Power-Expected-Posterior Priors for Generalized Linear Models

The power-expected-posterior (PEP) prior developed for variable selection in normal regression models 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 further considered. Under these approaches the resulting PEP prior can be asymptotically represented as a double mixture of g-priors. For estimation of posterior model and inclusion probabilities we introduce a tuning-free Gibbs-based variable selection sampler. Several simulation scenarios and one real data 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. Empirical results indicate that the GLM-PEP adaptations are more effective when the aim is parsimonious inference.