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Suppose my sample comprises 350 instances. Each instance has two independent binary (pos and neg) evaluations, A and B. If my alternative hypothesis is that A is more often positive than B, how would I express whether the difference is statistically significant?
To be more precise on the data: This question came to mi... |
In a data set with thousands of data points, I am testing different short-term and longer term data outputs based on 5 rolling data points all the way to 100 rolling data points (which each value being a separate column in excel: 5, 6,..., 100).
The test I developed (with rudimentary knowledge of the whole thing) is t... |
The input is a bunch of numbers. How can I calculate a threshold that there are 10% of the totally amount of numbers are above this threshold. I think this is equally as to calculate the distribution function, but what I need is the threshold number, not the
|
Using Pearson's Correlation Coefficient, I have several variables that are highly correlated ($\rho = 0.978$ and $\rho = 0.989$ for 2 pairs of variables that are in my model).
The reason some of the variables are highly correlated is because one variable is used in the calculation for another variable.
Example:
$B = V ... |
Disclaimer: I posted this question on Stackoverflow, but I thought maybe this is better suited for this platform.
How do you test your own k-means implementation for multidimensional data sets?
I was thinking of running an already existing implementation (i.e., Matlab) on the data and compare the results with my algori... |
I have a data frame like this
User OS
A Windows
A Linux
B MacOS
C Linux
C FreeBSD
C Windows
D Windows
What I want to do is plot two types of statistics.
The share of users with different number of OSs. So, it would be the fraction of the users with 1 OS, with OS ... |
Are there any good papers or books dealing with the use of coordinate descent for L1 (lasso) and/or elastic net regularization for linear regression problems?
|
What are the pros and cons of using LARS [1] versus using coordinate descent for fitting L1-regularized linear regression?
I am mainly interested in performance aspects (my problems tend to have N in the hundreds of thousands and p < 20.) However, any other insights would also be appreciated.
edit: Since I've posted th... |
I am given 15 points. The control limits are at +/- 3 $\sigma$. Points 1, 4, 5, 6, 7, 8, 9, 10, 11, 13, and 15 fall within the control limits. Points 2, 3, 12, and 14 are outside of the control limits, with 2 being below the lower control limit and 3, 12, and 14 being above the upper control limit.
How do I know if po... |
The fisher linear classifier for two classes is a classifier with this discriminant function:
$h(x) = V^{T}X + v_0$
where
$V = \left[ \frac{1}{2}\Sigma_1 + \frac{1}{2}\Sigma_2\right]^{-1}(M_2-M_1)$
and $M_1$, $M_2$ are means and $\Sigma_1$,$\Sigma_2$ are covariances of the classes.
$V$ can be calculated easily but t... |
I posted a question earlier but failed miserably in trying to explain what I am looking for (thanks to those who tried to help me anyway). Will try again, starting with a clean sheet.
Standard deviations are sensitive to scale. Since I am trying to perform a statistical test where the best result is predicted by the lo... |
If two classes $w_1$ and $w_2$ have normal distribution with known parameters ($M_1$, $M_2$ as their means and $\Sigma_1$,$\Sigma_2$ are their covariances) how we can calculate error of the Bayes classifier for them theorically?
Also suppose the variables are in N-dimensional space.
Note: A copy of this question is als... |
I am trying to estimate parameters of a two dimensional Normal distribution using Gibbs sampling. While it was very easy transform the posterior equation for mean vector to a single dimension normal function for sampling, I am not able to same for sigma(covariance).
Do I need to use the Wishart distribution as prior an... |
If $X_i$ is exponentially distributed $(i=1,...,n)$ with parameter $\lambda$ and $X_i$'s are mutually independent, what is the expectation of
$$ \left(\sum_{i=1}^n {X_i} \right)^2$$
in terms of $n$ and $\lambda$ and possibly other constants?
Note: This question has gotten a mathematical answer on https://math.stackexch... |
Unlike other articles, I found the wikipedia entry for this subject unreadable for a non-math person (like me).
