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I'm looking for a simple and easy to read introduction to using MCMC with a dirichlet process prior. Or perhaps using MCMC in any machine learning scenario, eg Gaussian Process. I've been circling around various papers and tutorials (Neal, Teh, Sahu, Ghahramani, Ferguson, Escobar and West, ... ), but I can't find anyt...
I'm trying to build a generative model to run a Monte Carlo simulation. The existing data consist of a combination of discrete and continuous variables. Suppose I have a number of people... Age Sex Non-white 21 1 1 35 1 1 I can easily use a mixture of Gaussians to model this data set and just use EM to estimat...
Possible Duplicate: Why ANOVA/Regression results change when controlling for another variable I have used SPSS to run two RM two-way ANOVA with the same data. RM ANOVA #1 has two within subject variables A & B RM ANOVA #2 has two within subject variables A & C Variable A is represented in both ANOVAs. What is stran...
I am trying to do text classification using Naive Bayes. Before training, I would like to make feature selection in order to reduce the feature space dimension. In order to do so, I have thought of using a method that weights 2 filters for scoring the features and then select the top K features. For example, let's supp...
I need to compare sample distributions with theoretical ones, which is typically done with a chi-squared test. The problem is that I have distributions where one or more cells have low values, and consequently the chi-squared test reports very small p-values. For example, a typical expected and observed frequencies ar...
In the following second order equation $ax^2+2bx+1.5=0$ where $a$ and $b$ are given by random points $(a,b)$ in the $[0,2]\times[0,1]$ rectangle, what is the probability of having two real solutions? I'm a little lost here. I tried integrating $4b^2-6a$ with $a=0\to 2$ and $b=0\to 1$ as limits but the integral comes up...
I implemented decision tree according by Russell and Norvig AIMA (in the 3rd edition, p.704). Assumption The given formula for calculating entropy does not work for the cases when you have all positives examples, or all negative ones. For binary outcomes: $$B(q) = -(q * lg_2(q)+(1-q) * lg_2(1-q))$$ $$q=\frac{p}{p+n}...
I am preparing for an exam, I've been reading through Likelihood Ratio Test, but don't get it. Example 8.2.3 (page 376 in "Statistical Inference" Casella and Berg) Let ${{x}_{1}},...{{x}_{n}}$ be a random sample from an exponential population with pdf $$f(x\|\theta )=\left\{ \begin{array}{*{35}{l}} {{e}^{-(x-\theta ...
A two-way ANOVA yields 3 F ratios. Each F ratio has alpha of .05. Does that mean the experimentwise alpha level of the ANOVA is not .05 but rather is 1 - .95^3? If so, is there a recommended way to maintain the experimentwise alpha for two-way ANOVA?
I'm totally not a pro in statistics so i hope the question is not too simple! I have two groups of patients. One group are smokers, the second are non-smokers. I want to compare the level of some hormones in the two groups to see if they are influenced by smoking. On many articles I found researchers using Mann-Whitne...
I recently read a post from R-Bloggers, that linked to this blog post from John Myles White about a new language called Julia. Julia takes advantage of a just-in-time compiler that gives it wicked fast run times and puts it on the same order of magnitude of speed as C/C++ (the same order, not equally fast). Furthermore...
Are there any open source software packages, (Java, Matlab, R) that can generate a feature representation for a text document using N-gram model?
I am trying to compare the performance of a classification result with Bayes classifier, K-NN, principal component analysis (PCA). I have doubts regarding the following (please excuse my lack of programming skills since I am a biologist and not a programmer thus finding hard to follow the matlab documentation) In the...
For a simple 2 variables (say X and Y) cointegration test, how does it affect our analysis, if we perform regression on X and Y with and without the intercept, and then test the spread for stationarity. I am doing this analysis for stocks.
Could anyone please elucidate the difference between Vector Autoregressive Models with exogenous variables, VARX(p,q) and autoregressive distributed lag models ADL(p,q)? Based on the descriptions of two models, they appear to be the same so why different names are given?
Say I have a 24x7 matrix in which the rows represent hours in the day and the columns represent the days of the week. The values in this matrix represent the number of people present at a particular place. Mathematically speaking the values are thus the result of a function: presence(hour, day) I am looking for a way t...
