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<p>Let $x_1,\ldots,x_n$ be a random sample with pdf $$f(x)= \begin{cases} (\alpha+1)x^\alpha, &amp; 0 \le x \le 1, \\ 0,&amp; \mbox{otherwise}. \end{cases}$$ Find the MLE of $\alpha.$</p> <p>So, I've found the log-likelihood and taken the derivative, but I'm not quite sure if I've done it right. This is what I have so...
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<p>i am trying to understand if the following statement is true: $$ E(XY)= E(X^2)=E(Y^2) $$ if $X$ and $Y$ are identically distributed but not necessarily independent r.v. This means that if the variables are identically distributed calculate the expectation of the multiplication of any pair of them is the same that c...
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<pre><code>Document/Term Freq C1 C2 C3 C4 C5 C6 C7 C8 C9 Tag D1 0 1 3 1 1 0 0 1 0 X1 D2 1 1 3 0 1 0 0 2 0 X2 D3 2 0 2 0 1 0 0 0 0 X3 D4 0 0 4 0 1 0 0 0 ...
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<p>I want to find the moment generating function (mfg) and mean deviation of this distribution:</p> <p>$$f(x,\epsilon,k,\theta) = k\theta^{(1+1/k+\epsilon/k)}x^{(k+\epsilon)}\exp{(-\theta x^k )}/(\Gamma(1+(1+\epsilon))/k)$$</p> <p>where $\epsilon, k, \theta$ are the three parameters of this distribution. HERE x is fr...
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<p>I've been trying to solve this problem reading different material but I just can't figure it out. It's pretty simple and takes about 5 seconds to do in languages that work with arrays, but I can't work it out in Stata.</p> <p>Please ignore the substitution of the backticks in some places, I couldn't get them to app...
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<p>I sampled the data qtl_500(50,000 points), and get the density curve of it as follow:</p> <blockquote> <p>plot(density(qtl_500k)) <img src="http://i.stack.imgur.com/hajiN.png" alt="enter image description here"></p> </blockquote> <p>Now I hope to get the inflection point of this curve. Could anyone please give...
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<p>My question might be a bit ambiguous, but I started to wonder what does the "effective parameters" mean in machine learning? I have heard few professors of machine learning in my university talk about effective parameters (the context was about k-nearest neighbors or Gaussian mixture models etc.).</p> <p>Any clarif...
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<p>I try to self-learn Bayesian machine learning (mostly by studying Bishop and Kevin Murphy's books). </p> <p>While working with formulas I was puzzled by the quote that "Note that the likelihood function is not necessary a density function".</p> <p>The Bayes formula stated in terms of data $D$ and hypothesis $h$ is...
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<p>I quote the question:</p> <blockquote> <p>In some cultures, it is important to have at least one son. The plan is to have children <em>until one son</em> is born. Find the PDF of the number of daughters in a family. The success rate of having a son is <em>p</em>. </p> </blockquote> <p>My first approach: </p> ...
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<p>I've got a set of data that I'm trying to model. Lots of the data is missing, so I'm using multiple imputation. I've got about 360 observations and 13 variables. I'm also using GAMs, but that should be really relevant (I specify the knots in advance). In addition, I've got 4 interactions -- 2 two-way interaction...
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<p>Suppose <em>n</em> couples are invited to a party. What is the probability that there are at least two husband–wife pairs such that the husbands have the same birthdays and so do their wives?</p>
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<p>I was just wondering if it is possible to use a normal mixed model for count data. Would it be better to use a Poisson regression if your response is count data?</p>
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<p>I conduct a small meta-analysis of the preferences ratings for objects in two different conditions. I compute Fisher's z and SE for each study.</p> <p>1) There are studies with totally different number of trials. For example, there is a study with 24 subjects and 2 trials per subject and a study with the same 24 su...
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<p>I'm looking for articles that describe methods of how to calculate CIs for the omega-squared effect size from an one-way ANOVA. The closest I've come is Finch &amp; French (2011) <em>A Comparison of Methods for Estimating Confidence Intervals for Omega-Squared Effect Size</em> <a href="http://epm.sagepub.com/conten...