I understood the basic idea, that you favor models with fewer rules. What I don't get is how do you get from a set of rules to a 'regularization score' which you can use to sort the models from least to most ... |
All of my variables are continuous. There are no levels. Is it possible to even have interaction between the variables?
|
The matrix could be as large as $2500\times 2500$, what is the best algorithm to do that, is there some algorithm that is easy to write a program, is there any convenient packages for that?
|
I am a novice in statistics so please correct me if I am doing something fundamentally wrong. After wrestling for a long time with R in trying to fit my data to a good distribution, I figured out that it fits the Cauchy distribution with the following parameters:
location scale
37.029894 18.678936
( 3.... |
I'm in no way a statistician (I've had a course in mathematical statistics but nothing more than that), and recently, while studying information theory and statistical mechanics, I met this thing called "uncertainty measure"/"entropy". I read Khinchin derivation of it as a measure of uncertainty and it made sense to me... |
What open-source implementations -- in any language -- exist out there that can compute lasso regularisation paths for linear regression by coordinate descent?
So far I am aware of:
glmnet
scikits.learn
Anything else out there?
|
I am using SVM-light with Matlab, for linear SVM. I would like to understand the output model, but I cannot find any documentation or help about it.
Here is the output:
sv_num: 639
upper_bound: 547
b: 1.4023
totwords: 576
totdoc: 2000
loo_error: -1
loo_recall: -1
loo_prec... |
I must have generated at least 5 Q-Q plots until now when trying to fit my data into a known distribution but I just noticed something that I could not understand. In the figure shown below, from what I've read from the wiki, X-axis is supposed to read "Negative Binomial Theoretical Quantiles" and Y-axis is supposed to... |
Suppose we have a distribution for $\mathbf{x}\in \{-1,1\}^n$ and are interested in representing $p(\mathbf{x})$ as a linear exponential family with sufficient statistics of the form $1,x_1,x_2,\ldots,x_1 x_2,\ldots,x_1 x_2 \cdots x_n$
Suppose we know that entropy some measure of complexity of target distribution is b... |
My data consists of individual level observations nested within countries over time. I would like to use multilevel models along with some sort of selection model.
I have three related questions.
1) Are there any issues or concerns with using a Heckman selection model twice?
I have a model with two selection stages.... |
I want to implement (in R) the following very simple Dynamic Linear Model for which I have 2 unknown time varying parameters (the variance of the observation error $\epsilon^1_t$ and the variance of the state error $\epsilon^2_t$).
$
\begin{matrix}
Y_t & = & \theta_t + \epsilon^1_t\\
\theta_{t+1} & = & \theta_... |
I'm using AIC (Akaike's Information Criterion) to compare non-linear models in R. Is it valid to compare the AICs of different types of model? Specifically, I'm comparing a model fitted by glm versus a model with a random effect term fitted by glmer (lme4).
If not, is there a way such a comparison can be done? Or is th... |
I recently came across the following paper: "Stochastic Methods for $\ell_1$ Regularized Loss Minimization" by Shai Shalev-Shwartz and Ambuj Tewari, ICML 2009.
In the paper, the authors propose a modification of the coordinate descent algorithm for the LASSO in which the coordinates (the $\beta$s) are updated in a ran... |
What is the Unscented Kalman Filter and when is it used in preference to other types of filters?
edit: I find the Wikipedia explanation a bit too technical to be readily understood.
|
The following piece of Perl code randomly maps a set of ranges onto a circumference of a circle. In the example, the circumference is of length 1000 and legal ranges are e.g. (0,8)=0,1,2,...,8 and (995,2)=995,996,...,999,0,1,2 (i.e. zero-based coordinates; both start and end are inclusive).