I am computing the interaction in several 2X2X2 tables (i.e. in each case, I have eight frequencies), see for an example this file. I have two predictors (low vs high 'threat' and low vs high 'efficacy') and one dependent variable (whether people perform the desirable behavior ('good') or not ('bad'). My question is wh...
I am familiar with using multiple linear regressions to create models of various variables. However, I was curious if regression tests are ever used to do any sort of basic hypothesis testing. If so, what would those scenarios/hypotheses look like?
I have data for many time series. Each time series can be modeled by a particular nonlinear function of several parameters and, though I want point estimates of the model parameters for each of the many time series, I am more interested in the uncertainty associated with the parameter estimates (i.e., in the strength o...
Does anyone know how to determine the significance of the slope from linear model fitted using generalised least squares (GLS)? I am fitting a linear model to temperature time series with the aim of assessing for trends using gls function in nlme package, but I could not figure out the p-value (s) for the slope in mod...
A traditional approach of feature construction for text mining is bag-of-words approach, and can be enhanced using tf-idf for setting up the feature vector characterizing a given text document. At present, I am trying to using bi-gram language model or (N-gram) for building feature vector, but do not quite know how to ...
Let's assume I have a NxD matrix X with the N rows being observations and the D columns being features. I would now like to know which are the most "interesting" features of this dataset. I.e. which features depend on each other, which are redundant etc. At the end, I would like to have a dataset of dimensionality k < ...
I get a little bit confused by the conclusions I can take or not with these small samples. I have been measuring the degradation of a pollutant for 9 days. I measured the remaining concentration and only took triplicates each day, so that gives me a very small sample size. I want to check at which point there is no sig...
I have spent much time looking for a special package that could run the Pesaran(2007) unit root test (which assumes cross-sectional dependence unlike most others) and I have found none. So, I decided to do it manually; however, I don't know where I'm going wrong, because my results are very different from Microsoft Exc...
We draw $N$ samples, each of size $n$, independently from a Normal $(\mu,\sigma^2)$ distribution. From the $N$ samples we then choose the 2 samples which have the highest (absolute) Pearson correlation with each other. What is the expected value of this correlation ? Thanks [P.S. This is not homework]
I should not be here, I am a designer by trade and all these numbers scare me. I am attempting to help someone display their information; they sent me an excel spreadsheet and asked me to make graphs out of certain information. Unfortunately the spreadsheet contains ~13,000 rows and 32 columns, and I need to find out ...
I recently learned about using bootstrapping techniques to calculate standard errors and confidence intervals for estimators. What I learned was that if the data is IID, you can treat the sample data as the population, and do sampling with replacement and this will allow you to get multiple simulations of a test statis...
Possible Duplicate: Comparing smoke and hormones level in two groups of people. Which test? I'm analyzing some data for an article about hormones concentrations and smoking. I was unsure whether to use parametric or non parametric tests to compare the groups, but since the sample number is high (> 100) i thought the...
I have a servlet-based application wherein I measure the time taken to complete each request to that servlet. I already compute simple statistics like the mean and maximum; I'd like to produce some more sophisticated analysis however, and to do so I believe I need to properly model these response times. Surely, I say, ...
I am building a classification model (binary outcome) and would like to include an external cluster membership code as a predictor. For training the model, this is straight forward. When "scoring" new data with the model, it is less so. If the clustering was k-means and used euclidean distance, assigning the new dat...
It is admission season for graduate schools. I (and many students like me) am now trying to decide which statistics program to pick. What are some things those of you who work with statistics suggest we consider about masters programs in statistics? Are there common pitfalls or mistakes students make (perhaps with re...
I've been using nlme and more recently lmer to fit multi-level models of time course data using orthogonal polynomials. My colleagues and I originally chose polynomials because we believed that "nonlinear" functions such as the logistic could not be used for multi-level modeling because they are not dynamically consist...
I recently conducted my first study looking at parental education as a determinant of risk. I conducted a survey which measured risk in several contexts and also recorded information about the individuals such as gender, height and all the other usual suspects. Little work has been done on the effect of ethnicity on ri...
Is there a problem looking for clusters of trajectory patterns in longitudinal data, when much of the longitudinal values were imputed from the baseline data?
