The Highest Posterior Density Posterior Prior for Bayesian Model Selection

Abstract

In this paper a new type of prior is proposed that could be suitable in the context of model selection using Bayes factors. The Highest Posterior Density Posterior Prior (HPDPP) consists of a uniform distribution over the highest posterior density area, and basically results in truncation of low-density parameter space. The behavior and properties of the new prior are illustrated using constrained analysis of variance models. Both theoretical justification and simulations are used to argue that this prior has attractive properties for model selection. Because the HPDPP only uses relevant parameter space to determine the size of a model, results do not heavily depend on sample size or number of parameters. To avoid complications for interpretation it is recommended only to test exclusive models when using the HPDPP.