I take some arbitrary positi... |
I have a plot I'm making in ggplot2 to summarize data that are from a 2 x 4 x 3 celled dataset. I have been able to make panels for the 2-leveled variable using facet_grid(. ~ Age) and to set the x and y axes using aes(x=4leveledVariable, y=DV). I used aes(group=3leveledvariable, lty=3leveledvariable) to produce the ... |
Kernel density estimator is given by
$$\hat{f}(x,h)=\frac{1}{nh}\sum_{i=1}^{n}K(\frac{x-X_{i}}{h})$$
where $X_1,...X_n$ i.i.d with some unknown density $f$, $h$ - bandwith,
$K$ - kernel function (
$\int_{-\infty}^{\infty}K(x)dx=1$,
$\int_{-\infty}^{\infty}K(x)xdx=0$,
$\int_{-\infty}^{\infty}K(x)x^2dx<\infty$).
Th... |
N=2762
I've been exploring a data set that seems to give rise to this kind of plot rather frequently. Would you say this is one population with a different than normal population? Or are two populations confounding the normal distribution?
It used matplotlib and scipy.stats:
(x,y), (slope, inter, cor) = stats.pr... |
I am interested in learning (and implementing) an alternative to polynomial interpolation.
However, I am having trouble finding a good description of how these methods work, how they relate, and how they compare.
I would appreciate your input on the pros/cons/conditions under which these methods or alternatives would ... |
I'm trying to compute some p-values for samples from a distribution of sums of ~1000 random variables. The exact distribution of these random variables isn't known, but I have empirical estimates that I think are pretty accurate.
So far I've been using the central limit theorem to produce a normal approximation for thi... |
Is there any comprehensive reference on (or introduction to) how people have tried to model non-independent random variables? I already know about mixing processes, which express in various ways according to various coefficients how "future" events depend on "past" events, but that's about it...
|
Suppose we have a simple linear regression model $Z = aX + bY$ and would like to test the null hypothesis $H_0: a=b=\frac{1}{2}$ against the general alternative.
I think one can use the estimate of $\hat{a}$ and $SE(\hat{a})$ and further apply a $Z$-test to get the confidence interval around $\frac{1}{2}$. Is this ok?... |
What is the difference between data mining, statistics, machine learning and AI?
Would it be accurate to say that they are 4 fields attempting to solve very similar problems but with different approaches? What exactly do they have in common and where do they differ? If there is some kind of hierarchy between them, what... |
I have a study which gives the hazard ratios for certain interventions like:
Intervention 1, HR: .9
Intervention 2, HR: .8
...
Is there any way in which I could predict the relative risk for e.g. someone who has intervention 1 and 2?
I think if I assume that the interventions are independent, then the HR of doing bo... |
I'm experimenting with R and found that an anova() needs an object of type lm. But why should I continue with an anova after this:
> x <- data.frame(rand=rnorm(100), factor=sample(c("A","B","C"),100,replace=TRUE))
> head(x)
rand factor
1 0.9640502 B
2 -0.5038238 C
3 -1.5699734 A
4 -0.8422324 ... |
For classification, what theoretical results are between cross-validation estimate of accuracy and generalisation accuracy?
I particularly asking about results in a PAC-like framework where no assumptions are made that your function class contains the "true" function.
I would love to know if there are theorems of the f... |
So, I have 16 trials in which I am trying to authenticate a person from a biometric trait using Hamming Distance. My threshold is set to 3.5. My data is below and only trial 1 is a True Positive:
Trial Hamming Distance
1 0.34
2 0.37
3 0.34
4 0.29
5 0.55
6 0.47
7 0.47
8 0.32
9 0.39
10 0.45
11 0.42
... |
I'm currently looking at the unconstrained primal form of the one-vs-all classifier
$$\sum\limits_{i=1}^{N_I} \sum\limits_{k=1,\atop k \neq y_i}^{N_K} L(1+ \mathbf{w_k}\cdot\mathbf{x_i}-\mathbf{w_{y_i}}\cdot\mathbf{x_i})$$
where
$N_I$ is the number of instances,
$N_K$ is the number of classes,
$N_F$ is the number of... |
Consider a series like CPI (inflation), which I know is composed of a series of component prices (e.g. meat prices, grain prices, non-food prices, etc.), which in turn are also composed of a series of component prices (e.g. average meat prices are a combination of pork, beef, and chicken prices).