Please correct me if I am wrong as I am not good at R. I think I can find a linear combination maximizing correlation between predictors and dependent variables by running partial least squares analysis with standardized X without intercept and standardized Y matrix. But how can I do that with pls or any other package...
Is there anyway to perform a BCa, a tilted, and an ABC bootstrap in R without using the built in packages, namely 'boot'? Thanks
I'm analysing one paper on bayesian inference for network reliability and got stuck at trying to validate some (quite simple at first sight) formulas. Suppose the probabilities of failure has truncated beta distribution as a prior: $$ \pi _{1}\left ( p_{i}\|\gamma ,\alpha \right )=\frac{\alpha \left ( 1-p_{i} \right )...
I have a model for data in my experiment that states that the data has a Gumbel distribution with known location and scale. I am then looking at observations with very high scores that I suspect to be outliers. Is there a Bayesian approach (or otherwise) to get the probability that this observation is from the underlyi...
I have a panel chart composed of 4 panels, each with 12 bars that essentially show data from a pivot table. The default layout has the first 11 rows show individual points, with the 12th row showing a total of the entire column. Similarly, the final column shows a total of the 3 preceding columns. The result is the ...
Recent research has attempted to determine if certain psychological constructs are latently dimensional or taxonic (i.e., including taxons or classes). For example, researchers may be interested in finding out if there is a certain "class" of people who are more likely to develop chronic pain after an injury, or if the...
So I'm currently training a stack of RBMs (Restricted Boltzmann Machines), eventually to be build into a DBN (Deep Belief Net), on a set of gray-scale images featuring objects placed in different locations on a complex background. After training for a good long while, I tried generating from the RBMs and found that fo...
Whilst reading up on the Deep learning literature, I noticed that a few variations on the standard network structure that were created specifically to better model "Natural/Real Images". For example, this paper says that: Deep belief nets have been successful in modeling handwritten characters, but it has proved mor...
In reviewing a paper, the authors state, "Continuous outcome variables exhibiting a skewed distribution were transformed, using the natural logarithms, before t tests were conducted to satisfy the prerequisite assumptions of normality." Is this an acceptable way to analyze non-normal data, particularly if the underlyin...
What is the optimal case/control ratio in a case-control study? Why do most textbooks or monographs suggest that it is more than 1? Can it be less than 1 (what are the drawbacks?)? Thank you.
In Statistica one can do a "two series"/bivariate/cross spectrum Fourier analysis to examine the coherency, gain, and phase spectrum across a pair of signals. It is probably a failing on my part, but my attempts to use those search terms to come up with similar values from R have come up blank. What functions/package...
What are some useful guidelines for testing parameters (i.e. interaction depth, minchild, sample rate, etc.) using GBM? Let's say I have 70-100 features, a population of 200,000 and I intend to test interaction depth of 3 and 4. Clearly I need to do some testing to see what combination of parameters holds up best out-o...
The theory of propensity score (PS) suggests that it should only be used for the cohort study because PS matches the "treated/exposed" to the "un-treated/un-exposed" groups. However, cases and controls are the outcomes (not the exposures) in a case-control study. What are the pitfalls if PS is used in a case-control st...
What do you think about the best way to perform a search for two discrete group membership in data that consist of four Fourier series coefficients like this: $an [1] -1.099759e+02 -3.277411e+01 -2.069982e+01 1.294945e+00 -4.557681e+00 [6] 3.659611e+00 -2.266350e+00 2.290051e+00 -1.165922e+00 4.290447e-01 [11] -...
I have several distributions (10 distributions in the figure below). In fact these are histograms: there are 70 values on the x-axis which are the sizes of some particles in a solution and for each value of x the corresponding value of y is the proportion of particles whose size is around the value of x. I would like ...
What I have: There is one base with already classified cases. There are 23 independent variables that were used in this classification and 10 groups. Another base has new unclassified cases. There are also these 23 independent variables. I do discriminant analysis in SPSS on the first base (I choose 'Within-Groups c...
I have a data set that clusters block groups in the US into either 15 broad neighborhood categories or 72 fine-grained segments with goofy names. The segments were constructed using factor analysis using mainly age, income, ethnicity, education, marital status, dwelling type, and the presence of children. The categorie...
I have collected data about test subjects which are classified into 4 categories, and I want to calculate the probabilities (odds ratios?) of developing some condition for a test subject in one category. The data are as follows: Condition present Condition not present Category A 4 ...
