Objective Bayesian testing on the common mean of several normal distributions under divergence-based priors

Abstract

This paper considers the problem of testing on the common mean of several normal distributions. We propose a solution based on a Bayesian model selection procedure in which no subjective input is considered. We construct the proper priors for testing hypotheses about the common mean based on measures of divergence between competing models. This method is called the divergence-based priors (Bayarri and Garcia-Donato in J R Stat Soc B 70:981---1003, 2008). The behavior of the Bayes factors based DB priors is compared with the fractional Bayes factor in a simulation study and compared with the existing tests in two real examples.