# All Questions

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### Is frequentist conditional inference still being used in practice?

I've recently reviewed some old papers by Nancy Reid, Barndorff-Nielsen, Richard Cox and, yes, a little Ronald Fisher on the concept of "conditional inference" in the frequentist paradigm, which ...
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### What does the Akaike Information Criterion (AIC) score of a model mean?

I have seen some questions here about what it means in layman terms, but these are too layman for for my purpose here. I am trying to mathematically understand what does the AIC score mean. But at ...
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### Help in how the paper derives the CRLB for Gaussian ARMA model

An univariate autoregressive process AR(p) process is expressed as $$y(n) = \sum_{j=1}^p a_jy(n-j) + u(n)$$ is excited by Gaussian sequence, $u$. Paper : On the Computation of the Cramer-Rao Bound ...
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### How does Krizhevsky's '12 CNN get 253,440 neurons in the first layer?

In Alex Krizhevsky, et al. Imagenet classification with deep convolutional neural networks they enumerate the number of neurons in each layer (see diagram below). The network’s input is 150,528-...
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### Model selection with Firth logistic regression

In a small data set ($n\sim100$ ) that I am working with, several variables give me perfect prediction/separation. I thus use Firth logistic regression to deal with the issue. If I select the best ...
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### Switch from Modelling a Process using a Poisson Distribution to use a Negative Binomial Distribution?

We have a random process that may-or-may-not occur multiple times in a set period of time $T$. We have a data feed from a pre-existing model of this process, that provides the probability of a number ...
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### Link Anomaly Detection in Temporal Network