If we want to determine the variable types, will it be as follows for the below variables? Age ---> quantitative, discrete (we can count) Fitness ---> If the values that we will enter here are 0 and 1 only, will the type of this variable be qualitative, nominal? Thanks a lot.
I have what I would call a pseudo panel, where my dependent variable varies over time and space (regional death counts), but my x variable of interest does not (national wage time series). Basically, I want to look at the effect of real wage variation on mortality, so $\log (D_{it})=f(\log (W_{t}))$. However, I have ru...
I am really new with R and time series. But, I have understood most concept. Part where I am (very) confused is the xreg= argument in arima() from tseries package and forecast package. As I have read most of the related threads on this site, I understand that xreg is used for exogenous data. See for example, How to fit...
Say, I have a normal distribution $ X \sim N(\mu, \sigma)$, where $\mu$ unknown and $\sigma^2$ known Then, $-E[2/\sigma]=2/\sigma$ or $-2/\sigma$ This is in reference to the Fisher Information where you have $-E(\cdot)$ of something. Edit: I was taking expectation of Fisher Information. $$-E[\frac{1}{2\sigma^4}-\frac{...
I am developing a neuroscience-inspired training algorithm for feed-forward neural networks. The natural benchmark for comparison is backpropagation. So I need to know to know what sort of classification problems backpropagation (and thus feed-forward NNs) is most suited for. Also, since I ultimately want to move beyo...
What are some ways to prepare/pre-process time series data to use the series data as a predictor(s) in a predictive model (classification or regression)? Specifically, what are the methods to be considered in order to Get the most predicatively useful signal from the data? Reduce the dimensionality of the series As ...
What are hierarchical priors? How do they differ from the general concept of priors?
I need to test for correlation of 4 sets of weather parameters between 2 sites. I am not interested in interactions between the parameters. Because no weather parameter is independent from other weather parameters, if I was simply trying to determine if each parameter differed between the 2 sites, I would use a MANOVA ...
I'm trying to implement an ordered probit model in pymc, and I'm stuck. The model is similar to Welinder's "multidimensional wisdom of crowds", with coders (indexed by i) and documents (indexed by j). Coders assign codes to documents, but the coding process is noisy. We wish to estimate two things. First, $z_j$, the...
For a method calculating expected claims in insurance I have to assume lognormal distribution. For testing I would use annual cumulated data. With a small sample capped at 20 years, my idea is to use disaggregated data - monthly, or individual claims. Now I have found hat the sum of lognormal claims is not a lognormall...
This is probably a far too basic question for this board - but on the other hand, I know I'll get good answers. "Stats 101" is a metaphor, by the way. I'm asking for help with my work, not my homework! I am looking at aggregate financial data for hospitals. I have identified two hospital systems that accumulate unus...
I am fitting an lm() model to a data set that includes indicators for the financial quarter (Q1, Q2, Q3, making Q4 a default). Using lm(Y~., data = data) I get a NA as the coefficient for Q3, and a warning that one variable was exclude because of singularities. Do I need to add a Q4 column?
I've collected data for individuals on a team about their daily mood. Each day, individuals rate their mood on a scale that is assigned the following values: 0 (bad), 5 (so-so), 10 (good). Using the data from the individuals, I can come up with an average mood for the team for that day. I have several months worth of d...
I am a graduate student in economics who recently converted to R from other very well-known statistical packages (I was using SPSS mainly). My little problem at the moment is that I am the only R user in my class. My classmates use Stata and Gauss and one of my professors even said that R is perfect for engineering, bu...
Not sure if this belongs to CrossValidated, Computational Science, or something else entirely. I've got some code and data that's going into a publication, but I'd like to make said code and data publicly available so that the analysis can be replicated. If I was having it hosted by the publisher, I'd ignore this and l...
I have some non-Gaussian distributed variable and I need to check if there are significant differences between the values of this variable in 5 different groups. I have performed Kruskal-Wallis one-way analysis of variance (which came up significant) and after that I had to check which groups were significantly differe...
Is it possible to calculate AIC or BIC values for lasso regression models and other regularized models where parameters are only partially entering the equation. How does one determine the degrees of freedom? I'm using R to fit lasso regression models with the glmnet() function from the glmnet package, and I'd like to...