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<p>I need some help with the statistical analysis of a study of a particular surgery to remove a particular cancer. I am using the statistical program R to conduct my analysis. My data are saved in the object <code>study_data</code>.</p> <h3>Data</h3> <pre><code># Create reproducible example data set.seed(50) study_...
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<p>I was wondering what does it mean when time series residuals have autocorrelation? How should I deal with it?</p>
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<p>(if this venue is inappropriate, feel free to migrate it)</p> <p>In many natural language processing applications such as spelling correction, machine translation and speech recognition, we use language models. Language models are created usually by counting how often sequences of words (n-grams) occur in a large c...
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<p>Suppose are three time series, $X_1$, $X_2$ and $Y$</p> <p>Running ordinary linear regression on $Y$ ~ $X_1$ ($Y = b X_1 + b_0 + \epsilon$ ), we get $R^2 = U$. The ordinary linear regression $Y$ ~ $X_2$ get $R^2 = V$. Assume $U &lt; V$</p> <p>What's the minimum and maximum possible values of $R^2$ on regression $Y...
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<p>If someone wants to estimate a non-standard model -- for instance, one where the functional form is not explicitly spelled out in statistics textbooks -- can most such models be estimated using maximum likelihood optimization?</p> <p>The assumption would be that the residuals are normally distributed, and then the ...
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<p>I have my own implementation of the Expectation Maximization (EM) algorithm based on the following paper <a href="http://pdf.aminer.org/000/221/588/fuzzy_k_means_clustering_with_crisp_regions.pdf" rel="nofollow">http://pdf.aminer.org/000/221/588/fuzzy_k_means_clustering_with_crisp_regions.pdf</a> I would like to com...
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<p>Assuming it's the standard SVD (no variation of it) with $A = USV^T$, would the $A$ matrix always have positive values (0 to $\infty$)? I noticed that the $U$ and $V^T$ matrices had some negative values with the sample data I used, but I want to be sure that the $A$ matrix has only positive values so that I can choo...
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<p>I would like to report the power observed with my mixed model analysis (or repeated measures ANOVA). My experiment followed a completely within subject design with 2 independent factors (two levels &amp; 5 levels, respectively). 12 participants were recruited to run the 10 combos (5x2) twice (repeated observations),...
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<p>I want to include time spent doing something (weeks breastfeeding, for example) as an independent variable in a linear model. However, some observations do not engage in the behavior at all. Coding them as 0 isn't really right, because 0 is qualitatively different from any value >0 (i.e. women who don't breastfeed m...
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<p>We are testing an e-mailing marketing campaign. On our initial test, we sent out two different e-mail types and had a third control group that did not receive an e-mail. Now we are getting back "results" as proportion of users who returned to our app. Here are the results:</p> <pre><code>Group | received e-mail | r...
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<p>First time posting here, so thank you ahead of time for your help. I'd like to estimate the variances associated with two factors in a relatively simple, but unbalanced GLS model, and I am unsure how to extract that information (or how to manually calculate it). For the two factors I'm using, DS3 and DS4, DS3 has ...
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<p>Suppose I have some dataset. I perform some regression on it. I have a separate test dataset. I test the regression on this set. Find the RMSE on the test data. How should I conclude that my learning algorithm has done well, I mean what properties of the data I should look at to conclude that the RMSE I have got is ...
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<p>I am new to R. Now my team is building forecasting models for monthly sales. Our sales correlates quite well with a industry index. As a forward index, we can get both past 5 years' index and next 3 years' data. </p> <p>Now we are using auto.arima to generate models. We'd like to use xreg in R to correlate with thi...
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<p>It is possible to calculate the c-index for time dependent outcomes (such as disease) using the <a href="http://cran.r-project.org/web/packages/survivalROC/survivalROC.pdf" rel="nofollow">survivalROC</a> package in R. My question is : is it possible to produce a p-value for the c-index that is calculated (at a spec...
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<p>I have developed a recent interest in propensity scores. I have been using the SPSS tool created by Dr. F. Thoemmes to calculate propensity scores using bivariate "treatment" variables (e.g., depression) and several covariates (e.g., age, sex, persons in household). I am then given a resulting propensity score, but ...
