_repo_head_hexsha": "2ff4962767a9cfe206620f1fc870839e249dde96", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Ex5/ex5_2.r", "max_issues_repo_name": "omartrinidad/ml_bioinformatics", "max_issues_repo_head_hexsha": "2ff4962767a9cfe206620f1fc870839e249dde96", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Ex5/ex5_2.r", "max_forks_repo_name": "omartrinidad/ml_bioinformatics", "max_forks_repo_head_hexsha": "2ff4962767a9cfe206620f1fc870839e249dde96", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2019-05-15T02:23:47.000Z", "max_forks_repo_forks_event_max_datetime": "2019-05-15T02:23:47.000Z", "avg_line_length": 36.9292929293, "max_line_length": 81, "alphanum_fraction": 0.7067833698, "num_tokens": 1146, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9184802350995702, "lm_q2_score": 0.8175744739711883, "lm_q1q2_score": 0.7509259950644644}} {"text": "### power and sample size function for TSLS estimator\r\n\nTSLS.power=function(n, beta, rho_ZD, sigmau, sigmaDsq, alpha=0.05){\n return(c(1+pnorm(-qnorm(1-alpha/2)-beta*rho_ZD*sqrt(n*sigmaDsq)/sigmau)-pnorm(qnorm(1-alpha/2)-beta*rho_ZD*sqrt(n*sigmaDsq)/sigmau)))\n}\n\nTSLS.size=function(power, beta, rho_ZD, sigmau, sigmaDsq, alpha=0.05){\n return(ceiling(c((qnorm(1-alpha/2)+qnorm(power))^2*sigmau^2/beta^2/rho_ZD^2/sigmaDsq)))\n}\r\n", "meta": {"hexsha": "b8f63422813eebc88f6a4a1f7553cc3da4a8f127", "size": 428, "ext": "r", "lang": "R", "max_stars_repo_path": "R/TSLS.r", "max_stars_repo_name": "qingyuanzhao/ivmodel", "max_stars_repo_head_hexsha": "ad59c7cbd32734b25b12c9aef3deb8ba1559cacb", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 8, "max_stars_repo_stars_event_min_datetime": "2018-09-22T13:38:52.000Z", "max_stars_repo_stars_event_max_datetime": "2021-06-23T02:04:23.000Z", "max_issues_repo_path": "R/TSLS.r", "max_issues_repo_name": "qingyuanzhao/ivmodel", "max_issues_repo_head_hexsha": "ad59c7cbd32734b25b12c9aef3deb8ba1559cacb", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 2, "max_issues_repo_issues_event_min_datetime": "2020-11-09T19:20:30.000Z", "max_issues_repo_issues_event_max_datetime": "2022-02-01T13:44:24.000Z", "max_forks_repo_path": "R/TSLS.r", "max_forks_repo_name": "qingyuanzhao/ivmodel", "max_forks_repo_head_hexsha": "ad59c7cbd32734b25b12c9aef3deb8ba1559cacb", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2020-06-01T16:33:38.000Z", "max_forks_repo_forks_event_max_datetime": "2020-06-01T16:33:38.000Z", "avg_line_length": 42.8, "max_line_length": 135, "alphanum_fraction": 0.7219626168, "num_tokens": 163, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9407897442783527, "lm_q2_score": 0.7981867849406659, "lm_q1q2_score": 0.7509259412906896}} {"text": "# Example : 1 Chapter : 5.3 Page No: 269\r\n# Cramers rule for solving system of equations\r\nA<-matrix(c(3,5,4,6),ncol=2)\r\nb<-c(2,4)\r\nB1<-A\r\nB1[,1]<-b\r\nB2<-A\r\nB2[,2]<-b\r\nx1<-det(B1)/det(A)\r\nx2<-det(B2)/det(A)\r\nprint(\"SOlution is \")\r\nprint(x1)\r\nprint(x2)\r\n", "meta": {"hexsha": "1e6818aab1e95628c5f7dc826fb82698b08bd909", "size": 258, "ext": "r", "lang": "R", "max_stars_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH5/EX5.3.1/Ex5.3_1.r", "max_stars_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_stars_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH5/EX5.3.1/Ex5.3_1.r", "max_issues_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_issues_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH5/EX5.3.1/Ex5.3_1.r", "max_forks_repo_name": "prashantsinalkar/R_TBC_Uploads", "max_forks_repo_head_hexsha": "b3f3a8ecd454359a2e992161844f2fb599f8238a", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 3, "max_forks_repo_forks_event_min_datetime": "2020-04-07T16:44:56.000Z", "max_forks_repo_forks_event_max_datetime": "2020-11-13T06:35:28.000Z", "avg_line_length": 18.4285714286, "max_line_length": 47, "alphanum_fraction": 0.5813953488, "num_tokens": 117, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9407897426182322, "lm_q2_score": 0.7981867849406659, "lm_q1q2_score": 0.7509259399656033}} {"text": "closestdata <- function(target, database, weight=NULL) {\r\n ## Function to sort database based on distance from target datapoint\r\n ## target = dataframe containing only the parameters to be searched for\r\n ## database = dataframe containing database\r\n ## can list more parameters than in target\r\n ## weight = vector of weights for target parameters\r\n ## = NULL results in value of 1 for all parameters\r\n ## = 0 for a particular parameter, results in the value not mattering at all\r\n ## = any large number for a particular parameter weight relative to scale of \r\n ## parameters can result in parameter having to be matched exactly\r\n\r\n ## create dataframe from database with only target parameters\r\n df <- subset(database, select=names(target))\r\n\r\n ## reorder subset dataframe to have the same order as target\r\n df <- df[names(target)]\r\n \r\n ## convert target to a vector and subtract from dataframe\r\n vec <- as.numeric(as.vector(target))\r\n dif <- sweep(df, 2, vec, \"-\")\r\n\r\n ## multiply each difference by the weights\r\n if (is.null(weight)) weight <- rep(1, ncol(target))\r\n difw <- sweep(dif, 2, weight, \"*\")\r\n\r\n ## rename columns to indicate these are differneces\r\n colnames(difw) <- paste(\"dif\", colnames(difw), sep = \"_\")\r\n \r\n ## sumsquare each row of dataframe of diferences and add to difference dataframe\r\n sq <- function(x) { sum(x^2) }\r\n distance <- sqrt( apply(difw, 1, sq) )\r\n difw <- cbind( distance, difw )\r\n \r\n ## combine the dataframe of weighted differences with the original dataframe then sort\r\n dfnew <- cbind(difw, database)\r\n dfnew <- dfnew[order(dfnew$distance),]\r\n \r\n ## return sorted dataframe\r\n return(dfnew)\r\n}\r\n\r\n## ## test\r\n## df <- '\r\n## name param3 param1 param2\r\n## point1 1 1 1\r\n## point2 0 1 2\r\n## point3 