Uniform sampling over a $n$-dimensional standard simplex is described here: Uniform sampling from a simplex
I want to sample one point from a non-standard simplex with vertices at:
- $s_{i}\vec{e_{i}}$, where $\vec{e_{i}}$ is the $i^{th}$ vector in the standard basis, and $s_{i} \ge 0$.
- the origin is : $\vec{0}$
How to do that? It seems to be no longer a special case of the Dirichlet distribution.
Hit-and-run sampling would need a lot of cycle to diffuse throughout the simplex. When I only need one point, the other points are wasted.
Currently, $n \approx 15$