If I wanted to use a r... |
I have a time serie that I want to analyse through a wavelet decomposition.
I am using the R package WaveThres.
I am interested in the wavelet autocorrelation, but I struggle to understand what does it mean precisely.
I have from the book Wavelet Methods in Statistics with R the following formula
$\Psi_j(\tau)=\sum... |
Let $A$ be a finite set and suppose we want to compute the size of some subset $X$.
Motivation: If we can generate elements $x$ of $A$ uniformly at random, then we can estimate the size of $A$ by random sampling. That is, we take $n$ random samples from $A$, if $m$ of them belong to $X$, then $|X|/|A| \approx m/n$. U... |
Say we are studying Twitter hashtags over time. We monitor how popular they are day to day. Some hashtags may be volatile (i.e. "lunch", "Celtics", "Friday"). Their popularity rises and falls frequently. Some hashtags may be in the process of becoming unpopular (i.e. "Gulf oil spill", "Transformers 2", "Christine O'... |
Given the support vectors of a linear SVM, how can I compute the equation of the decision boundary?
|
In a social experiment that I was conducting, I was trying to count the number of people each user contacted in a period of 10 days. The population size was 100 for the experiment. Based on the values that I calculated, I fit a negative binomial distribution to the data (the Q-Q plot is given below).
Conventional wisdo... |
I have data points from a half circle and I already know the radius. I want to find the circle which best fits the points using a fixed radius. How can I do this? If I solve the problem using a typical circle fit algorithm the radius is too unstable due to "noise".
|
I want to find $\theta$ such that
$ \theta = argmin_{\theta} \left( \left|\left| Y - \sum_{i=1}^k \theta_i X_i \right|\right| \right) $
where $X_i$ and $Y$ are N x N matrices and $\theta$ is a weight vector that specifies how to linearly combine the $k$ $X$'s to approximate Y.
This smells like a linear optimization pr... |
If we have a loaded coin that plays out 75% heads, 25% tails, what would be the best way to bet on the outcome of each of $n$ trials? How could we maximize our probability of winning?
Is it possible to generalize for a coin that's loaded $n:(100-n)$?
|
I have a data-frame whose first column is the name of an item and the second column is the frequency of that item in the dataset.
names freq
1 tomato 7
2 potato 4
3 cabbage 5
4 sukuma-wiki 8
5 terere 20
I would like to have a stacked bar column that depicts the ... |
I'm trying to implement the hit and run MCMC algorithm, but I'm having a bit of trouble understanding how to go about it. The general idea, is as follows:
To generate a proposal jump in MH, we:
Generate a direction $d$ from a
distribution on the surface of the
unit sphere $\mathcal{O}$
Generate
a signed dist... |
Sorry for a possibly ignorant question.
I have fit a mixed-effects model using the lmer function from the lme4 package, and the main fixed effect (a factor with three levels) in the model was significant according to a run with pvals.fnc (from the languageR package).
To illustrate the effect in an appealing way, I woul... |
I have some data which describe residential units for people with learning disability, variables like how nice the furnishings are, the level of psychiatric symptomology on the unit, how happy the staff are, stuff like that.
I want to check to see if we are measuring the right things- e.g. do units with happier staff h... |
As the headline suggest, I am looking for a java library for learning and inference of Bayesian Networks. I have already found some, but I am hoping for a recommendation.
