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

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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 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.