I have four continuous variables drawn from secondary data of companies. The combination of these four variable represent my dependent variable. These four variables are real values. They are just only four values with no items. I am using PCA to combine them together. The results I have got are that three variables ar...
I am studying LDA, but have very weak statistical knowledge. I have a question regarding Gibbs sampling, one of the methods for inferring the distribution of topics and words-topic given a document, which basically iterates and computes the probability of words from being assigned to each topic after removing the speci...
I think I have already answered my question, but am not completely sure and would like some input. Please feel free to correct my terminology or misconceptions, I learned stats by osmosis rather than formal courses so my knowledge is somewhat patchy and I often seem to use the wrong terminology. We need to predict the ...
I saw a comment by mpiktas that "The sum of two independent t-distributed random variables is not t-distributed". Is it then of any known distribution? Actually, I am using piece-wise linear regression. $E(y) = \beta_0 + \beta_1x + \beta_2(x - break)\cdot d$ where break = value of predictor x at the breakpoint d = du...
A colleague has collected data on plant root gene expression. Gene expression is expected to change over time, and be dependent upon the environment that each plant is grown in (i.e fertilizer mix). Measuring gene expression kills the plant, so each plant can only be sampled once. My colleague has two groups (high v...
I'm trying to come up with a metric for measuring non-uniformity of a distribution for an experiment I'm running. I have a random variable that should be uniformly distributed in most cases, and I'd like to be able to identify (and possibly measure the degree of) examples of data sets where the variable is not uniform...
I recently took a course on Bayesian statistics based on The Bayesian Choice by C. Robert (aka Xi'an). I couldn't solve one of the exercises regarding minimax estimators and was hoping that someone here can give me a clue as to have it can be solved. This is not homework; this is me wanting to fully understand the mate...
First off, I'll say I am a biologist and new to the statistics side of things so excuse my ignorance I have a data set that consists of a binary outcome and then a bunch of trinary explanatory variables that looks something like this: head() Category block21_hap1 block21_hap2 block21_hap3 block21_check 1 1 ...
Let $X_1, ..., X_n$ be a random sample from $\mathrm{Exp}(\lambda_1)$ and $Y_1, ..., Y_m$ be a random sample from $\mathrm{Exp}(\lambda_2)$. I have found the generalized likelihood ratio test (GLRT) statistic $\Lambda$ for testing $H_0:\lambda_1 =\lambda_2$ vs $H_1:\lambda_1 \neq \lambda_2$ is $\Lambda=\frac{n^n m^m}{(...
i'm writing a few convenience functions for exploring datasets. For that, I have to guess the type of data from the values. What I'm looking for are some good rules of thumb. Some easy cases: ['spam', 'eggs'] is nominal, because the dataset contains strings. [true, false, false] is nominal, too. [0, 1, 0, 0, 0, 1, 1] ...
I have run 13 data-stream classification approaches on 8 different datasets, giving a 8x13 result table. I was hoping to use the Friedman test to test for a significant difference between the approaches. However one of the approaches can not be used on two of the datasets so there are two missing values in my result ta...
I have a monthly average for a value and a standard deviation corresponding to that average. I am now computing the annual average as the sum of monthly averages, how can I represent the standard deviation for the summed average ? For example considering output from a wind farm: Month MWh StdDev January ...
I have the following experiment. My predictors are: Plant area, 6 types of plants, 5 time points and 12 replicates for class. Time points are not equally spaced. A normal plot of Area vs. time will show $6\times 12\times 5$ points in the plot which doesn't reflect the fact that 5 of those points correspond to the same ...
It's well known that members of the public have difficulty comprehending numbers over a certain size. A common tricky issue for people communicating demographic trends is helping people make sense of rates out of 100,000. This is an important issue in helping people make sense of changing health and crime statistics, f...
The alpha-expansion algorithm described here (Probabilistic Graphical Models: Principles and Techniques By Daphne Koller, Nir Friedman, Page 593: algorithm 13.5), is designed for graphs where each vertex has the same set of labels. I am interested in a more general problem where each vertex can have different set of la...
Possible Duplicate: Simple combination/probability question based on string-length and possible-characters Suppose I have a collection of 1,000,000 unique strings where each string is exactly 10 characters long, the characters being A-Z, a-z, 0-9. What is the probability of having a string colliding with existing da...