Requirements in a quick overview:
written in Java (my overlord tells me that this is no point of discussion)
configuration is possible via code (and... |
The signal to noise ratio is simple, and is usually defined in the context of simple Gaussian local-level models. In the cause of non-gaussian signal or noise models, do people do things more complicated then the ratio of the variances of the two distributions?
|
There are numerous procedures for functional data clustering based on orthonormal basis functions. I have a series of models built with the GAMM models, using the gamm() from the mgcv package in R. For fitting a long-term trend, I use a thin plate regression spline. Next to that, I introduce a CAR1 model in the random ... |
The R package dlm implements filtering and smoothing (dlmFilter and dlmSmooth) for models with regression effects, but forecasting is not (yet) available for these models:
mod <- dlmModSeas(4)+dlmModReg(cbind(rnorm(100),rnorm(100)))
fi <- dlmFilter(rnorm(100),mod)
f <- dlmForecast(fi,nAhead=12)
Error in dlmForecast(fi,... |
I am a stats newbie, so apologies in advance if I'm asking a braindead question. I have searched for answers to my question, but I find that many of the topics are either too specific, or quickly go beyond what I currently comprehend.
I have some simulation work that includes large datasets which become infeasible to s... |
I am currently working on a RandomForest based prediction method using protein sequence data. I have generated two models first model (NF) using standard set of features and the second model (HF) using hybrid features. I have done Mathews Correlation Coefficient (MCC) and Accuracy calculation and the following are my r... |
This is a follow-up of the question I posted earlier.
I am assessing the two RF models which are generated using two different set of features
NF - Test_Accuracy > Training accuracy (500 features)
HF - Test_Accuracy < Training accuracy (125 features)
Testing and Training is done using independent data sets and the ac... |
this is my first question on this site, so please be patient with me. I am doing a random walk, where I build a timeseries curve. I do that a preset number of times ( let's say 100 times ). Now I was wondering what should I do with all the generated curves. Eventually I want to have 1 curve that is the best representat... |
Say I have a set of sample points generated by a multivariate normal distribution D whose parameters I don't know.
I want to be able to measure the distance from an arbitrary point to the distribution D.
One way of doing this would be to get an estimate of the parameters of D, and use it to get the manalanobis distance... |
When minimizing a function by general Metropolis-Hastings algorithms, the function is viewed as an unnormalized density of some distribution.
(1) As density functions are required to be nonnegative, I was wondering if there is some restriction on functions that can be minimized by Metropolis-Hastings algorithms?
(2) T... |
I have a question regarding the sign test when the individual measurements may be correlated. Let me start off with some background. Suppose we have 4 Organisms (a,b,c,d),and we make measurements in two separate ways, say A and B. Our data may look as follows
a = 3 for measurement A and 1 for measurement B
b = 4 for me... |
I am trying to state a prior distribution for a Bayesian meta-analysis.
I have the following information about a random variable:
Two observations: 3.0, 3.6
a scientist who studies the variable has told me that $P(X<2)=P(X>8)=0$, and that values as high as 6 have nonzero probability.
I have used the following approa... |
What are the most important statisticians, and what is it that made them famous?
(Reply just one scientist per answer please.)
|
I asked this question on mathoverflow yesterday and got a suggestion to try it here. I apologize if this is an easy question, but I can't seem to find an answer anywhere.
I'm trying to duplicate a macroeconomic paper that uses MCMC analysis to derive time series and parameter values. For the variance of a white noise t... |
We are preparing a manuscript and the editor asked us to convert a figure with a boxplot into a table "because of the more exact data content". While I think boxplots are pretty decent in revealing something about the data, I was wondering what you guys think about this? Do you (often) opt for tables over boxplots for ... |
The help pages in R assume I know what those numbers mean, but I don't.
I'm trying to really intuitively understand every number here. I will just post the output and comment on what I found out. There might (will) be mistakes, as I'll just write what I assume. Mainly I'd like to know what the t-value in the coefficien... |
The problem is to define when a variable might be considered as a latent variable. I am interested in how to describe a latent variable, and what are the properties of latent variables.
My twofold question is:
When you try to explain what a latent variable is, what do you consider as the main differences between a ma... |
I have an experiment with any possible (reasonable) number of parameters (independent variables). I run the experiment several times for each possible combination of my variables. The data I get will be generally numeric.
However I know nothing (and any assumptions are difficult) about the distribution of my data.
