All Questions

29
votes
0answers
1k views

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 ...
23
votes
0answers
571 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, ...
20
votes
0answers
1k views

How to create a multivariate Brownian Bridge

It is known, that a standard multivariate Brownian bridge $ y(\mathbf u) $ is a centered Gaussian process with covariance function $$ \mathbb E(y(\mathbf u) y(\mathbf v)) = \prod_{j=1}^d (u_j \wedge ...
18
votes
0answers
705 views

How does a Relevance Vector Machine (RVM) work?

Relevance Vector Machines (RVMs) are really interesting models when contrasted with the highly geometrical (and popular) SVMs. In the light of a question like How does a Support Vector Machine (SVM) ...
16
votes
0answers
510 views

Fitting custom distributions by MLE

My question relates to fitting custom distributions in R but I feel it has enough of a probability element to remain on CV. I have an interesting set of data which has the following characteristics: ...
16
votes
0answers
793 views

Diagnostic plot for assessing homogeneity of variance-covariance matrices

Is there a handy plot for comparing the variance-covariance matrices of two (or perhaps more) groups? An alternative to looking at lots of marginal plots, especially in the multivariate Normal case?
16
votes
0answers
519 views

Distribution of inverse Wishart to a power?

In a related question, I had asked about the norm induced by an inverse Wishart matrix. I am interested in generalizing that result somewhat. Let $A\sim\mathcal{W}_p\left(I,n\right)$, a Wishart matrix ...
16
votes
0answers
879 views

Least stupid way to forecast a short multivariate time series

I need to forecast the following 4 variables for the 29th unit of time. I have roughly 2 years worth of historical data, where 1 and 14 and 27 are all the same period (or time of year). In the end, I ...
15
votes
0answers
293 views

Pooling calibration plots after multiple imputation

I would like advice on pooling the calibration plots/statistics after multiple imputation. In the setting of developing statistical models in order to predict a future event (e.g. using data from ...
15
votes
0answers
670 views

Bootstrapping Generalized Least Squares

Scenario: Consider the use of bootstrapping to estimate the distribution of model parameters fitted per a linear or nonlinear generalized least squares model. In particular, assume there is a ...
14
votes
0answers
326 views

Distribution of $\frac{\sum_{i=1}^n X_iY_i}{\sum_{i=1}^n X_i^2}$ where $X_i,Y_i$s are i.i.d Normal variables

Suppose $X_1,\ldots,X_n,Y_1,\ldots,Y_n$ are i.i.d $\mathcal N(0,1)$ random variables. I am interested in the distribution of $$U=\frac{\sum_{i=1}^n X_iY_i}{\sum_{i=1}^n X_i^2}$$ I define $$Z=\...
14
votes
0answers
536 views

Is there a general expression for ancillary statistics in exponential families?

It is known that an i.i.d sample $X_1,\dots,X_n$ from a scale family with c.d.f. $F(\frac{x}{\sigma})$ has $S(X)$ as an ancillary statistic if $S(X)$ depends on the sample only through $\frac{X_1}{X_n}...
13
votes
0answers
3k views

Multivariate Beta distribution (no Dirichlet!)

What is a multidimensional generalization of the Beta distribution, in compliance with the following specification? I am not looking for the Dirichlet distribution. I am looking for a generalization ...
13
votes
0answers
626 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 ...
12
votes
0answers
733 views

Bayesian Q-learning

Suppose that, for every state $s$, there is a set of actions $\mathcal{A}(s)$ that can be chosen in that state. Let $Q(s, a)$ denote the expected utility of choosing action $a \in \mathcal{A}(s)$ in ...
12
votes
0answers
857 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 ...
12
votes
0answers
2k views

When does a UMP test fail to exist?

I have a sample $X=(X_1, ...,X_n)\sim N(\mu,\sigma^2)$ with $\sigma^2$ known. The hypotheses are $H_0: \mu=\mu_0, H_1:\mu \neq \mu_0$. I know that in such a case an UMP test does not exist and so ...
12
votes
0answers
401 views

Can I use optimally scaled variables for a factor analysis to account for rotation? If I can then how?