I came across this paper that uses link anomaly detection to predict trending topics, and I found it incredibly intriguing: The paper is "Discovering Emerging Topics in Social Streams via Link Anomaly ...
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If $p(x)$ is a probability distribution with non-zero values on $[0,+\infty)$, for what type(s) of $p(x)$ there exist a constant $c>0$ such that $\int_0^{\infty}p(x)\log{\frac{ p(x)}{(1+\epsilon)... 0answers 192 views ### Speed, computational expenses of PCA, LASSO, elastic net I am trying to compare computational complexity / estimation speed of three groups of methods for linear regression as distinguished in Hastie et al. "Elements of Statistical Learning" (2nd ed.), ... 0answers 128 views ### 10 % false positives from nonlinear mixed effect models : Why? I've run a simulation study in order to estimate type I error rate of the test of group effect in a nonlinear mixed effects model, using nlmer from lme4 package. The results show there is 8-10 % false-... 0answers 135 views ### Derivation of normalizing transform for GLMs How is the$A(\cdot) = \int\frac{du}{V^{1/3}(\mu)}$normalizing transform for the exponential family derived? More specifically: I tried to follow the Taylor expansion sketch on page 3, slide 1 of ... 0answers 83 views ### Bridge penalty vs. Elastic Net regularization Some penalty functions and approximations are well studied, such as the LASSO ($L_1$) and the Ridge ($L_2$) and how these compare in regression. I've been reading about the Bridge penalty, which is ... 0answers 125 views ### Restricted maximum likelihood with less than full column rank of$X$This question deals with restricted maximum likelihood (REML) estimation in a particular version of the linear model, namely: $$Y = X(\alpha)\beta + \epsilon, \epsilon\sim N_n(0, \Sigma(\alpha)),$$ ... 0answers 109 views ### Jaynes'$A_p$distribution In Jaynes' book "Probability Theory: The Logic of Science", he has a chapter (Ch 18) entitled "The$A_p$distribution and rule of succession" in which he introduces the idea of$A_pdistribution; ... 0answers 205 views ### A question related to Borel-Cantelli Lemma Note: Borel-Cantelli Lemma says that $$\sum_{n=1}^\infty P(A_n) \lt \infty \Rightarrow P(\lim\sup A_n)=0$$ $$\sum_{n=1}^\infty P(A_n) =\infty \textrm{ and } A_n\textrm{'s ... 0answers 427 views ### Goodness of fit test: question about Anderson–Darling test and Cramér–von Mises criterion I'm reading web pages for goodness of fit tests, when I came to the Anderson–Darling test and the Cramér–von Mises criterion. So far I got the point; it seems the Anderson–Darling test ... 0answers 2k views ### pdf of the product of two independent random variables, normal and chi-square what is the pdf of the product of two independent random variables X and Y, if X and Y are independent? X is normal distributed and Y is chi-square distributed. Z = XY if X has normal distribution ... 0answers 889 views ### Simulating time-series given power and cross spectral densities I am having trouble generating a set of stationary colored time-series, given the covariance matrix (their PSDs and CSDs). I know that, given two time-series y_{I}(t) and y_{J}(t), I can ... 0answers 116 views ### Estimation and functional space In the first chapter of the book Algebraic Geometry and Statistical Learning Theory which talks about the convergence of estimations in different functional space, it mentions that the Bayesian ... 0answers 435 views ### Physical/pictoral interpretation of higher-order moments I'm preparing a presentation about parallel statistics. I plan to illustrate the formulas for distributed computation of the mean and variance with examples involving center of gravity and moment of ... 0answers 140 views ### Wavelet-domain gaussian processes: what is the covariance? I've been reading Maraun et al, "Nonstationary Gaussian processes in wavelet domain: Synthesis, estimation, and significant testing" (2007) which defines a class of non-stationary GPs that can be ... 0answers 63 views ### Show estimate converges to percentile through order statistics Let X_1, X_2, \ldots, X_{3n} be a sequence of iid random variables sampled from an alpha stable distribution, with parameters \alpha = 1.5, \; \beta = 0, \; c = 1.0, \; \mu = 1.0. Now consider ... 0answers 99 views ### Specifying prior for effect size in meta-analysis My question concerns priors on effect sizes, in my project the measure is Cohen's D. Through reading the literature, it seems vague priors are often used, such as in the well-know eight schools ... 0answers 63 views ### How can we simulate from a geometric mixture? If f_1,\ldots,f_k are known densities from which I can simulate, i.e., for which an algorithm is available. and if the product$$\prod_{i=1}^k f_i(x)^{\alpha_i}\qquad \alpha_1,\ldots,\alpha_k>0... 0answers 172 views ### Implementation of CoVaR (a systemic risk measure) in R I'm trying to estimate CoVaR using bivariate DCC GARCH in R. The concept of CoVaR is the dependence adjusted of VaR, which was first introduced by Adrian and Brunnermeier (2011). However, this ... 0answers 68 views ### Are contours h^{-1}(y) interesting features of a function h:X\to \mathbb R^n obtained by regression? I assume a general setup of regression, that is, a continuous function h_\theta:X\to \mathbb R^n is chosen from a family \{h_\theta\}_\theta to fit given data (x_i,y_i)\in X\times \mathbb R^n, i=... 0answers 164 views ### State of art streaming learning I have been working with large data sets lately and found a lot of papers of streaming methods. To name a few: Follow-the-Regularized-Leader and Mirror Descent: Equivalence Theorems and L1 ... 0answers 119 views ### Tail of the inverse cdf I am almost sure I have already seen the following result in statistics but I can't remember where. If X is a positive random variable and E(X)<\infty then \epsilon F^{-1}(1-\epsilon) \to 0 ... 0answers 331 views ### ANOVA: testing assumption of normality for many groups with few samples per group Assume the following situation: we have a large number (e.g. 20) with small group sized (e.g. n = 3). I noticed that if I generate values from the uniform distribution, the residuals will look ... 0answers 251 views ### Blind source separation of convex mixture? Suppose I have n independent sources, X_1, X_2, ..., X_n and I observe m convex mixtures: \begin{align} Y_1 &= a_{11}X_1 + a_{12}X_2 + \cdots + a_{1n}X_n\\ ...&\\ Y_m &= a_{m1}X_1 + ... 0answers 347 views ### Convolutional neural networks: Aren't the central neurons over-represented in the output? [This question was also posed at stack overflow] The question in short I'm studying convolutional neural networks, and I believe that these networks do not treat every input neuron (pixel/parameter)... 0answers 495 views ### Understanding Singular Value Decomposition in the context of LSI My question is generally on Singular Value Decomposition (SVD), and particularly on Latent Semantic Indexing (LSI). Say, I have A_{word \times document} that contains frequencies of 5 words for ... 0answers 162 views ### What if probabilities are not equal in the “.632 Rule?” This question is derived from this one about the ".632 Rule." I am writing with particular reference to user603's answer/notation to the extent it simplifies matters. That answer begins with a ... 0answers 422 views ### Distribution of the convolution of squared normal and chi-squared variables? the following problem came up recently while analyzing data. If the random variable X follows a normal distribution and Y follows a \chi^2_n distribution (with n dof), how is Z = X^2 + Y^2 ... 0answers 250 views ### Negative binomial Jeffreys prior The negative binomial distribution NB(m,r) is defined as\Pr(X = k) = \left(\frac{r}{r+m}\right)^r \frac{\Gamma(r+k)}{k! \, \Gamma(r)} \left(\frac{m}{r+m}\right)^k \quad\text{for }k = 0, 1, 2, \... 0answers 2k views ### Confusion with Vowpal Wabbit's multiple-pass behavior when performing ridge-regression I have encountered many peculiarities/misunderstandings of Vowpal Wabbit when trying to do online multiple-pass learning. Specifically, I need to solve a Ridge Linear regression problem, with ... 0answers 70 views ### Example Of Strict von Neumann Inequality Letr(\pi, \delta)$denote the Bayes risk of an estimator$\delta$with respect to a prior$\pi$, let$\Pi$denote the set of all priors on the parameter space$\Theta$, and let$\Delta$denote the ... 0answers 266 views ### Bound for Arithmetic Harmonic mean inequality for matrices? NOTE: This question has originally been posted in MSE, but it did not generate any interest. It was first posted there, because the question itself is a pure matrix-algebra question. Nevertheless, ... 0answers 345 views ### Luce choice axiom, question about conditional probability I'm reading Luce (1959). Then I found this statement: When a person chooses among alternatives, very often their responses appear to be governed by probabilities that are conditioned on the ... 0answers 193 views ### Penalized spline confidence intervals based on cluster-sandwich VCV This is my first post here, but I've benefited a lot from this forum's results popping up in google search results. I've been teaching myself semi-parametric regression using penalized splines. ... 0answers 1k views ### Sample size formula for an F-test? I am wondering if there is a sample size formula like Lehr's formula that applies to an F-test? Lehr's formula for t-tests is$n = 16 / \Delta^2$, where$\Delta$is the effect size (e.g.$\Delta = (\...
In certain cases, the Jeffreys prior for a full multidimensional model is clearly inadequate, this is for example the case in: $$y_i=\mu + \epsilon_i$$ where $\epsilon \sim N(0,\sigma^2)$, $\mu$ and ...