Bayesian nonparametric tests for multivariate locations

TL;DR

This paper introduces Bayesian nonparametric tests for multivariate location problems using Dirichlet process priors, providing a flexible approach that adapts to the data and offers competitive performance.

Contribution

It develops novel Bayesian nonparametric tests for multivariate location hypotheses based on the Dirichlet process and posterior credible regions, extending existing methods.

Findings

The tests have good finite-sample performance in simulations.

The methods are applicable to both one-sample and two-sample problems.

Theoretical analysis shows favorable local asymptotic power.

Abstract

In this paper, we propose novel, fully Bayesian non-parametric tests for one-sample and two-sample multivariate location problems. We model the underlying distribution using a Dirichlet process prior, and develop a testing procedure based on the posterior credible region for the spatial median functional of the distribution. For the one-sample problem, we fail to reject the null hypothesis if the credible set contains the null value. For the two-sample problem, we form a credible set for the difference of the spatial medians of the two samples and we fail to reject the null hypothesis of equality if the credible set contains zero. We derive the local asymptotic power of the tests under shrinking alternatives, and also present a simulation study to compare the finite-sample performance of our testing procedures with existing parametric and non-parametric tests.