Power-Expected-Posterior Priors as Mixtures of g-Priors

Abstract

One of the main approaches used to construct prior distributions for objective Bayes methods is the concept of random imaginary observations. Under this setup, the expected-posterior prior (EPP) offers several advantages, among which it has a nice and simple interpretation and provides an effective way to establish compatibility of priors among models. In this paper, we study the power-expected posterior prior as a generalization to the EPP in objective Bayesian model selection under normal linear models. We prove that it can be represented as a mixture of $g$-prior, like a wide range of prior distributions under normal linear models, and thus posterior distributions and Bayes factors are derived in closed form, keeping therefore computational tractability. Comparisons with other mixtures of $g$-prior are made and emphasis is given in the posterior distribution of g and its effect on Bayesian model selection and model averaging.

References in corpus (5)

• Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem
• The formal definition of reference priors
• Criteria for Bayesian model choice with application to variable selection
• Mixtures of g-priors in Generalized Linear Models
• MultiBUGS: A parallel implementation of the BUGS modelling framework for faster Bayesian inference