Expected Posterior Priors in Selecting the Largest Mean of the Exponential Distributions

Abstract

In reliability theory or survival analysis, selecting the largest mean among many exponential distributions is an important issue. Such a problem can also be viewed as a model selection problem via the Bayesian approach. It is well known that Bayes factors under proper priors have been very successful in Bayesian model selection or testing problems. However, Bayes factors are typically invalid with respect to improper noninformative priors. Objective Bayesian criteria are thus desired. In this work, we consider to use the expected posterior priors originally proposed by Pérez and Berger (2002) to select the largest exponential mean. Specific expected posterior priors are derived in recursive formulas. Some simulation results are also given to illustrate the method.