10 10 10\r\n## point4 3 2 4\r\n## '\r\n## df <- readall(df)\r\n## \r\n## closestdata(data.frame(t(c(param1=1.2, param2=2.1, param3=-0.1))), df) # correctly returns points 2, 1, 4, 3\r\n## \r\n## closestdata(data.frame(t(c(param1=2.5, param2=4.5, param3=10))), df) # 4,3,1,2\r\n## closestdata(data.frame(t(c(param1=2.5, param2=4.5, param3=10))), df,\r\n## weight=c(1, 1, 1000)) # weight correctly moves point 3 to the closest\r\n## \r\n## closestdata(data.frame(t(c(param1=1, param2=2, param3=10))), df) # 4, 1, 2, 3\r\n## closestdata(data.frame(t(c(param1=1, param2=2, param3=10))), df,\r\n## weight=c(1, 1, 0)) # weight correctly ignores param3 and correctly identifies 2 as closest\r\n", "meta": {"hexsha": "a78bc8ba545f760b4a5cff66c2b08a83283df590", "size": 2643, "ext": "r", "lang": "R", "max_stars_repo_path": "modules/closestdata.r", "max_stars_repo_name": "TECComputing/R-setup", "max_stars_repo_head_hexsha": "f4b5e45c6e2e55fcc6f58f804bb50cea3a697fe0", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "modules/closestdata.r", "max_issues_repo_name": "TECComputing/R-setup", "max_issues_repo_head_hexsha": "f4b5e45c6e2e55fcc6f58f804bb50cea3a697fe0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "modules/closestdata.r", "max_forks_repo_name": "TECComputing/R-setup", "max_forks_repo_head_hexsha": "f4b5e45c6e2e55fcc6f58f804bb50cea3a697fe0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-06-16T12:06:21.000Z", "max_forks_repo_forks_event_max_datetime": "2021-06-16T12:06:21.000Z", "avg_line_length": 43.3278688525, "max_line_length": 114, "alphanum_fraction": 0.613318199, "num_tokens": 725, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9032942171172603, "lm_q2_score": 0.8311430499496096, "lm_q1q2_score": 0.7507667106166847}} {"text": "#importa pacote\nlibrary('readr')\n\n# Lê/coleta dados no arquivo\n\ndados_cliente <- read.csv(\"./clientes.csv\",sep=\";\")\n\nhead(dados_cliente)\n\n# Definimos que a variável Grau.Instrução deve ser tratada como ordinal\n\nlevels(dados_cliente$Grau.Instrução)\n\ndados_cliente$Grau.Instrução <- factor(dados_cliente$Grau.Instrução,\n levels = c('Fundamental','Médio','Superior','Mestrado','Doutorado'))\n\nlevels(dados_cliente$Grau.Instrução)\n\n# Frequência absoluta\n\nfa <- with(dados_cliente,table(Estado.civil,Grau.Instrução))\nfa\n\n\n# Frequência relativa\n# Em relação ao total geral\n# Em relação aos totais por linha (`margin = 1`)\n# Em relação aos totais por coluna (`margin = 2`)\n\nfrg <- prop.table(fa)\nround(frg,digit=2)\n\nfrl <- prop.table(fa,margin=1)\nround(frl,digit=2)\n\nfrc <- prop.table(fa,margin=2)\nround(frc,digit=2)\n\n\nbarplot(fa, legend = TRUE)\n\nbarplot(t(fa), legend = TRUE)\n\n\nbarplot(fa, beside = TRUE, legend = TRUE)\n\n\nbarplot(t(prop.table(fa)), beside = TRUE, legend = TRUE)\n\n## Quartis de salario\nquantile(dados_cliente$Salário)\n\n## Classificação de acordo com os quartis\ngrupo_sal <- cut(dados_cliente$Salário, breaks = quantile(dados_cliente$Salário),include.lowest = TRUE)\n\n\n\n## Tabela de frequências absolutas\nfa <- table(dados_cliente$Grau.Instrução, grupo_sal)\nfa\n\n\nfrg <- prop.table(fa)\nfrg\n\nfrl <- prop.table(fa,margin=1)\nfrl\n\nfrc <- prop.table(fa,margin=2)\nfrc\n\n\nboxplot(Salário ~ Grau.Instrução, data = dados_cliente)\n\nprint('Media')\nwith(dados_cliente, tapply(Salário, Grau.Instrução, mean))\nprint('Desvio Padrão')\nwith(dados_cliente, tapply(Salário, Grau.Instrução, sd))\nprint('Quartil')\nwith(dados_cliente, tapply(Salário, Grau.Instrução, quantile))\n\nhead(dados_cliente)\n\n## Classes de Idade (Anos)\ngrupo_idade <- with(dados_cliente, cut(Anos, breaks = quantile(Anos),include.lowest = TRUE))\n\nfa_idade <- table(grupo_idade)\n\nfa_idade\n\n## Quartis de salario\nquantile(dados_cliente$Salário)\n\n## Classificação de acordo com os quartis\ngrupo_sal <- cut(dados_cliente$Salário, breaks = quantile(dados_cliente$Salário),include.lowest = TRUE)\n\n\nfa_sal <- table(grupo_sal)\nfa_sal\n\n## Tabela combinada cruzada\nfa <- table(grupo_idade, grupo_sal)\nfa\n\nfrg <- prop.table(fa)\nfrg\n\nfrl <- prop.table(fa,margin=1)\nfrl\n\nfrc <- prop.table(fa,margin=2)\nfrc\n\nhead(dados_cliente)\n\n# Plotar gráfico de dispersão entre as variáveis\n\n#plot(x = dados_cliente$Anos, y = dados_cliente$Salário)\nplot(Salário ~ Anos, data = dados_cliente)\n\n#Coeficiaente de relação\nprint('Coeficiaente de relação Pearson')\nwith(dados_cliente, cor(Anos, Salário)) #Pearson\n\nprint('Coeficiaente de relação kendall')\nwith(dados_cliente, cor(Anos, Salário, method = \"kendall\"))\n\nprint('Coeficiaente de relação spearman')\nwith(dados_cliente, cor(Anos, Salário, method = \"spearman\"))\n\n\n", "meta": {"hexsha": "d4fe01e0d58c4428c2b7fbc004935c68cd705eb3", "size": 2787, "ext": "r", "lang": "R", "max_stars_repo_path": "BootCamp Engenheiro de Dados/Modulo 1 - Materiais/Material_complementar_videoaulas/Analise_bivariada.r", "max_stars_repo_name": "MarceloEbed/IGTI", "max_stars_repo_head_hexsha": "8b0f56c4b9bcbbfe81fd540cb34d39ad8ae0d306", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "BootCamp Engenheiro de Dados/Modulo 1 - Materiais/Material_complementar_videoaulas/Analise_bivariada.r", "max_issues_repo_name": "MarceloEbed/IGTI", "max_issues_repo_head_hexsha": "8b0f56c4b9bcbbfe81fd540cb34d39ad8ae0d306", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "BootCamp Engenheiro de Dados/Modulo 1 - Materiais/Material_complementar_videoaulas/Analise_bivariada.r", "max_forks_repo_name": "MarceloEbed/IGTI", "max_forks_repo_head_hexsha": "8b0f56c4b9bcbbfe81fd540cb34d39ad8ae0d306", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 21.1136363636, "max_line_length": 107, "alphanum_fraction": 0.7348403301, "num_tokens": 848, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9005297914570319, "lm_q2_score": 0.8333246015211008, "lm_q1q2_score": 0.7504336296238111}} {"text": "\nrm(list=ls())\n\nlibrary('radolc')\n\nfr <- function(x) { ## Rosenbrock Banana function\n y <- 100 * (1 - x * x)* (1 - x * x) + (1 - x)*(1 - x)\n y }\n\ngrr <- function(x) { ## Gradient of 'fr'\n g <- 0-400 * x * (1 - x * x) - 2 * (1 - x)\n g }\n\n#---- building the gradient function with ADOLC\ntrace_on(1)\nx <- adouble(1.0)\nbadouble_declareIndependent(x)\ny <- fr(x)\nbadouble_declareDependent(y)\ntrace_off()\n\ngrrADOLC <- function(x) { ## Gradient of 'fr'\n y <- c(0.0)\n gradient(1,1,x,y);\n y }\n\n#---- ADOLC gradient\ngrrADOLC(3)\n\n#---- Abalytical gradient\ngrr(3)\n\n#---- optim with the gradients \nres0 <- optim(c(-1), fr, method = \"L-BFGS-B\", control = list(type = 3, trace = 2))\nres1 <- optim(c(-1), fr, grr, method = \"L-BFGS-B\", control = list(type = 3, trace = 2))\nres2 <- optim(c(-1), fr, grrADOLC, method = \"L-BFGS-B\", control = list(type = 3, trace = 2))\n\n#Always detach the package\ndetach(package:radolc, unload=TRUE) \n\nprint(res0)\n\nprint(res1)\n\nprint(res2)\n\n", "meta": {"hexsha": "0c3b2cb39452a06cd5ca4ea0f7633ab9090c1eeb", "size": 966, "ext": "r", "lang": "R", "max_stars_repo_path": "tests/rosenbrock_univariate_optim.r", "max_stars_repo_name": "sriharikrishna/autodiffadolc", "max_stars_repo_head_hexsha": "67d6e9beb20395f2910ecb9d5ac9bc4a7bda9333", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "tests/rosenbrock_univariate_optim.r", "max_issues_repo_name": "sriharikrishna/autodiffadolc", "max_issues_repo_head_hexsha": "67d6e9beb20395f2910ecb9d5ac9bc4a7bda9333", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2018-07-27T16:44:03.000Z", "max_issues_repo_issues_event_max_datetime": "2018-07-27T16:44:03.000Z", "max_forks_repo_path": "tests/rosenbrock_univariate_optim.r", "max_forks_repo_name": "sriharikrishna/autodiffadolc", "max_forks_repo_head_hexsha": "67d6e9beb20395f2910ecb9d5ac9bc4a7bda9333", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 20.5531914894, "max_line_length": 92, "alphanum_fraction": 0.5910973085, "num_tokens": 357, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9005297941266013, "lm_q2_score": 0.8333245973817158, "lm_q1q2_score": 0.7504336281207894}} {"text": "#Series temporais e analises preditivas - Fernando Amaral\r\n\r\nlibrary(ggplot2)\r\nlibrary(forecast)\r\nlibrary(seasonal)\r\nlibrary(seasonalview)\r\n\r\n#sazonalidade e tendencia\r\nplot(co2)\r\nabline(reg=lm(co2~time(co2)))\r\n\r\n#decomposicao classica\r\nclassicdecco2 = decompose(co2)\r\nautoplot(classicdecco2)\r\n\r\n#decomposicao classica\r\nautoplot(fdeaths)\r\nx = decompose(fdeaths)\r\nautoplot(x)\r\n\r\n#X-13ARIMA-SEATS\r\nx13ap = seas(AirPassengers)\r\nautoplot(x13ap)\r\n\r\n#mstl\r\nmsap = mstl(AirPassengers)\r\nautoplot(msap)\r\n\r\n#vizao grafica\r\nview(x13ap)\r\n\r\nggseasonplot(AirPassengers) \r\nggseasonplot(AirPassengers, polar = T)\r\nggmonthplot(AirPassengers)\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n", "meta": {"hexsha": "d87f630a4aa34cc41cf641a577e35792abdbe373", "size": 645, "ext": "r", "lang": "R", "max_stars_repo_path": "Udemy/Series Temporais e Analises Preditivas/Resources/Codigo/5.4.Decomposicao.r", "max_stars_repo_name": "tarsoqueiroz/Rlang", "max_stars_repo_head_hexsha": "b2d4fdd967ec376fbf9ddb4a7250c11d3abab52e", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Udemy/Series Temporais e Analises Preditivas/Resources/Codigo/5.4.Decomposicao.r", "max_issues_repo_name": "tarsoqueiroz/Rlang", "max_issues_repo_head_hexsha": "b2d4fdd967ec376fbf9ddb4a7250c11d3abab52e", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Udemy/Series Temporais e Analises Preditivas/Resources/Codigo/5.4.Decomposicao.r", "max_forks_repo_name": "tarsoqueiroz/Rlang", "max_forks_repo_head_hexsha": "b2d4fdd967ec376fbf9ddb4a7250c11d3abab52e", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 15.0, "max_line_length": 58, "alphanum_fraction": 0.7348837209, "num_tokens": 205, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9399133498259924, "lm_q2_score": 0.7981867801399695, "lm_q1q2_score": 0.7502264103081816}} {"text": "## cosmological distances\n\ndcos <- function(z, H0=70, Omega.m=0.27, Omega.l=1-Omega.m) {\n \n c <- 299792.458\n\n nz <- length(z)\n\n # Hubble distance (MPc)\n\n dH <- c/H0\n\n Omega.k <- 1-Omega.m-Omega.l\n\n E <- function(z) sqrt(Omega.m*(1+z)^3+Omega.k*(1+z)^2+Omega.l)\n\n fc <- function(z) 1/E(z)\n ft <- function(z) 1/((1+z)*E(z))\n\n # comoving distance\n\n dC <- numeric(nz)\n\n for (i in 1:nz) dC[i] <- dH*integrate(fc, lower=0, upper=z[i])$value\n\n # transverse comoving distance and \n # comoving volume out to z\n\n if (Omega.k == 0) {\n dM <- dC \n Vc <- (4*pi/3)*dM^3\n } else if (Omega.k > 0) {\n dM <- dH/sqrt(Omega.k)*sinh(sqrt(Omega.k)*dC/dH)\n Vc <- (2*pi*dH^3/Omega.k)*\n (dM/dH*sqrt(1+Omega.k*(dM/dH)^2) -\n 1/sqrt(Omega.k)*asinh(sqrt(Omega.k)*dM/dH))\n } else {\n dM <- dH/sqrt(-Omega.k)*sin(sqrt(-Omega.k)*dC/dH)\n Vc <- (2*pi*dH^3/Omega.k)*\n (dM/dH*sqrt(1+Omega.k*(dM/dH)^2) -\n 1/sqrt(-Omega.k)*asin(sqrt(-Omega.k)*dM/dH))\n }\n\n # angular diameter distance\n\n dA <- dM/(1+z)\n\n # luminosity distance\n\n dL <- (1+z)*dM\n\n # distance modulus\n\n dm <- 5*log10(dL)+25\n \n # comoving volume element per (steradian * delta z)\n \n dVc <- dH*(1+z)^2*dA^2*fc(z)\n\n # light travel distance (M light years)\n\n dT <- numeric(nz)\n\n for (i in 1:nz) dT[i] <- 3.261564*dH*integrate(ft, lower=0, upper=z[i])$value\n\n list(dC=dC, dM=dM, dA=dA, dL=dL, dm=dm, dT=dT, dVc=dVc, Vc=Vc)\n}\n\n## Flux to luminosity over solar bolometric luminosity\n## note: solar bolometric luminosity is 3.839 e33 erg/sec.\n## note: I've also seen 3.827 e 33. Which is it??\n## 1 Mpc = 3.086 e24 cm\n## sdss fluxes are in units of 1e-17 erg/cm^2/sec\n## multiplying & dividing all the powers of 10 produces the net .01\n\nlum.sol <- function(flux, z, ...) {\n dL <- dcos(z, ...)$dL\n lum <- 4*pi*0.01*(3.085678)^2/3.839*flux*dL^2\n lum[lum<0] <- NA\n lum\n}\n\nloglum.ergs <- function(flux, z, ...) {\n dL <- dcos(z, ...)