  The power-expected-posterior (PEP) prior provides an objective, automatic,
consistent and parsimonious model selection procedure. At the same time it
resolves the conceptual and computational problems due to the use of imaginary
data. Namely, (i) it dispenses with the need to select and average across all
possible minimal imaginary samples, and (ii) it diminishes the effect that the
imaginary data have upon the posterior distribution. These attributes allow for
large sample approximations, when needed, in order to reduce the computational
burden under more complex models. In this work we generalize the applicability
of the PEP methodology, focusing on the framework of generalized linear models
(GLMs), by introducing two new PEP definitions which are in effect applicable
to any general model setting. Hyper-prior extensions for the power parameter
that regulates the contribution of the imaginary data are introduced. We
further study the validity of the predictive matching and of the model
selection consistency, providing analytical proofs for the former and empirical
evidence supporting the latter. For estimation of posterior model and inclusion
probabilities we introduce a tuning-free Gibbs-based variable selection
sampler. Several simulation scenarios and one real life example are considered
in order to evaluate the performance of the proposed methods compared to other
commonly used approaches based on mixtures of g-priors. Results indicate that
the GLM-PEP priors are more effective in the identification of sparse and
parsimonious model formulations.
