Power-Expected-Posterior Priors as Mixtures of g-Priors in Normal Linear Models

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 powerexpected-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 its computational tractability. Following this result, we can naturally prove that desiderata (criteria for objective Bayesian model comparison) hold for the PEP prior. Comparisons with other mixtures of g-prior are made and results are presented in simulated and real-life datasets.