Currently, I am sampling points from:
i) a convex polytope (i.e. Ax <= b)
ii) a high dimensional simplex
The algorithms I am using are hit-and-run and a simple version of Bayesian bootstrap. I want to know whether my sampling is uniform.
From a holistic point of view, what would be some good tests to see whether my sampling is truly uniform or not? I am confused as to how to begin.
(My implementation is in R. The sampled points are N dimensional vectors, and the simplex and polytope are represented by matricies. Both general ideas and specific implementation would be much appreciated. Thank you so much!)