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1
vote
1answer
58 views

Sampling from random unimodular matrices of a particular type?

Is there a nice way to parametrize unimodular matrices of form $$\begin{bmatrix} a1& a2& 0& 0\\ b1& b2& a1& a2\\ c1& c2& b1& b2\\ 0& 0& c1& c2 ...
6
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0answers
136 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
224 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
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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. ...
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0answers
2 views

Mean and variance for unequal samples

I have a sampling of variable sized plots. Each plot contains the number of trees present on the plot. Given: $n=$ the number of plots $s_i=$ the size of the $i^{th}$ plot $y_i=$ the number of trees ...
0
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0answers
30 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 ...