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### SVD of correlated matrix should be additive but doesn't appear to be

I'm just trying to replicate a claim made in the following paper, Finding Correlated Biclusters from Gene Expression Data, which is: Proposition 4. If $X_{IJ}=R_{I}C^{T}_{J}$. then we have: ...
335 views

### When is binomial distribution function above/below its limiting Poisson distribution function?

Let $B(n,p,r)$ denote the binomial distribution function (DF) with parameters $n \in \mathbb N$ and $p \in (0,1)$ evaluated at $r \in \{0,1,\ldots,n\}$: B(n,p,r) = \sum_{i=0}^r ...
513 views

### Stability of cross-validation in Bayesian models

I'm fitting a Bayesian HLM in JAGS using k-fold cross-validation (k=5). I'd like to know whether estimates of parameter $\beta$ are stable across all folds. What's the best way to do this? One idea ...
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### Can the Mantel test be extended to asymmetric matrices?

The Mantel test is usually applied to symmetric distance/difference matrices. As far as I understand, an assumption of the test is that the measure used to define differences must be at least a ...
2k views

### What is the difference between PCA and asymptotic PCA?

In two papers in 1986 and 1988, Connor and Korajczyk proposed an approach to modeling asset returns. Since these time series have usually more assets than time period observations, they proposed to ...
755 views

### Gaussian Ratio Distribution: Derivatives wrt underlying $\mu$'s and $\sigma^2$s

I'm working with two independent normal distributions $X$ and $Y$, with means $\mu_x$ and $\mu_y$ and variances $\sigma^2_x$ and $\sigma^2_y$. I'm interested in the distribution of their ratio ...
272 views

### Inference on fixed effects in a mixed effects model

I have correlated data and am using a logistic regression mixed effects model to estimate the individual level (conditional) effect for a predictor of interest. I know that for standard marginal ...
1k views

### Inverting the Fourier Transform for a Fisher distribution

The characteristic function of Fisher $\mathcal{F}(1,\alpha)$ distribution is: C(t)=\frac{\Gamma \left(\frac{\alpha +1}{2}\right) U\left(\frac{1}{2},1-\frac{\alpha }{2},-i t \alpha \right)}{\Gamma ...
280 views

### Phylogenetic dependent variables: ANOVA?

I understand deriving a covariance matrix from phylogenetic data to make $cov(X,Y) = 0$ for two variables you're making a regression on. But what happens if you have one continuous variable, that ...
208 views

### Training a basic Markov Random Field for classifying pixels in an image

I am attempting to learn how to use Markov Random Fields to segment regions in an image. I do not understand some of the parameters in the MRF or why the expectation maximisation I perform fails to ...
273 views

### Rao-Blackwellization of sequential Monte Carlo filters

In the seminal paper "Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks" by A. Doucet et. al. a sequential monte carlo filter (particle filter) is proposed, which makes use of a ...
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Suppose we have a multiple comparisons scenario like such as post hoc inference on pairwise statistics, or a multiple regression, where we are making a total of $m$ comparisons. Suppose also, that we ...
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### Test if people drop out or decrease bets after repeated losses

I have data on a series of winning and losing bets over 5 rounds of betting with attrition after each round. I am using a decision tree like the following to display the data. The nodes towards ...
### Tail bounds on Euclidean norm for uniform distribution on $\{-n,-(n-1),…,n-1,n\}^d$
What are known upper bounds on how often the Euclidean norm of a uniformly chosen element of $\:\{-n,~-(n-1),~...,~n-1,~n\}^d\:$ will be larger than a given threshold? I'm mainly interested in bounds ...
Let's say I have a model selection problem and I am trying to use AIC or BIC to evaluate the models. This is straightforward for models that have some number $k$ of real-valued parameters. However, ...