Wha... |
When trying to find the mode of a nonnegative function $f$ (i.e. maximize the function), one way to do it is to sampling the function viewed as an unnormalized density of some distribution via MCMC.
Suppose we have had a sufficiently long sequence of samples via this method, I was wondering how to determine the mode fr... |
I have some time series data and want to test for the existence of and estimate the parameters of a linear trend in a dependent variable w.r.t. time, i.e. time is my independent variable. The time points cannot be considered IID under the null of no trend. Specifically, the error terms for points sampled near each ot... |
I have a biometric authentication system that is using a person's gait to authenticate them. I extract features from gait, run it through a comparison versus a template and produce a similarity score (where if this similarity score is below a certain threshold, then the user is authenticated). So, I have 72 trials tota... |
I am conducting a study on a cohort of people with a follow-up period of 7 years. I wish to use Cox Proportional Hazard model to estimate HR between an exposure and the length of time of an event. One missing information is the date of birth for the all subjects, but month and year are available.This prevents the calcu... |
I understand that when sampling from a finite population and our sample size is more than 5% of the population, we need to make a correction on the sample's mean and standard error using this formula:
$\hspace{10mm} FPC=\sqrt{\frac{N-n}{N-1}}$
Where $N$ is the population size and $n$ is the sample size.
I have 3 questi... |
The height for 1000 students is approximately normal with a mean 174.5cm and a standard deviation of 6.9cm. If 200 random samples of size 25 are chosen from this population and the values of the mean are recorded to the nearest integer, determine the probability that the mean height for the students is more than 176cm.... |
I am looking for a good tutorial on clustering data in R using hierarchical dirichlet process (HDP) (one of the recent and popular nonparametric Bayesian methods).
There is DPpackage (IMHO, the most comprehensive of all the available ones) in R for nonparametric Bayesian analysis. But I am unable to understand the exa... |
I am sampling covariance matrix from a Inverse Wishart distribution. In one dimensional case, after doing sufficient iterations I am taking the mode value for variance (after removing the burn-in values). How to do the same in a multivariate case?
|
I am new to forecasting in R and am trying to automatically fit an ARIMA model to what I believe is a univariate dataset.
> str(p1.z)
'zoo' series from 2009-04-05 to 2010-10-31
Data: int [1:83] 360 570 540 585 570 690 495 660 510 690 ...
Index: Class 'Date' num [1:83] 14339 14346 14353 14360 14367 ...
> head(p1.... |
I hope this isn't either far too basic or redundant. I have been looking around for guidance but so far I am still uncertain of how to proceed.
My data consists of counts of a particular structure used in conversations between pairs of interlocutors. The hypothesis I want to test is the following: more frequent use of ... |
I have several sets of data, unfortunately the data comes to me in a "summary" form. My job is to consolidate the several data sources into one general summary. I'm currently using the median to summarise the data, but I don't know if this is statistically sound. Here's a description of my problem:
There are $N_P$ samp... |
"Spurious regression" (in the context of time series) and associated terms like unit root tests are something I've heard a lot about, but never understood.
Why/when, intuitively, does it occur? (I believe it's when your two time series are cointegrated, i.e., some linear combination of the two is stationary, but I don'... |
Say I'm doing stats on the height of adults from various countries.
I assume the heights of adults from one country are normally distributed, and ignore sex differences (I also ignore the fact that neighbouring countries tend to have similar populations).
I have a bunch of data by country, but for some countries I have... |
In a recent paper, I fitted a three-way fixed effects model. Since one of the factors wasn't significant (p > 0.1), I removed it and refitted the model with two fixed effects and an interaction.
I've just had referees comments back, to quote:
That time was not a significant factor
in the 3-way ANOVA is not of itself a... |
I am new to Gibbs Sampling, and have been using WinBUGS, but I find that it is not well-suited towards storing/presenting results, so I have been calling it from R using the R2WinBUGS package. The data is apparently stored as a "bug" class.
