6
votes
0answers
105 views

Sampling from a Convex Body with Many Extremal Points

Let $p_{1}, \ldots, p_{N}$ be a collection of points in $\mathbb{R}^{n}$. I would like to sample uniformly from the convex hull of these $N$ points in an `efficienct' way. In my setting, I have $n$ ...
0
votes
0answers
42 views

Nice conditional distribution / Closure under noisy observation

Let $X, Y, Z$ be Polish spaces; $M$ a collection of full-support Borel measures on $X$; $\nu$ a Borel measure on $Y$; $f:X\times Y \to Z$ continuous with the property that $f(\cdot,y)$ is injective ...
1
vote
2answers
243 views

A sampling and learning question

Suppose there is an oracle that returns a number $b \in \mathbb{Z}_{n}$ whenever I press the button. We have $b = a + e$, where $a \in \mathbb{Z}_n$ is a fixed number and $e$ is sampled according to ...
0
votes
1answer
313 views

transform a polynomial into another one upto a constant

I have a polynomial $p(x)=a_Nx^N+a_{N-1}x^{N-1}+\dots+a_0$. I want to convert this into another polynomial of same order, say $b_Ny^N+b_{N-1}y^{N-1}+\dots+b_0$. Is it possible to find a transformation ...
3
votes
1answer
377 views

When can you describe a population and its component subpopulations with the same parametric family of distributions?

I believe that it is often the case that you are trying to select the best probability distribution to use to describe some phenomenon you are studying, and you have data not only for a population, ...
6
votes
2answers
817 views

Sampling uniformly from a sphere

Let $B^{n} _p= ${$ (x_1, \dots, x_n) : |x_1|^p + \dots |x_n|^p = 1 $} be the unit ball in $\mathbb{R}^n$ in the $\ell^p$ norm. If $X_1,\dots,X_n$ are iid $\exp(1)$ -distributed random variables, then ...