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<p>I was asked how much I know of "empirical regression." I have never heard the expression. A web search yielded nothing useful. I suspect it is a term coined by someone to refer to some ad hoc procedure which might be known by other name. Has anyone have a reference?</p>
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<p>How can I perform a two sample test of means with unequal variances for a very large sample in R? </p> <p>In case of large samples the statistic will asymptotically follow a normal distribution.</p> <p>Which R function will help me to do this?</p>
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<p>is there like a diagnostic checking(like those in the time series) done for logistic regression and complementary loglog model? </p>
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<p>In detail, I have these relations (in order of causality):</p> <p>$u_1 = ax_0$ </p> <p>$x_1 = u_1 + x_0$</p> <p>$y = x_1 + w$</p> <p>where $w = N(0,1), x_0 = N(0,\sigma^2)$.</p> <p>This was my approach: I know the distribution of $x_1 = N(0,(1+a)^2\sigma^2)$ and I know $y = N(0,(1+a)^2\sigma^2 + 1)$ The expecta...
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<p>I have two Cox proportional hazards models (in R), using same outcomes and predictors, one for $n_m$ males and one for $n_f$ females. Is it possible to combine them into one equivalent model over all $n_m+n_f$ individuals, using for example an interaction between the predictors and the sex?</p> <p>For example, this...
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<p>I want to simulate the frequentist properties of a Bayesian model. So, for example, I might want to fit a Bayesian model 1,000 times to 50 different configurations each of which takes about 10 seconds to fit on my machine. i.e., total computing time = 1000 * 50 * 10 / 60 second / 60 minutes / 24 hours = 5.7 days on ...
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<p>I am trying to decompose a weekly time series using the R function 'stl'. One of the important argument of this function is the number of data per cycle. Naturally in this case one would choose 52.</p> <p>However, my data is published every week, on the same weekday. Hence I have sometimes 53 data per year. Not a b...
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<p>My problem is the following: I'm evaluating the fit to a function $f(\mathbf{x},\theta)$ via MCMC (because I have some priors on the parameters), and I'm trying to evaluate the DIC, given by:</p> <p>$$\rm{DIC}=\bar{D}+p_D,\ \ \ \ (1)$$</p> <p>where, if we define the deviance $D(\theta)=-2\log(\mathcal{L(\theta|\ma...
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<p>The plot below shows the ecdf of the p-values from to different statistics, let us identify the blue graph as vector x and the red graph as vector y. Now I execute a ks.test for x and y compare these vectors with a uni distribution in a small range.</p> <pre><code>ks.test(x[x&lt;=0.2],function(x){punif(x,0.01,0.2)}...
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<p>At least two questions (<a href="http://stats.stackexchange.com/questions/8019/averaging-correlation-values">1</a>, <a href="http://stats.stackexchange.com/questions/55930/p-value-of-an-average-correlation-coeficient/55936#55936">2</a>) have addressed the question of how to handle the analysis of multiple correlatio...
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<p>I'm having difficulty modeling something… I think it's fairly simple, but I'm just not confident enough in my ability.</p> <p>I setup an experiment with two treatment groups, six replicates in each treatment group, and measured "diversity" at three time points. I want to see whether "treatment" has an effect and if...
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<p>Consider three random variables $X,Y,Z$, which are jointly normally distributed. I know that $Y$ is orthogonal to $X$ conditional on $Z$, in the sense that $\beta_{YX;Z}=0$ (i.e. the regression coefficient of Y on X conditional on Z is zero). I'd like to know if it is correct to state this orthogonality condition as...
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<p>I'm just getting started with survival analysis and I'm having trouble finding something in <code>R</code> that will do what I'm looking for. </p> <p>Most of the packages use survival objects that have an individual record for each patient being looked at (so, patient $1$ at time $0$ was <em>alive</em>, patient $2$...
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<p>I want to test the fixed and random effects of some covariates on a discrete variable with non negative values. In exploratory analysis I fitted a null Poisson GLM and an null Poisson GLMM. However, the GLMM underestimated the mean value of the response variable even after inclusion of fixed and/or random covariates...
