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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: ...
406 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 ...
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### Random forests for multivariate regression

I have a multi-output regression problem with $d_x$ input features and $d_y$ outputs. The outputs have a complex, non-linear correlation structure. I'd like to use random forests to do the ...
532 views

### How the Pearson's Chi Squared Test works

Following a recent down vote I have been trying to check my understanding of the Pearson Chi Squared test. I usually use the chi squared statistic (or reduced chi squared statistic) for fitting or ...
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### 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 ...
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### Testing certain contrasts: Is this provably a hard problem, or not?

I posted this to mathoverflow and no one's answering: Scheffé's method for identifying statistically significant contrasts is widely known. A contrast among the means $\mu_i$, $i=1,\ldots,r$ of $r$ ...
377 views

### What are the options in proportional hazard regression model when Schoenfeld residuals are not good?

I am doing a Cox proportional hazards regression in R using coxph, which includes many variables. The Martingale residuals look great, and the Schoenfeld residuals ...
295 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 ...
95 views
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### Why does adding a lag effect increase mean deviance in a Bayesian hierarchical model?

Background: I'm currently doing some work comparing various Bayesian hierarchical models. The data $y_{ij}$ are numeric measures of well-being for participant $i$ and time $j$. I have around 1000 ...
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### Prediction interval based on cross-validation (CV)

In the text books and youtube lectures I learned a lot about iterative models such as boosting, but I never saw anything about deriving a prediction interval. Cross validation is used for the ...
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### Are data handling errors already 'priced in' to statistical analysis?

Ok, fair warning--this is a philosophical question that involves no numbers. I've been thinking a lot about how errors creep into data sets over time and how that should be treated by analysts--or if ...
269 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 ...
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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 ...
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 ...