  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.

Methodology