$dL\n lum <- 4*pi*(3.085678)^2*flux*dL^2\n lum[lum<0] <- NA\n 31+log10(lum)\n}\n\n\n## Transverse comoving distance from (ra, dec) to (z0, ra0, dec0)\n\ndtrans <- function(ra, dec, z0, ra0, dec0, ...) {\n dm <- dcos(z0, ...)$dM\n ra <- pi/180*ra\n dec <- pi/180*dec\n ra0 <- pi/180*ra0\n dec0 <- pi/180*dec0\n dx <- cos(ra)*cos(dec)-cos(ra0)*cos(dec0)\n dy <- sin(ra)*cos(dec)-sin(ra0)*cos(dec0)\n dz <- sin(dec)-sin(dec0)\n dm * sqrt(dx^2+dy^2+dz^2)\n}\n\n## angular diameter scale at z in kpc/arcsec\n\nascale <- function(z, ...) {\n dA <- dcos(z, ...)$dA*1000\n dA * tan(pi/(180*3600))\n}\n\n# velocity relative to a reference z = zbar\n\nvrel <- function(z, zbar) 299792.458*(z-zbar)/(1+zbar)\n", "meta": {"hexsha": "ab4a1f005038165a1c191249f16235f4f0e3730e", "size": 2620, "ext": "r", "lang": "R", "max_stars_repo_path": "R/cosmo.r", "max_stars_repo_name": "mlpeck/cosmo", "max_stars_repo_head_hexsha": "bf68c9ffa5eeb21c4bf214491ea20deb9ca60fd6", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "R/cosmo.r", "max_issues_repo_name": "mlpeck/cosmo", "max_issues_repo_head_hexsha": "bf68c9ffa5eeb21c4bf214491ea20deb9ca60fd6", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "R/cosmo.r", "max_forks_repo_name": "mlpeck/cosmo", "max_forks_repo_head_hexsha": "bf68c9ffa5eeb21c4bf214491ea20deb9ca60fd6", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.7826086957, "max_line_length": 79, "alphanum_fraction": 0.5770992366, "num_tokens": 1072, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9553191348157373, "lm_q2_score": 0.785308580887758, "lm_q1q2_score": 0.7502203140570675}} {"text": "########################################\n# An example of Rejection sampling\n# author: Alberto Lumbreras\n########################################\n\n# A gamma distribution\ndugly2 <- function(x) {\n dgamma(x, shape=20)\n}\n\n# A mixture of gammas\ndugly <- function(x) {\n 0.5*dgamma(x, shape=15) + 0.5*dgamma(x, shape=30)\n}\n\n# Proposal distribution \n#(the pretty one from which we how how to sample from)\nrproposal <- function(){\n rnorm(1, 22, 12)\n}\ndproposal <- function(x){\n dnorm(x, 22, 12)\n}\n\n# Scale factor to make the proposal be always above the target\nk <- 4\n\n# Plot the ugly distribution\nx <- seq(-10,75, by=0.1)\nplot(x, dugly(x), type='l', lwd=3, ylim=c(0,.15))\nlines(x, dproposal(x), col='red', lwd=2)\nlines(x, k*dproposal(x), col='red', lwd=3, lty=2)\ntitle(\"Rejection Sampling\")\n\n# Rejection sampler\n###########################\nnsamples <-100000\nsamples <- rep(NA,nsamples)\nfor(i in 1:nsamples){\n candidate <- rproposal()\n # accept with probabity (1/k)*p(candidate)/q(candidate)\n # k factor guarantees that there are no areas where samples are \n # automatically accepted (p/q > 1)\n if (runif(1)*(k*dproposal(candidate)) < dugly(candidate)){\n samples[i] <- candidate\n }\n}\n\nhist(samples, breaks=100, add=TRUE, probability = TRUE)", "meta": {"hexsha": "a72aa09ac50b4732af433f16f1859bd904830550", "size": 1243, "ext": "r", "lang": "R", "max_stars_repo_path": "examples/rejection.r", "max_stars_repo_name": "alumbreras/MCMC_intro", "max_stars_repo_head_hexsha": "a07022fb09b0cc65b7c4741917ee02364ec4c6b1", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "examples/rejection.r", "max_issues_repo_name": "alumbreras/MCMC_intro", "max_issues_repo_head_hexsha": "a07022fb09b0cc65b7c4741917ee02364ec4c6b1", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "examples/rejection.r", "max_forks_repo_name": "alumbreras/MCMC_intro", "max_forks_repo_head_hexsha": "a07022fb09b0cc65b7c4741917ee02364ec4c6b1", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2019-05-16T18:13:26.000Z", "max_forks_repo_forks_event_max_datetime": "2019-05-16T18:13:26.000Z", "avg_line_length": 25.3673469388, "max_line_length": 66, "alphanum_fraction": 0.6178600161, "num_tokens": 367, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9553191297273498, "lm_q2_score": 0.7853085834000791, "lm_q1q2_score": 0.7502203124611815}} {"text": "################################################################################\r\n# Demographic stochasticity in a simple Malthusian model \r\n# for a homogeneous population (i.e., without age/size/spatial structure).\r\n# by Giulio De Leo. First created in 2017, Updated in Dec. 2020\r\n################################################################################\r\n\r\n################################################################################\r\n# Learning goals\r\n################################################################################\r\n# Here we will learn to:\r\n# - simulate a small population whose abundance is described by integer numbers\r\n# - run the code in a smart way by using the binomial probability distribution \r\n# - replicate simulations one at a time\r\n# - replicate lot of simulations a large number of times\r\n# - speed up the computation by \"vectorizing\" the for loop for the replicates\r\n# - assess probability of extinction and quasi-extinction\r\n# - assess how these probability changes with time and initial conditions\r\n# - derive the probability distribution of the population at any given time step\r\n# - compute the average time to reach a quasi-extinction threshold \r\n################################################################################\r\n\r\n# Let's start by removing all previous variables from R's memory\r\nrm(list=ls(all=TRUE)) \r\n################################################################################\r\n\r\n################################################################################\r\n# Chunk 1: simulate the deterministic Malthusian growth\r\n################################################################################\r\n\r\n# Let's define model parameters for a semelparus, asexual, Malthusian population\r\nfec <- 2 # this is per-capita fecundity\r\nsigma <- 0.51 # this is probability of surviving to next time step\r\n\r\n# compute the finite growth rate:\r\n(lambda<- sigma*fec) \r\n\r\n# note that lambda is slightly larger than 1 so, we expect the population to\r\n# increase\r\n\r\n# For instance, we can compute the doubling time, from:\r\n# N(x) = 2*N(t=0) = N(t=0)*lambda^x\r\n# where \"x\" is the (unknown) time at which the population doubles in size, so is\r\n# twice as large as the initial population size at time t=0.