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<p>I have some numbers $X={x_1,x_2,...,x_n}$. I add some small numbers to them and get $Y={y_1,y_2,...,y_n}$ where $y_i=x_i+\epsilon_i$. How can I find $Z={z_1,z_2,...,z_n}$ to minimize $\sum_{i=1}^n(z_i-y_i)^2$ such that $\hat{\text{mean}}(Z)=\hat{\text{mean}}(X)$ and $\hat{\text{var}}(Z)=\hat{\text{var}}(X)$. I have ...
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<p>I'm interested in finding out more about the use of <em>a priori</em> planned contrasts within a one-way repeated measures ANOVA design. </p> <p>Predictions:</p> <ul> <li>Grps 2+3 &lt; Grp 1</li> <li>Grp 2 &lt; Grp 3</li> </ul> <p>My questions are:</p> <ol> <li><p><strong>If the data violates RM ANOVA assumption...
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<p>I am new to statistics especially in the topic of estimators and sufficient statistic. </p> <p>I am reading a note which says "<strong>unbiasedness is a desirable (but not necessary) property of a good estimator</strong>". Then it gives an example where unbiased estimators don't exist. Since there is no further exp...
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<p>What are relation and difference between time series and regression?</p> <p>For <strong>models and assumptions</strong>, is it correct that the regression models assume independence between the output variables for different values of the input variable, while the time series model doesn't? What are some other diff...
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<p>I am working with behavioral data of male sea lions, with a binomial model to understand the effect of different variables in determining the location where the encounters between males occur (Land -vs- water). For this I have several quantitative and categorical variables. </p> <p>I am testing the significance of ...
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<p>I want to understand the distribution of orientation angles in a 3D image (represented as a triangular mesh). </p> <p>For each triangle in the image I have zenith ($\Theta$) and azimuth ($\phi$)</p> <p><img src="http://i.stack.imgur.com/APStV.png" alt="enter image description here"></p> <p>And I can compute histo...
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<p>we consider a sparse autoregressive time series of length 1000 obeying the model X(t)=0.2X(t-1)+0.1X(t-3)+0.2X(t-5)+0.3X(t-10)+0.1X(t-15)+Z(t) with nonzero coefficients at lags 1,3,5,10 and 15,where the innovations Z(t) are i.i.d.Garussians with mean zero and standard deviation 0.1. the question is how to simulated ...
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<p>Disclaimer: This is for a homework project.</p> <p>I'm trying to come up with the best model for diamond prices, depending on several variables and I seem to have a pretty good model so far. However I have run into two variables that are obviously collinear:</p> <pre><code>&gt;with(diamonds, cor(data.frame(Table, ...
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<p>I am approaching graph theory (I have a background in social sciences) to map a discussion forum. My forum/network has four types of vertices: author of thread, thread, comment and author of comments (users writing comments do not coincide with users writing thread). In this case I call "thread" the first post that ...
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<p>I am applying a GLM model with binomial family:</p> <pre><code>glm(response ~ Treatment, family = binomial, data=dat) </code></pre> <p>The only explaratory variable <em>treatment</em> is a categorical variable. The model fit turns out that the residuals clearly do not have equal variances among the treatment level...
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<p>We are trying to figure out an intuitive reasoning behind integrate out the unobserved random effect. The specific formula is:</p> <p>$f\big(y_i|x_i;\beta, \sigma_c\big)=\int_{-\infty}^{+\infty}\Big(\prod_{i=1}^{T}f_t(y_{it}|x_{it};c,\beta)\Big)(1/\sigma_c)\phi(c/\sigma_c)dc$</p> <p>I think we get most of the idea...
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<p>I'm looking for a method to calculate the area of overlap between two kernel density estimates in R, as a measure of similarity between two samples. To clarify, in the following example, I would need to quantify the area of the purplish overlapping region:</p> <pre><code>library(ggplot2) set.seed(1234) d &lt;- data...
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<p>I am using logistic regression to benchmark the performance of some students in different years. I created a scenario as below:</p> <pre><code>mydata &lt;- read.csv("http://www.ats.ucla.edu/stat/data/binary.csv") benchmark.data &lt;- mydata[1:300,] # students form year 1990-1995 as benchmark compare.data &lt;- myda...
