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As fedja noted in the comments, I am essentially asking a classical moment problem. I'm not sure if the $x=p/(1-p)$ change of variables reduction quite works (consider, e.g., the singleton probabilit …

Suppose I have a (possibly infinite) bag of coins with various weights. I select a coin and flip it $n$ times. Averaging over the choice of coins from the bag, there is some probability of seeing e …

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 …

Kostya_I is correct, of course, but taking the closure under convolution can sometimes be a bit ugly. If you're interested in a simple, parametric family, consider the hyperbolic secant distribution. …

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 …

Let $D$ be a probability distribution on the unit interval $[0,1]$ with moments $\mu_i=\mathbb{E}_D [x^i]$. Let $\delta(x)$ be a singleton probability distribution with all weight at $x\in [0,1]$. L …

[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 …

Here's a few empirical results that might be helpful, particularly in lending credence towards some of the theories suggested in other posts. I ran 10,000 simulations, and for each one, broke the sti …

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& …

Let $\mathcal{D}(m)$ be the set of phase-type distributions constructed from $m+1$-state Markov chains. Recall that the coefficient of variation of a distribution $D$ is the ratio of the standard dev …

(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 …