\r\n# Dividing both sides by N(t=0), we get:\r\n# 2 = lambda^x\r\n# We then take the natural logarithm of each side \r\n# log(2) = x * log(lambda)\r\n# and solve for x, namely:\r\n# x = log(2)/log(lambda)\r\n\r\nlog(2)/log(lambda)\r\n\r\n# Let's now set initial condition and the length of the simulation window\r\nTmax <- 100 # simulation time\r\nNo <- 20 # initial conditions\r\nN <- numeric(Tmax) # set memory apart for the vector of pop. density\r\nN[1] <- No # assign the initial condition\r\n\r\n# now run the deterministic model...\r\nfor(t in (1:(Tmax-1))) { \r\n N[t+1] = lambda * N[t] }\r\n\r\n# and plot the result\r\nplot(N, type = \"l\", col = \"grey\", ylim=c(0,max(N)*1.5), lwd=5)\r\n\r\n################################################################################\r\n# Chunk 2: simulation of a Bernoulli trial\r\n################################################################################\r\n\r\n# Now, let's see how a stochastic simulation looks like.\r\n# \r\n# For simplicity, we will first simulate the stochastic dynamics of a \r\n# semelparous population where the individuals reproduces and then die.\r\n# We will track only females in the population, and assume that \"fec\" is the \r\n# (exact) number of female offspring/female, so, there is no stochasticity \r\n# in reproduction (We will later relax this hypothesis).\r\n# \r\n# Here we will assume that stochasticity is only in the survival process: \r\n# basically, we will flip a (slightly biased) coin to check whether it will be\r\n# able to survive to the next time step \r\n\r\nNs = numeric(Tmax) # initialize the vector for pop. density\r\nNs[1] = No # set the same initial conditions\r\n\r\n# Let set the seed for the random sequence to a common value, so we can all\r\n# have the same sequence:\r\nset.seed(3)\r\n\r\nfor (t in (1:(Tmax-1))) {\r\n\tNG = fec * Ns[t] \t# compute the number of recruits at this time step\r\n\tj = 0\t\t\t\t # initialize the variable\r\n\t\r\n\t # Here is where we simulate the Bernoulli trial\r\n\tfor(k in 1:NG) { # here we flip a coin for each new recruit in the population\r\n\t \r\n\t if (runif(1)<=sigma) j <- j+1 # in runif() is smaller than sigma, then this \r\n\t # individual survives, otherwise it does not \r\n\t}\r\n\tNs[t+1] <- j \t\t# this is the overall number of individual that survived\r\n\tif (j==0) break\r\n}\r\n\r\n# now plots the result, along with that of the deterministic model\r\n\r\npoints(Ns, type = \"l\", col = sample(colors(),1))\r\n\r\n# Repeat the exercise by running again the for cycle (but do NOT run the\r\n# set.seed(3) line again!) and plotting the results. Because you get a different\r\n# sample of random numbers, you should get each time a different\r\n# demographic trajectory\r\n\r\n\r\n################################################################################\r\n# Chunk 3: The Binomial distribution\r\n################################################################################\r\n\r\n# There is a way much faster than flipping a coins for each individual to\r\n# determine who dies or survives: we can use the *binomial*\r\n# distribution and the random generation rbinom() function in R, to simulate\r\n# a sequence o Bernoulli trial is just one strike\r\n# \r\n# For instance, if I want to flip an unbiased coin just one time (i.e., the\r\n# Bernoulli trial), this is how I do it:\r\n# \r\nrbinom(n = 1, size = 1, prob = 0.5)\r\n\r\n# If I want to do it 4 times:\r\nrbinom(n = 4, size = 1, prob = 0.5) \r\n\r\n# If I have 10 coins, I flip them all and I want *to count* how many heads, \r\n# I can do it in this way:\r\nrbinom(n = 1, size = 10, prob = 0.5) \r\n\r\n# this is equivalent to say that I have 10 individuals in the population and\r\n# I want to check how many of them survive, by using their specific \r\n# survival to the next time step\r\n\r\n# so, let's now use \"rbinom\" to re-run our simulations\r\nNs <- Ns*0 # re-set to zero all the elements on Ns\r\nNs[1] <- No\r\n# plot first the deterministic simulations\r\nplot(N, type = \"l\", col = \"grey\", ylim = c(0,max(N, Ns)), lwd=5)\r\n\r\n# in the case of our Malthusian model, this is how we change the code:\r\nset.seed(3) \r\n\r\n\r\nfor(t in (1:(Tmax-1))) {\r\n\tNG <- fec * Ns[t]\r\n\tNs[t+1] <- rbinom(1,NG,sigma)\r\n\tprint(c(t, NG, Ns[t+1]))\r\n\tif (Ns[t+1]==0) {break}\r\n}\r\npoints(Ns, type = \"l\", col = sample(colors(),1))\r\n\r\n# so, each time we generate a different realization of the stochastic process.\r\n\r\n################################################################################\r\n# Chunk 4: Replicates\r\n################################################################################\r\n\r\n# now, let's repeat this exercise a number of times, for instance 10\r\nNrep <- 10 # number of replicates\r\nNr <- matrix(0, nrow = Tmax, ncol=Nrep) # initialize the matrix\r\nNr[1,] <- No # set the the initial conditions \r\nng <- 0 # this is a dummy variable to temporary store the number \r\n # of new recruits\r\n\r\nfor (r in 1:Nrep) { # two nested for loops\r\n\tfor (t in (1:(Tmax-1))) {\r\n\t\tng <- fec * Nr[t,r]\r\n\t\tNr[t+1,r] <- rbinom(1,ng,sigma)\r\n\t}\r\n}\r\n\r\n# print the results, 10 years for the first 5 replicates\r\nNr[1:10, ]\r\n\r\n\r\n# and plot these replicates\r\nmatplot(Nr, type = \"l\")\r\npoints(N, type = \"l\", col = \"grey\", lwd=4)\r\n\r\n################################################################################\r\n# Note that in some replicates the population grows, in others it vanishes. We\r\n# can compute# the number of times the population goes extinct and divide for\r\n# the total number of times we replicated this exercise. In order to get a\r\n# robust statistics not overly affected by the stochastic nature of the process,\r\n# we have to repeat this exercise a very large number of times, at least 1,000\r\n# or more...