A Bayesian nonparametric multi-sample test in any dimension

Abstract

This paper considers a general Bayesian test for the multi-sample problem. Specifically, for M independent samples, the interest is to determine whether the M samples are generated from the same multivariate population. First, M Dirichlet processes are considered as priors for the true distributions generated the data. Then, the concentration of the distribution of the total distance between the M posterior processes is compared to the concentration of the distribution of the total distance between the M prior processes through the relative belief ratio. The total distance between processes is established based on the energy distance. Various interesting theoretical results of the approach are derived. Several examples covering the high dimensional case are considered to illustrate the approach.