I have discussed this issue several times in this site, but I am asking it again for a final justification from the experts of our community. I wanted to extract four factors (I should call dimensions ...
11
votes
0answers
650 views

What is the intuition behind the expected transaction value for a customer in the gamma-gamma model?

Background and Motivation: I was reading the paper RFM and CLV: Using Iso-Value Curves for Customer Base Analysis by Peter S. Fader, Bruce G. S. Hardie and Ka Lok Lee, in an attempt to gain some ...
11
votes
0answers
993 views

Rademacher complexity of logistic regression

Consider logistic regression. We have the logistic loss function, $\phi: R\rightarrow [0,1], \phi(u)=\log(1+\exp(-u))$, which is Lipschitz, and we have the linear function class $F=\{f_w:R^d \...
11
votes
0answers
1k views

Ratios in Regression, aka Questions on Kronmal

Recently, randomly browsing questions triggered a memory of on off-hand comment from one of my professors a few years back warning about the usage of ratios in regression models. So I started reading ...
11
votes
0answers
1k views

The role of scale parameter in GEE

I am learning the generalized estimating equations (GEE) and the geepack R package. There are some questions that I am a little confused. In a GEE-constructed ...
11
votes
0answers
321 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. ...
11
votes
0answers
4k views

How to compute confidence interval in ANOVA with repeated measures?

I made a model using repeated measures univariate ANOVA in R. ...
11
votes
0answers
952 views

Testing for a significant difference between ML estimates: Likelihood ratio or Wald test?

I am trying to test whether or not there is a significant difference between maximum likelihood estimates of two genetic parameters (selection and dominance) across two environments with genotype data ...
11
votes
0answers
317 views

Are non-square latin hypercubes viable?

At https://github.com/OpenMDAO/OpenMDAO-Framework/issues/599 it is stated that non-square Latin Hypercube experimental design is not well defined (I assume that for higher dimensions that means ...
11
votes
0answers
2k views

How to use G Power 3 to calculate statistical power in mixed design ANOVA with unequal group sample sizes

In G power 3, ANOVA repeated measures within-between interaction: Only the total sample size is reported assuming equal sample size for the two groups. My questions are: How would it work if the ...
10
votes
0answers
167 views

Maximum Entropy with bounded constraints

Assume we have the problem of estimating the probabilities $\{p_1,p_2,p_3\}$ subject to: $$0 \le p_1 \le .5$$ $$0.2 \le p_2 \le .6$$ $$0.3 \le p_3 \le .4$$ with only the natural constraint of $p_1+...
10
votes
0answers
172 views

Empirical Bayes (In)Admissibility

Sticking to a pure Bayesian approach to statistics with proper priors most of the time leads to admissible estimators. Nevertheless there is good reason to use Empirical Bayes in many cases, and the ...
10
votes
0answers
2k views

Getting started with bayesian structural models using MCMC

I'm trying to learn bayesian structural time series analysis. For a variety of reasons I need to use Python (mostly pymc3) not R so please do not suggest the ...
10
votes
0answers
7k views

Interpreting negative cosine similarity

My question may be a silly one. So I shall apologize in advance. I was trying to use the GLOVE model pre-trained by Stanford NLP group (link). However, I noticed that my similarity results showed ...
10
votes
0answers
553 views

Picking block length in a block bootstrap

I am using the Mann-Kendall test to assess trends in a data time-series. I believe there is autocorrelation in my data and therefore need to use a block bootstrap to correct for it. I have plotted ...
10
votes
0answers
381 views

Asymptotic property of tuning parameter in penalized regression

I'm currently working on asymptotic properties of penalized regression. I've read a myriad of papers by now, but there is an essential issue that I cannot get my head around. To keep things simple, I'...
10
votes
0answers
1k views

Tail inequality on sum of product of normal variables

For independent random variables $ x_1,..,x_n$ and $y_1,...,y_n$ following normal distribution $N(0,1)$, I need a simple estimate formula for $P(| \sum_1^n x_iy_i | \leq nt ) \leq e^{(?)}$ for $t>...
10
votes
0answers
831 views

What is Shannon's source entropy?

