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5
votes
1answer
39 views

Uniform Sampling Subject to Linear Equalities and Non-Negativity Constraint

I'm trying to sample uniformly on the intersections of faces of several simplicies, with all coordinates being non-negative. That is, given constraints $$A\vec{x}=\vec{b} \ \ and \ \ \vec{x} \geq ...
6
votes
0answers
133 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 $n$ ...
2
votes
0answers
118 views

Probabilities involving Beurling density

I am interested in calculating probabilities involving Beurling densities. Since it's likely probabilists are not familiar with the definitions, I give them below. Definitions. A metric space is ...
2
votes
0answers
222 views

Sampling from a partition of a hypercube by convex polytopes.

I have a binary space partitioning (BSP) tree which recursively partitions a hypercube using linear hyperplanes. That is, a hyperplane splits the hybercube in half, creating two convex polytopes. Each ...
1
vote
0answers
63 views

Stochastic process inference from partial observations

Consider a set $U$. My signal is a piece-wise constant "function" $Sig: t \mapsto s$, i.e. the signal at time $t$ equals to some subset $s \subset U$. One can see $Sig(t)$ as a stochastic process. ...
0
votes
0answers
29 views

How to sample from the ratio between two distributions?

I want to sample a lot of $\theta$s from the density function below: $$ r(\theta) = \frac{prior(\theta)}{Z}\frac{\int p(\theta,z_1)dz_1}{\int q(\theta,z_2)dz_2} $$ where $Z$ is the constant for ...
-1
votes
0answers
17 views

Sample discrete multivariate normal

I have asked this quesiton on the stats stack exchange with no response, so I'm posting here in hopes that someone may be able to help. What is an efficient way of sampling from a discrete ...