A Bayesian nonparametric multi-sample test in any dimension

Luai Al-Labadi (), Forough Fazeli Asl () and Zahra Saberi ()
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Luai Al-Labadi: University of Toronto Mississauga
Forough Fazeli Asl: Isfahan University of Technology
Zahra Saberi: Isfahan University of Technology

AStA Advances in Statistical Analysis, 2022, vol. 106, issue 2, No 3, 217-242

Abstract: 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.

Keywords: Dirichlet process prior; Energy distance; Multi-sample hypothesis testing; Relative belief ratio; Simulation; 62F15; 62G10; 62H15 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10182-021-00419-3

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