Objective Bayesian multiple testing for k normal populations

Abstract

This article proposes objective Bayesian multiple testing procedures for a normal model. The challenging task of considering all the configurations of true and false null hypotheses is addressed here by ordering the null hypotheses based on their Bayes factors. This approach reduces the size of the compared models for posterior search from \(2^k\) to \(k+1\), for k null hypotheses. Furthermore, the consistency of the proposed multiple testing procedures is established and their behavior is analyzed with simulated and real examples. In addition, the proposed procedures are compared with classical and Bayesian multiple testing procedures in all the possible configurations of true and false ordered null hypotheses.