\r\n\r\nNrep <- 10000 # number of replicates\r\nNr <- matrix(0, nrow = Tmax, ncol=Nrep) # set memory aside\r\nNr[1,] <- No #initial conditions\r\n\r\n# in this case, let's track precisely the time required to compute \r\n# the 10,000 simulations of 100 years each. In order to do so, we use the \r\n# R function system.time. The reasons will be clear in a moment\r\n\r\nsystem.time(\r\nfor (r in 1:Nrep) {\r\n\tfor (t in (1:(Tmax-1))) {\r\n\t\tng <- fec * Nr[t,r]\r\n\t\tNr[t+1,r] <- rbinom(1,ng,sigma)\r\n\t}\r\n}\r\n)\r\n\r\n# and write down the computation time (it was about 17 seconds \r\n# on my old laptop and now it is only 2.29 !)\r\n# Note also that above we have two nested for-loops: \r\n# - the internal one is for the recursive equation to cycle through time\r\n# - the external one is to replicate the exercise Nrep times\r\n################################################################################\r\n\r\n################################################################################\r\n# Chunk 5: Vectorizing\r\n################################################################################\r\n\r\n# there is a way to speed up these computations a lot, i.e.\r\n# by \"vectorizing\" the replicates. First we define the dummy variable: \r\n# first we reset the matrix to store the results.\r\nNr <- matrix(0, nrow = Tmax, ncol=Nrep) \r\n\r\n# and assign again the initial conditions\r\nNr[1,] <-No \r\n\r\n# we also create a dummy vector to temporary store the number of recruits for\r\n# each of the NRep replicates at a specific time step\r\nNG <- matrix(0, nrow = 1, ncol=Nrep) \r\n\r\n# and run the model again, but this time with only *one* (1) for-loop!\r\nsystem.time(\r\nfor(t in (1:(Tmax-1))) {\r\n # these is how simple is to run all the replicates altogether: we select a row\r\n # of Nr, multiply for fecundity and assign the result to the dummy vector\r\n\tNG <- fec * Nr[t,] \r\n\t\r\n\t# then, we extract for each of the Nrep replicate how many individuals survive \r\n\tNr[t+1,] <- rbinom(NG,NG,sigma) \r\n}\r\n)\r\n\r\n# check the time: the vectorize computation should take substantially less than\r\n# the two nested cycles\r\n################################################################################\r\n\r\n################################################################################\r\n# Chunk 6: Demographic Stochasticity in the number of offaspring\r\n################################################################################\r\n\r\n# So far, we assumed that demographic stochasticity is only about the discrete\r\n# number of individuals that survive to the next generation. With the notable\r\n# exception of broadcast spawners, which are actually quite common in the\r\n# marine environment, marine mammals and elasmobranch produce only few\r\n# offsprings.\r\n# \r\n# If you have precise information on the distribution probability of number of\r\n# offspring generated by a mother, then it is worth using it. For grey reef\r\n# shark, for instance, the number of offspring ranges between 2 and 6, with\r\n# probability 0.3,0.4,0.2,0.1 of generating 3, 4, 5 and 6 baby shark\r\n# respectively. For Leopard shark, the mean is about 20 +/- 7 (SD). \r\n# Anyway, when information on the exact range and probability distribution is\r\n# lacking, ecologists often use the discrete Poisson (as a side note, for the\r\n# majority of marine organisms that are broadcast spawner and produce a large\r\n# number of eggs at each reproductive event, environmental stochasticity is\r\n# probably more relevant, or the number of individuals that are actually\r\n# reproducing). \r\n# We can simulate demographic stochasticity by using, for instance a Poisson\r\n# distribution \"rpois(n,lambda)\" with lambda=fec and n = Nr, i.e., the number of\r\n# individual in the population at a given time t. Accordingly, we can change\r\n# the r line:\r\n# NG <- fec * Nr[t,]\r\n#\r\n# with: \r\n# NG <- sum(rpois(Nr[t,],fec))\r\n#\r\n# Note that the larger Nr[t,], the better is the mean approximation NG = fec *\r\n# Nr[t,] As usual, it is a small population size that demographic stochasticity\r\n# plays a very relevant role.\r\n\r\n\r\n# and assign again the initial conditions\r\nNr[1,] <-No \r\n\r\n# and run the model again, but this time with only *one* \"for-loop\"!\r\nsystem.time(\r\n for(t in (1:(Tmax-1))) {\r\n # these is how simple is to run all the replicates altogether: we select a\r\n # row of Nr, multiply for fecundity and assign the result to the dummy\r\n # vector\r\n NG <- sapply(Nr[t,], function(z) {sum(rpois(z,fec))}) \r\n \r\n # then, we extract for each of the Nrep replicate how many individuals\r\n # survive\r\n Nr[t+1,] <- rbinom(NG,NG,sigma) \r\n }\r\n)\r\n\r\nmatplot(Nr, type = \"l\")\r\npoints(N, type = \"l\", col = \"grey\", lwd=4)\r\n\r\n\r\n################################################################################\r\n# Extinction probability\r\n################################################################################\r\n\r\n# now, let's finally compute the probability of extinction in 100(=Tmax) years\r\nNend <- Nr[Tmax,]# extract the last row\r\n\r\n# this tells us in which specific replicate the population got extinct \r\nwhich(Nend==0) \r\n\r\n# well... you see, they are way too many...