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<p><strong>Problem</strong></p> <p>For my machine learning task, I create a set of predictors.</p> <p>Predictors come in "bundles" - multi-dimensional measurements (3 or 4 - dimensional in my case).</p> <p>The hole "bundle" makes sense only if it has been measured, and taken all together.</p> <p>The problem is, dif...
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<p>recently, I had an ongoing discussion about ANOVA versus MANOVA, but yet, I am lacking of arguments for MANOVA. </p> <p>My colleque has tracked data for two times of measurement. It's known that there are two groups of people. Both groups are compared regarding their development over the time (t1 to t2) regarding p...
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<p>I have a random number generator that generate integers within <code>[0, r)</code>.</p> <p>I want to write a piece of code to test whether the numbers from it are truly uniformly distributed using chi-square test.</p> <p>I select <code>r</code> to be very big like <code>1,000,000</code>, and I generate random inte...
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<p>I have been wondering about the <em>F</em> test that is provided by many statistical packages along with the standard regression output. As I understand it, <em>F</em> can be computed by</p> <p>$$ F_{df_{reg},df_{res}} = \frac{R^2/df_{reg}}{(1-R^2)/df_{res}}. $$</p> <p>The hypothesis tested by this test can be for...
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<p>I'm trying to use LIBSVM's single class SVMs for some classification and need to extract the following sum post classification (i.e. the variable that the decision function takes in)</p> <p>$$ \Sigma_{i=1}^{N} \alpha_i K(z,z_i) $$</p> <p>I'm not too sure on this so I just want to check that I have the right idea, ...
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<p>As I understand, there are two ways to compute Kendall Tau for a data matrix $X$ (n rows of data points in $\mathbb{R}^p$):</p> <ol> <li><p>corr(X,'type','kendall')</p></li> <li><p><a href="http://www.mathworks.com/matlabcentral/fileexchange/27361-weighted-kendall-rank-correlation-matrix/content/kendalltau.m" rel="...
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<p>I've been trying to learn more about online learning lately (it's absolutely fascinating!), and one theme that I haven't been able to get a good grasp on is how to think about model selection in offline versus online contexts. Specifically, suppose we train a classifier $S$ offline, based on some fixed data set $D$....
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<p>I'm trying to calculate how good are my measurements in machine learning! Let's say that I have five choices, and that error is 4, 2, 0.002, 3, 6. Naturally, I will pick third one for the hit, but I would like to say following:</p> <ul> <li>I'm X% certain that hit is third pick </li> <li>I'm Y% certain that hit is...
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<p>I have a (symmetric) matrix <code>M</code> that represents the distance between each pair of nodes. For example,</p> <pre> A B C D E F G H I J K L A 0 20 20 20 40 60 60 60 100 120 120 120 B 20 0 20 20 60 80 80 80 120 140 140 140 C 20 20 0 20 60 80 80 80 120 140 1...
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<p>It is well known that <a href="http://en.wikipedia.org/wiki/Bessel%27s_correction" rel="nofollow">Bessel's correction</a> creates an unbiased estimator of variance. What it basically does is divide by $n-1$ instead of $n$.</p> <p>Now what I did is that I chose a few number, like $1,2,3,4,5,60$ and calculated it's p...
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<p>I like G van Belle's book on <a href="http://vanbelle.org/">Statistical Rules of Thumb</a>, and to a lesser extent <a href="http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0470457988.html">Common Errors in Statistics (and How to Avoid Them)</a> from Phillip I Good and James W. Hardin. They address common pitfalls ...
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<p>I am looking for a common trial design for comparing 6 different sunflower cultivars, and a way to analyze it as a part of a course I am taking.</p> <p>The common know-how in my class is to set the trial in 4 randomized blocks, each plot with 50-100 plants, gather the grain as bulk from each plot, and compare the ...
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<p>I am learning PCA, and while this seems like an obvious question, I can't seem to understand some of the ideas behind which eigenvectors to use when performing orthogonal regression with PCA. My code is below, and a diagram.</p> <p>I am using a parametric model of M=[X.^2;X;Y] to estimate a quadratic with parameter...
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<p>I have a question about nonlinear regression and confidence intervals for values estimated from the model. Here is my problem. I have sets of data where $X$ is the logarithm of the dose of a chemical substance and $Y$ is the response readout (normalized to be between 0 and 100%). </p> <p>I am fitting logistic funct...
