Limiting behavior of the Jeffreys Power-Expected-Posterior Bayes Factor in Gaussian Linear Models

TL;DR

This paper investigates the limiting behavior of Jeffreys Power-Expected-Posterior Bayes Factors in Gaussian linear models, demonstrating their consistency under mild conditions and highlighting their robustness in hypothesis testing.

Contribution

It proves the consistency of Bayes factors using power-expected-posterior priors with Jeffreys prior as baseline in Gaussian linear models, under mild conditions.

Findings

Bayes factors are consistent with power-expected-posterior priors.

The approach diminishes the influence of training samples.

Results hold under mild design matrix conditions.

Abstract

Expected-posterior priors (EPP) have been proved to be extremely useful for testing hypothesis on the regression coefficients of normal linear models. One of the advantages of using EPPs is that impropriety of baseline priors causes no indeterminacy. However, in regression problems, they based on one or more \textit{training samples}, that could influence the resulting posterior distribution. The power-expected-posterior priors are minimally-informative priors that diminishing the effect of training samples on the EPP approach, by combining ideas from the power-prior and unit-information-prior methodologies. In this paper we show the consistency of the Bayes factors when using the power-expected-posterior priors, with the independence Jeffreys (or reference) prior as a baseline, for normal linear models under very mild conditions on the design matrix.