\r\nlength(which(Nend==0)) # let's just track how many got extinct\r\n\r\n#this should be simply equal to Nrep, in fact I could have used Nrep directly\r\n#whatever, now we can compute what the fraction of replicates in which the\r\n#population got extinct - which is our probability of extinction after Tmax\r\n#years\r\nlength(Nend) \r\n\r\next.prob <- length(which(Nend==0))/length(Nend); ext.prob*100 \r\n\r\n\r\n################################################################################\r\n# Quasi extinction threshold\r\n################################################################################\r\n\r\n# A comment: extinction is just extinction, no doubt about this, zero\r\n# individual, period. But if the population drops below a very low number, say\r\n# 10 individuals, it is not going to be good anyway, because we do not want to\r\n# wait for the population to actually go extinct to take action, but we shall\r\n# move way before.... So, it might be important to compute not just the\r\n# probability to drop to zero, but the probability to drop below a given\r\n# population threshold. This is not true extinction, and that's why we call\r\n# these thresholds>0 \"quasi-extinction thresholds\" So, let's compute the\r\n# quasi-extinction risk first, let's define a wide range of quasi extinction\r\n# thresholds\r\n# \r\nqet <- seq(0,max(Nend), by = 1) \r\n\r\n# then define the function to compute the quasi extinction risk \r\nqetf <- function (qet) length(which(Nend<=qet))/length(Nend)\r\n\r\n# then \"apply\" this function for each \"qet\", namely: \r\next.prob <- sapply(qet, qetf) # NB sapply uses a vector and returns a vector\r\nplot(ext.prob~qet, type = \"l\", ylim = c(0,1), \r\n xlab = \"quasi-extinction threshold\",\r\n ylab = \"probability\") # natural scale\r\n\r\n# we are actually more interested to derive probability of extinction at low\r\n# abundances so, let's plot this graph in a semilogarithic scale\r\nplot(ext.prob~qet, type = \"l\", log = \"x\") \r\n\r\n# compute mean population size at each time step (i.e. the mean of each row). \r\n# The \"apply\" function applies the function \"mean\" to each row (margin = 1) of\r\n# the matrix Nr\r\nNmean <- apply(Nr, MARGIN=1, mean) \r\nplot(Nmean) # this is the mean at time t for the Nrep replicates\r\npoints(N, type = \"l\", col = \"red\") # this was the deterministic solution!\r\n# you can see that with so many replicates, the mean of the stochastic process\r\n# overlaps closely to the deterministic solution, as it should be\r\n\r\n# So, expected population size increases in a Malthusian way \r\n\r\n\r\n################################################################################\r\n# Time to Extinction\r\n################################################################################\r\n\r\n# Question:\r\n# Does it mean that the extinction risk decreases with time?\r\n# well, let's see it...\r\n\r\n# let's define a function to compute, at each time step (each row of the matrix\r\n# Nr) the fraction of replicates in which the population got extinct (zero\r\n# individuals):\r\n\r\nroe.f <-function (Nvect) length(which(Nvect==0))/Nrep\r\n\r\n# let's apply this function to each row of Nr (MARGIN = 1)\r\nroe <- apply(Nr, MARGIN = 1, roe.f) \r\nplot(roe, xlab = \"time\", ylab = \"risk of extinction\")\r\n\r\n\r\n# Multiple choice test (select the right answer)\r\n# while the mean population size increases, the risk of extinction : \r\n# a) also increases with time\r\n# b) decreases with time\r\n# c) remains constant with time\r\n# \r\n\r\n################################################################################\r\n# densoty distribution \r\n################################################################################\r\n\r\n# another interesting statistic is in fact the population size distribution at\r\n# any given time step\r\ngf <- par(mfrow=c(3,2), mai = c(0.3,0.35,0.25,0.25)) \r\nhist(Nr[5,]) # here it is population size distribution at year 5 \r\nhist(Nr[10,]) # here it is population size distribution at year 10 \r\nhist(Nr[20,]) # ...and so on and so for\r\nhist(Nr[30,])\r\nhist(Nr[40,])\r\nhist(Nr[Tmax,])\r\n\r\npar(gf)\r\n# we might be interested to compute some statistical property of this\r\n# distribution for instance the quantiles at each time step\r\nq0.975 = apply(Nr, 1, quantile, probs = 0.975)\r\nq0.025 = apply(Nr, 1, quantile, probs = 0.025)\r\nq0.750 = apply(Nr, 1, quantile, probs = 0.75)\r\nq0.250 = apply(Nr, 1, quantile, probs = 0.25)\r\n\r\n# and then make a plot of it \r\nplot(q0.975, type = \"l\", col = \"grey\", lwd=2, xlab=\"time\")\r\npoints(q0.025, type = \"l\", col = \"grey\", lwd=2)\r\npoints(q0.750, type = \"l\", col = \"green\", lwd=2)\r\npoints(q0.250, type = \"l\", col = \"green\", lwd=2)\r\npoints(Nmean, type = \"l\", col = \"red\", lwd = 4)\r\n\r\n# this is a nicer way to plot it (although, with ggplot2 now you can do so much\r\n# better!)\r\n\r\nxt = seq(1,Tmax, by=1)\r\nplot(Nmean, type = \"l\", col = \"red\", lwd = 4, ylim= c(0,max(q0.975)))\r\npolygon(c(xt, rev(xt)),c(q0.025, rev(q0.975)), col=\"light gray\", border = NA)\r\npolygon(c(xt, rev(xt)),c(q0.250, rev(q0.750)), col=\"dark gray\", border = NA)\r\npoints(Nmean, type = \"l\", col = \"red\", lwd = 4) # redraw the data\r\naxis(1, xlim=c(1,Tmax+1)) # redraw the x axis\r\n \r\n################################################################################\r\n# Finally, let's compute the time to reach a quasi extinction threshold\r\n################################################################################\r\n# we have to find for each replicate the time at which the pop.size drops below\r\n# a \"quasi-extinction threshol\" (qet) and pick up the first one in the list,\r\n# namely the first time the population reached the quasi extinction threshold:\r\nttqetf1 <- function(Nsim, qet) which(Nsim<=qet)[1] \r\n\r\n# here we set the quasi extinction threshold for instance to 1, instead of zero \r\nttqet <- apply(Nr, MARGIN=2,ttqetf1, qet=1) \r\n\r\n# \"ttqet\" is a vector whose elements report for each replicate the time when the\r\n# population reached the quasi-extinction threshold, if ever!: if, within a\r\n# specific replicate, the population never reached the quasi-extinction\r\n# threshold, the function returns NA\r\n\r\n# we can now compute the statistical properties of the distribution of the time\r\n# taken to drop at or below \"qet\". Note that na.rm is to remove \"NA\" values.