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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!)

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migrated from stackoverflow.com Jun 29 '15 at 2:25

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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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