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!)


You can divide the sampling space in half, and just check if the numbers of points in each half are roughly the same. You can visit my Github, where I have some implementations on this. Does that answer your question?

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