I know PCA and PLS are considered as alternative method to each other. But I am thinking about a kind of combination of the two in case of lots of predictors with little variability. In that case, when I run 1-component PLS with original predictors, it does not produce a meaningful model in terms of prediction. But if ...
As you know, there are many password generators out there to increase computer security. Suppose I am given such a password (say, a string of letters, numbers, symbols, etc.), is there a way for me to test how random it is? Is there some sort of index for this measurement? Thanks!
Basically, I want to manually compute what predict(princomp(somedata)) produces. In order to do that I need to have coefficients matrix so that newdata %*% coefficients would produce the predicted values of each component. Can anybody give me a clue to get the coefficients?
The experiment has $N$ observations $N_i$ which are Poisson Distributed random variables (i.e. we have histogram with $N$ bins. The width of bins is not fixed so I can adjust it ) . I have two hypothesis.The null hypothesis predicts $\lambda_i^{null}$ values of corresponding parameters of Poisson Distribution, alterna...
I have run a linear regression with five independent variables and two dependent variable I am using EPS and ROE as my dependent variable and Board meeting, Board size, leadership, Independend Non-Executive, Audit committee as my Independent variable and my resulting Model is shown as: Model Summary 1 (Dv: ROE) R. ...
When we build a classifier, like SVM or Naive Bayesian, are there any generic rules or theoretical derivations on the size of training data set? For example, to train a SVM-based classifier, what should be the minimum size of training data in terms of feature space and some target performance metrics, such as precision...
experts, I would like to ask for advice regarding the analysis of a dataset I am currently working on. In the experiment subjects were tested in a reaction time task (RT as dependent variable). In random order every subject was tested in two treatment conditions (factor 'A': placebo vs. drug). Also for subject in a th...
Question migrated form https://stackoverflow.com/questions/10019576/confidence-interval-scoring-with-programming-languages#comment12812602_10019576 I used a CI scoring algorithm from http://evanmiller.org/how-not-to-sort-by-average-rating.html, The data is most liked and disliked programming languages of each person. A...
I have 16 1D arrays with approximately 10-11 million double-precision elements each. I need to execute a cross-correlation across them, i.e., 1 with 2, 1 with 3, ..., 1 with 16, 2 with 3, 2 with 4, ..., 2 with 16, and so on. This cannot be done efficiently on my MacBook Intel Core 2 duo 2.4 GHz, with 4GB of RAM. My que...
I am trying to compute an expectation $E[f(X;\theta,n)]$ where $\theta$ and $n$ are known parameters. I have an easy-to-compute deterministic function $\tilde{f}(\theta,n)$ that provides an approximation to $E[f(X;\theta,n)]$ that gets better as $n\rightarrow\infty$ (but always underestimates the true value). I can als...
I know that dependence of $x$ and $y$ in my time series data changes in time. Suppose we have monthly time series from 1990 to 2011. If we independently regress $x$ and $y$ for 1990 to 2000 and from 2000 to 2011, the results are quite different. There is low dependence in the former sample and strong in the latter. Alt...
I have a few tens of thousands of observations that are in a time series but grouped by locations. For example: location date observationA observationB --------------------------------------- A 1-2010 22 12 A 2-2010 26 15 A 3-2010 45 16 A 4-2010 46 ...
I have a group of samples drawn from density function $p(x,y)$, so it has the marginal density $p(x)$ and $p(y)$, and conditional density $p(x\|y)$ and $p(y\|x)$. In what way I can construct another group of samples, with the SAME $p(x,y)$ but the $p(x)$, $p(y)$, $p(x\|y)$ and $p(y\|x)$ are changed?
I have a continuous dependent variable $y$ and two independent categorical variables $x_1$ and $x_2$. As well, they have been sampled from different sites (site). $x_1$ has 3 levels $x_2$ has 5 levels is it correct to do: dat <- aov(y ~ x1x2 + Error(site)) or dat <- lme(y ~ x1x2, random = ~1 \| site, data=data, na....
I have constructed a social capital index using PCA technique. This index comprises values both positive and negative. I want to transform / convert this index to 0-100 scale to make it easy to interpret. Please suggest me an easiest way to do so.

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