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<p>I'm a M.Tech student going through my academic project-work, here I have asked to develop a optimal design and a best equation to fit the data for a Leaching, Solvent extraction and Electrowinning process. So, regarding which I have tried a Uniform Design, simplex Design, Doehlert Design and trying a CCD too. Here t...
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<p>I have some experiences with time series modelling, in the form of simple ARIMA models and so on. Now I have some data that exhibits volatility clustering, and I would like to try to start with fitting a GARCH (1,1) model on the data. </p> <p>I have a data series and a number of variables I think influence it. So i...
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<p>If I don't have the data, but only have the estimates of mean and variance of two independent Gamma distributions. What type of test I can use to test the null hypothesis μ1=μ2?</p>
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<p>I have the following situation: General practitionar (gp), patient (pat) and consultation (cons). </p> <p>Each gp has several patient and each patient can have 1 and more consultations with a specific characteristics cons_x. The outcome is y=0/1 on level consultation. </p> <p>A possible model could be (in ...
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<p>I am solving a binary classification problem with 4 predictor variables. The variables didn't seem to be linearly separable. I have used <strong>Neural Networks and Kernel SVM</strong> which work and give desired accuracy , but in turn are too complex to interpret and have latency issues. </p> <p>Are there any tran...
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<p>I am trying to analyze why some individuals change their response to a categorical survey item Y between time T1 and T2, given some explanatory variables X1 and X2</p> <p>Specifically, the data looks like this</p> <pre><code> ID Y T X1 X2 1 1 1 a b 1 0 2 a b 2 1 1 b b 2 1 2 ...
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<p>I have been given a set of data points $(x_i,y_i)$. I have to plot a scatter plot and determine if there are any outliers. But I haven't been taught a method to measure which data point is an outlier and which is not. So how can I do it for example in Sage or R? I found by Google that there is at least two tests to ...
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<p>I'm studying computer science but am lost with statistical methods. An algorithm I've been studying needs a formal metric on the space of our data set.</p> <p>Our data set can be described as `voting data'. That is, each data point is a vector containing +1 or -1 as its entries, representing a voter's choices for/...
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<p>Following <a href="http://stats.stackexchange.com/questions/1676/i-just-installed-the-latest-version-of-r-what-packages-should-i-obtain">this question</a>, I wish to have some way of counting how many times I am using a package in my daily work.</p> <p>Is there a function/package to do that?</p> <p>In case there i...
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<p>I have a dataset with subjects ($\text{data}_0$). Each subject has a follow up time ($\text{fuy}$), an indicator for incidence ($\text{ind} = 0/1$) and a variable which indicates, for example, year of diagnosis ($\text{year}$).</p> <p>One way (I call it ($\text{A}$)) to show the incidence rates according to year wo...
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<p>Hi I'm trying to make the following moderated mediation but I'm missing the final step on testing differences between groups. The code below tests the indirect effects for each level of the categorical variable, but I have no clue how to test if the indirect effect differs between categories. </p> <p>I want to test...
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<p>I have a number of points $x_1,\ldots,x_m\in\mathbb{R}^n$ with weights $w_1,\ldots,w_m$ between 0 and 1. There is an ellipse which contains a very high concentration of points with weights close to one, but there are also many points scattered outside the ellipse with large weights, and not all the points in the ell...
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<p>I am attempting to evaluate the prediction error of a coxph model that was built after feature selection with glmnet.</p> <p>In the preprocessing stage I used na.omit (dataset) to remove NAs. I reconstructed all my factor variables into binary variables with dummies (using model.matrix) I then used glmnet lasso to ...
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<p>I am trying to use glmer to create logistic mixed effects models (LMEMs) and then run a model comparison between them. Respondents can click "Yes" (coded as 1) or "No" (0), which is used as the DV. They can make three responses to each stimulus across time. The fixed effects are viewing duration of a stimulus at the...
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<p>I am working to Text Document. I try to filter the document using Mallet Language Tool Kit. My questions are. 1. I use macintosh os. should i install ant ? 2. How can i use the packages in this directory class/cc/mallet/classify on Java eclipse?</p> <p>Thank you. </p>
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<p>Searching the internet for PCA tutorial gives thousands of results (even videos). Many of the tutorials are very good. But I am not able to find any practical example where PCA is explained using some data-sets which I can use for demonstration. I need a tutorial which provides some small data set which is easy to p...