\r\nquantile(ttqet, na.rm = TRUE) \r\n\r\n# manually change qet to 1, 2, etc., to see how time to extinction change \r\n\r\n# now let's do it in one shot for all the \"qet\" of interest\r\n# Let's look just at the time taken for the population to drop at or below a \r\n# threshold between 0 and 9:\r\nttqetf2 <- function(qet) apply(Nr, 2,ttqetf1, qet=qet)\r\nqet <- seq(0,9, by=1) \r\nttqet.all <- sapply(qet, ttqetf2) # apply this function for each threshold\r\ntime.quantile <- apply(ttqet.all, 2, quantile, na.rm = TRUE); time.quantile\r\n\r\n# and plot the result\r\nplot(time.quantile[5,]~qet, type = \"l\", ylim=c(0,Tmax+1), col=\"black\", \r\n ylab=\"Time to quasi extinction threshold\", xlab=\"quasi-exctintion threshold\")\r\npoints(time.quantile[4,]~qet, type = \"l\", col=\"green\")\r\npoints(time.quantile[3,]~qet, type = \"l\", col=\"red\", lwd=4)\r\npoints(time.quantile[2,]~qet, type = \"l\", col=\"green\")\r\npoints(time.quantile[1,]~qet, type = \"l\", col=\"black\")\r\n\r\n################################################################################\r\n# check whether the extinction probability depends upon the initial conditions,\r\n# i.e. the initial number of individual in the population\r\n################################################################################\r\n\r\n# here below is the function to generate random deviates of number of offspring\r\n# generated by a grey reef shark\r\nfv <- c(3,4,5,6)\r\nfp <- c(0.3, 0.4, 0.2, 0.1)\r\nfv[sample.int(n=4, size =1, prob = fp)]\r\nxv <- sapply(1:1000, function(z){fv[sample.int(n=4, size =1, prob =fp)]})\r\nmean(xv)\r\n\r\n\r\n \r\n\r\n", "meta": {"hexsha": "bd4136e61e29663e2da8f0c7bb81f545360aea8e", "size": 20751, "ext": "r", "lang": "R", "max_stars_repo_path": "demographic_stochasticity/demographic_stochasticity.r", "max_stars_repo_name": "elahi/bio143", "max_stars_repo_head_hexsha": "b434984dd5a1d77d451264bee6d568de973a7c32", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "demographic_stochasticity/demographic_stochasticity.r", "max_issues_repo_name": "elahi/bio143", "max_issues_repo_head_hexsha": "b434984dd5a1d77d451264bee6d568de973a7c32", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "demographic_stochasticity/demographic_stochasticity.r", "max_forks_repo_name": "elahi/bio143", "max_forks_repo_head_hexsha": "b434984dd5a1d77d451264bee6d568de973a7c32", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 42.6098562628, "max_line_length": 81, "alphanum_fraction": 0.5956821358, "num_tokens": 5135, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9124361604769414, "lm_q2_score": 0.822189123986562, "lm_q1q2_score": 0.7501950874761986}} {"text": "# Matrix operators for population models\n# place in R 'Resources/R/' folder\n\n## maximum lambda function\nmax.lambda <- function(x) Re((eigen(x)$values)[1]) ## where 'x' is a Leslie matrix\n\n## Maximum r function\nmax.r <- function(x) log(Re((eigen(x)$values)[1])) ## where 'x' is a Leslie matrix\n\n## Stable stage distribution\nstable.stage.dist <- function(x) ((x %*% (Re((eigen(x)$vectors)[,1])))/(sum((x %*% (Re((eigen(x)$vectors)[,1]))))))[,1]\n\n## Generation length function\nR.val <- function(X,age.max) ## reproductive value (R0) where X = Leslie matrix; age.max = maximum age of females\n{\t\t\n\t\t## define the transition matrix\n\t\tT <- X[1:age.max,1:age.max]\n\t\tT[1,1:(age.max)] <- 0\n\n\t\t## define the fertility matrix\n\t\tF <- X[1:age.max,1:age.max]\n\t\tdiag(F[2:age.max,1:(age.max-1)]) <- 0\n\n\t\t## define the identity matrix\n\t\tI <- matrix(data<-0,nrow<-age.max,ncol<-age.max)\n\t\tdiag(I) <- 1\n\n\t\t## define the fundamental matrix\n\t\tlibrary(MASS)\n\t\tN.fund <- ginv(I-T)\n\n\t\t## define the reproductive matrix\n\t\tR <- F %*% N.fund\n\n\t\t## define R0 (number of female offspring produced per female during lifetime)\n\t\tR0 <- Re((eigen(R)$values)[1])\n\t\t\n\t\t## output\n\t\tprint(\"number of female offspring produced per female during its lifetime\")\n\t\tprint(\"_________________________________________________________________\")\n\t\tprint(R0)\n\n}\n\n## Mean generation time function\nG.val <- function (X,age.max) ## where X is a Leslie Matrix\n{\t\n\t\tG <- (log(R.val(X,age.max)))/(log(Re((eigen(X)$values)[1])))\n\t\tprint(\"mean generation time\")\n\t\tprint(\"____________________\")\n\t\tprint(G)\n}\n", "meta": {"hexsha": "61a607a02f96c934a1532e9b7005b5fb51b64d68", "size": 1550, "ext": "r", "lang": "R", "max_stars_repo_path": "matrixOperators.r", "max_stars_repo_name": "cjabradshaw/KangarooPopModel", "max_stars_repo_head_hexsha": "6753a2843b96d54658d7cb2c0daa4197128585cd", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-10-06T03:16:33.000Z", "max_stars_repo_stars_event_max_datetime": "2021-10-06T03:16:33.000Z", "max_issues_repo_path": "matrixOperators.r", "max_issues_repo_name": "cjabradshaw/KangarooPopModel", "max_issues_repo_head_hexsha": "6753a2843b96d54658d7cb2c0daa4197128585cd", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "matrixOperators.r", "max_forks_repo_name": "cjabradshaw/KangarooPopModel", "max_forks_repo_head_hexsha": "6753a2843b96d54658d7cb2c0daa4197128585cd", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 29.2452830189, "max_line_length": 119, "alphanum_fraction": 0.66, "num_tokens": 466, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9489172615983309, "lm_q2_score": 0.7905303162021596, "lm_q1q2_score": 0.750147862861016}}