Variations of Power-Expected-Posterior Priors in Normal Regression Models

TL;DR

This paper investigates two new variants of the power-expected-posterior (PEP) prior for Gaussian linear models, analyzing their properties, consistency, and applicability in different model scenarios.

Contribution

It provides a thorough examination of the properties and consistency of two new PEP prior variants within normal linear models, extending their applicability.

Findings

Both PEP variants have larger variances than the g-prior.

They are M-closed consistent, matching BIC in the limit.

Their consistency under model misspecification is confirmed.

Abstract

The power-expected-posterior (PEP) prior is an objective prior for Gaussian linear models, which leads to consistent model selection inference, under the M-closed scenario, and tends to favor parsimonious models. Recently, two new forms of the PEP prior were proposed which generalize its applicability to a wider range of models. The properties of these two PEP variants within the context of the normal linear model are examined thoroughly, focusing on the prior dispersion and on the consistency of the induced model selection procedure. Results show that both PEP variants have larger variances than the unit-information g-prior and that they are M-closed consistent as the limiting behavior of the corresponding marginal likelihoods matches that of the BIC. The consistency under the M-open case, using three different model misspecification scenarios is further investigated.