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<p>I'veen asked to claculate a necessary sample size and I tought the best way to reduce costs and time is using cluster samplig protocol but I have few information and I don't have much experience with cluster sampling. The situation is as follows. </p> <p>I have a population of 83,201 individuals. I need to calculat...
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<p>I would like to know what are the common techniques to compare two histograms? I have histogram of two images and I want to see are they similar or not meaning that is there any correlation between them or not. The histograms are for two different parts of tissue.</p> <p><img src="http://i.stack.imgur.com/octv6.jp...
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<p>$F(x,y) =\frac{1}{6}(x^2\, y+x\, y^2)\,,\quad 0\leq x\leq 2,\, 0\leq y\leq 1$</p> <p>Above is the joint distribution given,</p> <ol> <li>how to find out cumulative distribution function of y?</li> <li>how to obtain joint probability density function of x and y?</li> </ol> <p>I am a beginner in R, I know basic com...
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<p>I want to obtain p-values for the significance of trading rule profits as described by LeBaron and Brock (1992). The author's use what is developed by Efron (1973) called Bootstrapping.</p> <p>It goes like this:</p> <ol> <li>Run a trading rule (i.e. SMA crossovers) on a price series </li> <li>Calculate the mean re...
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<p>When I compute the five-number summary on my sample, I obtain quantiles that differ from the quantiles I got from the empirical cdf, since they are not normally distributed data.</p> <p>Can you help me in the interpretation of this difference? </p> <p>For instance, with a randomly-generated Poisson dataset x</p> ...
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<p>Does there exists a Box-Cox method for linear Gaussian models with random effects ?</p>
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<p>I need a one-sentence explanation of the use of the AIC in model-building. So far I have "Simply put, the AIC is a relative measure of the amount of observed variation accounted for by different models and allows correction for the complexity of the model."</p> <p>Any advice much appreciated.</p> <p>R</p>
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<p>Okay, so, in the traditional Bernoulli Urn problem, we have an urn with a number N, possibly infinite, of coloured balls, and there are k possible colours. That one I grok.</p> <p>However, what if I don't actually <em>know</em> what k is? That is, what if I have an urn with N balls and an unknown but finite and str...
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<p>If you are running logistic regression on data, and the prior probability of the event is 50%, and there is no preference for sensitivity or specificity... </p> <p>When would you still want to use a cutoff? Can you please give an example to help me, a beginner, understand?</p>
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<p>I used conditional probability to find the probability that </p> <pre><code> A not A B 27 6 not B 12 C not C B 29 4 not B 50 C not C A 36 3 not A 43 </code></pre> <p>\begin{align} P(A|B) &amp;=.81 \\ ~\\ P(B|A) &amp;=.69 \...
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<p>To first provide some context, I have two boxplots (displaying median, 25th, and 75th percentiles), and I'm wondering what a boxplot of the difference between these two boxplots would look like. The random variables (RV's) aren't necessarily distributed normally. Specifically, the "random variables" are samples from...
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<p>Apologies for the rudimentary question. I'm taking on a project at work that's a bit out of my wheelhouse and I want to bounce my ideas off of those more experienced than myself.</p> <p>We use Salesforce.com at the software company where I work, and I want to identify which lead behaviors (whitepaper downloads, dem...
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<p>I'm investigating optimal bidding in auctions, and am using logistic regression to predict the probability of winning an auction given a set of explanatory variables (e.g. the price I bid, number of competing bids etc).</p> <p>One explanatory variable I want to use is the <em>second</em> highest price that was paid...
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<p>I am reading Bishop's Pattern Recognition and Machine Learning. </p> <p>In page 73, chapter 2.1. I can't understand the formula 2.19 :</p> <p>$$p(x=1|\mathcal{D})=\int_0^1 p(x=1|\mu)p(\mu|\mathcal{D})\text{d}\mu $$</p> <p>The author say, this is obtained by sum and product rules. </p> <p>The sum rule is:</p> <p...
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