Suppose that ${X_n; Y_n}$ is a random process with a discrete alphabet, that is, taking on values in a discrete set for $n$ data length. They correspond to the input and output of a communication ...
9
votes
0answers
3k views

Backpropagation on a convolutional layer

Online tutorials describe in depth the convolution of an image with a filter, etc; However, I have not seen one that describes the backpropagation on the filter (at least visually). First let me try ...
9
votes
0answers
4k views

Specify correlation structure for different groups in mixed-effects model (lme4/nlme)

I am trying to account for spatial autocorrelation in a linear mixed-effects model in R with measurements repeated in time. BodyMass has been collected once per <...
9
votes
0answers
330 views

Time series modeling of circular data

I'm building ARIMA models for some wind/waves data. I'm building a separate model for each variable. Two of the variables that I need to model are wave and wind direction. The values are in degrees (...
9
votes
0answers
188 views

What is tantile regression?

My question follows on this discussion of medials and tantiles vs medians and quantiles from earlier this year: When would we use tantiles and the medial, rather than quantiles and the median? As ...
9
votes
0answers
2k views

Gamma hurdle model for continuous response

I am modelling invertebrate.biomass ~ habitat.type * calendar.day + habitat.type * calendar.day ^ 2, with a random intercept of transect.id (50 transects were repeated 5 times) My response is zero-...
9
votes
0answers
2k views

How do I identify the “Long Tail” portion of my distribution?

I have a number of series that would typically be described as normal skewed or Gamma distributed. For example, say I have a group of customers and have calculated their spend over a fixed length of ...
9
votes
0answers
822 views

Understanding Sequential Probability Ratio Test (SPRT) Likelihood Ratio

I am a software developer looking to develop an alternative for the simple hypothesis testing scheme described here. In short, the test works as follows: Two URLs are compared for their ability to ...
9
votes
0answers
557 views

Variance of the Kaplan-Meier estimate for dependent observations

Can someone help me find a way to estimate the variance of the Kaplan-Meier estimate with dependent observations? Specifically, I have failure time data from patients with several different ...
8
votes
0answers
249 views

Validity of confidence interval for $\rho$ when $X\sim N_3(0,\Sigma)$ with $\Sigma_{ij}=(\rho^{|i-j|})$

Suppose $X\sim N_3(0,\Sigma)$, where $\Sigma=\begin{pmatrix}1&\rho&\rho^2\\\rho&1&\rho\\\rho^2&\rho&1\end{pmatrix}$. On the basis of one observation $x=(x_1,x_2,x_3)'$, I ...
8
votes
0answers
625 views

Compute partial $\eta^2$ for all fixed effects anovas from a lme4 model

Disclamer: I wasn't sure where to post this question: CV or SO, but eventually decided to try here first I've been asked by one of the reviewers to add effects sizes (preferably $\eta^2_p$ which is ...
8
votes
0answers
1k views

What is the logic behind “rule of thumb” for meaningful differences in AIC?

I've been struggling to find meaningful guidelines for comparing models based on differences in AIC. I keep coming back to the rule of thumb offered by Burnham & Anderson 2004, pp. 270-272: ...
8
votes
0answers
436 views

Difference between Multivariate Time Series data and Panel Data

Recently I got mix response on the difference between multivariate time series data and panel data. I completely understand the difference between cross sectional data, time series data and panel data....
8
votes
0answers
476 views

No-U-Turn Sampler (NUTS) for Hamiltonian Monte Carlo (HMC): how do I understand the doubling process?

I'm reading the original NUTS paper by Hoffman and Gelman, but couldn't fully understand the recursively doubling process. The following figure is taken from the paper. The NUTS process starts ...
8
votes
0answers
287 views

Why are Gaussian distributions the only “forbidden” source distribution for ICA?

I know it's commonly asked why Gaussians are forbidden from use in independent components analysis. This is because a gaussian source distribution will result in the same observed distribution no ...
8
votes
0answers
1k views

What loss function should I use to score a seq2seq RNN model?

I'm working through the Cho 2014 paper which introduced encoder-decoder architecture for seq2seq modeling. In the paper, they seem to use the probability of the output given input (or it's negative-...

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