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I'm going to provide two algorithms here: A super-exponential-time solution that works in all cases. A polynomial-time solution that applies if the mean values are known and if a certain matrix is p …

The obstruction that Bjørn Kjos-Hanssen describes can be made even worse-- it applies to any algorithm (not just von Neumann's trick) and also applies to randomized algorithms (i.e. even if the number …

This is an MCMC algorithm for uniform sampling over singular $n$ by $n$ Bernoulli matrices. Let $H$ (for "hypercube") be the set of all 0/1 vectors of length $n$. One step of the MCMC algorithm is a …

First, in case you haven't run across this before, a classic reference for this area of statistics is Mardia and Jupp's Directional Statistics, which includes a number of measures capturing circular a …

[Edit: After improving the rejection sampling algorithm and running it on a more powerful computer, I was able to extend my earlier numerical experiments. Improvements are described below in square b …

At the suggestion of the original poster, I am summarizing an alternate answer that has a few strengths relative to my original answer. It is related to the question and answer at this MathOverflow Q …

Yoav Kallus' comment above is correct; I'm going to sketch a few of the details below for the sake of completeness. Yoav points out that if we choose $X$ with parameter $$F=\begin{bmatrix}a&0&0\\0&0& …

(Edited to fix a bug.) I think the following bijection will do what you want. For $1\leq i,j\leq n-1$, define $$r_{ij}=\log(p_{ij}/p_i)$$ Given the $r_{ij}$ and the marginals, we can recover the $p …

Having explicit bounds on $\mathbb{E}[f(X)]$ does not appear to be useful. The variance can still be arbitrarily large, and the variance governs the rate of convergence for MC sampling. And if the v …

I think this conjecture is false, that is, there does not necessarily exist a subsequence that converges to a true probability distribution. Consider the following situation: Let $Q=(1,0,0,0,...)$, …

What about the symmetric-ized KL divergence? $$D(p,q) + D(q,p)$$ Recalling that $$D(p,q) = \sum_x p(x) \log \left(\frac{p(x)}{q(x)}\right)$$ then the $\log(p/q)$ is the order of magnitude of the ratio …

I think the OP is re-inventing Fisher's Exact Test, so perhaps an examination of that may be clarifying. FWIW, questions like this might be better suited to CrossValidated, which is a StackOverflow si …

I don't understand the specifics of the gateway problem well enough to comment, but on the broader question of "how do I perform inference or optimization when I have observational data, and it's prob …

Are matrix Fisher random variables closed under multiplication? For those unfamiliar with the jargon, let me unpack the terms above and repose my question. This is a question about probability distrib …

[Edit: for posterity, I'm adding two small comments to the code explaining how to fix it, in light of Iosef Pinelis' answer below. Look for "Should be:" to find the corrections.] Suppose we draw a sam …