I converted it to coda to run diagnostics, and it displays each of the chain... |
With some great help from this forum, I have been able to get up and running with some basic time series analysis in R. Right now, my needs are mostly univariate time series.
Here is my question:
I can read in daily data from database into a data frame. I have two columns, date which is understood by R as POSIXct a... |
This question is related to my previous question Bias for kernel density estimator (periodic case)
A kernel $K(x)$ is of the order $p$ if
$$\int_{-\infty}^{\infty}K(x)x^{j}=\delta_{0,j}\ j=0,...p-1$$
$$\int_{-\infty}^{\infty}K(x)x^{p}\neq0\ $$
Does it mean that for the kernel with period 1 the definition of the or... |
As title, I need to draw something like this:
Can ggplot, or other packages if ggplot is not capable, be used to draw something like this?
|
In order to calibrate a confidence level to a probability in supervised learning (say to map the confidence from an SVM or a decision tree using oversampled data) one method is to use Platt's Scaling (e.g., Obtaining Calibrated Probabilities from Boosting).
Basically one uses logistic regression to map $[-\infty;\infty... |
I have database of 78706 resident incidents in aged care facilities (5 years of data).
I want to to learn and implement a tool allowing analyzing these data using following attributes:
Resident
Date/Time
Location
Result
Injury
I want to be able to get following assumptions from my system which will be passed to speci... |
In Frank Schorfheide's class notes on likelihood functions of DSGE models, he expresses the value of the likelihood function for a given vector of parameters $\theta$, and time series $Y^T$ as:
$$p(Y^{T}|\theta)=(2\pi)^{-nT/2}\left(\prod_{t=1}^{T}\left|F_{t|t-1}\right|\right)^{-1/2}\exp\left\{-\frac{1}{2}\sum_{t=1}^{T}... |
This is the confidence interval estimated by prop.test
n <- 600; x <- 276; p <- 0.40
prop.test(x, n, p, alternative="two.sided", conf.level=0.95, correct=T)
95 percent confidence interval:
0.4196787 0.5008409
I tried to reproduce it, reading the code under prop.test. Here is a simplified way to get those two limits
... |
I tried to simulate from a bivariate density $p(x,y)$ using Metropolis algorithms in R and had no luck. The density can be expressed as $p(y|x)p(x)$, where $p(x)$ is Singh-Maddala distribution
$p(x)=\dfrac{aq x^{a-1}}{b^a (1 + (\frac{x}{b})^a)^{1+q}}$
with parameters $a$, $q$, $b$, and $p(y|x)$ is log-normal with lo... |
Suppose I observe a sample $(y_i,x_i)$, $i=1,...,n$. Suppose that I know the following:
$y_i=\alpha_0+\alpha_1x_i+\varepsilon_i$, $i \in J\subset\{1,...,n\}$
$y_i=\beta_0+\beta_1x_i+\varepsilon_i$, $i \in J^c$
where $\varepsilon_i$ are i. i. d. and $J$ is not known in advance. Is it possible to estimate $\alpha_0,\al... |
I have left censored data where the distribution is known (it's near enough lognormal, at least in theory).
I'd like to calculate some simple summary stats: geometric mean and standard deviation in this case.
I've previously used R's NADA package for this but it is no longer on CRAN. Is there an alternative available?... |
I have done a meta analysis and heterogeneity is too high. I am working with (even/Total) for experimental and control groups to calculate the Odds Ratio. I have done fixed-effect and random-effect modeling. I now need to use meta-regression via SPSS.
Can anyone direct me to a good set of materials to learn how t... |
If $X=[x_1,x_2,...,x_n]^T$ is an $n$-dimensional random variable and we have
$E\left\{X\right\} = M = \left[m_1,m_2,...,m_n\right]^T$
$Cov\left\{X\right\} = \Sigma = diag\left(\lambda_1,\lambda_2,...,\lambda_n\right)$
how can I express the following expectation in terms of $M$, $\Sigma$, and $n$ (and maybe raw $m_i$... |
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