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May 2016 Limiting behavior of the Jeffreys power-expected-posterior Bayes factor in Gaussian linear models
D. Fouskakis, I. Ntzoufras
Braz. J. Probab. Stat. 30(2): 299-320 (May 2016). DOI: 10.1214/15-BJPS281


Expected-posterior priors (EPPs) have been proved to be extremely useful for testing hypotheses on the regression coefficients of normal linear models. One of the advantages of using EPPs is that impropriety of baseline priors causes no indeterminacy in the computation of Bayes factors. However, in regression problems, they are based on one or more training samples, that could influence the resulting posterior distribution. On the other hand, the power-expected-posterior priors are minimally-informative priors that reduce 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 prove the consistency of the Bayes factors when using the power-expected-posterior priors, with the independence Jeffreys as a baseline prior, for normal linear models, under very mild conditions on the design matrix.


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D. Fouskakis. I. Ntzoufras. "Limiting behavior of the Jeffreys power-expected-posterior Bayes factor in Gaussian linear models." Braz. J. Probab. Stat. 30 (2) 299 - 320, May 2016.


Received: 1 May 2014; Accepted: 1 January 2015; Published: May 2016
First available in Project Euclid: 31 March 2016

zbMATH: 1381.62230
MathSciNet: MR3481105
Digital Object Identifier: 10.1214/15-BJPS281

Keywords: Bayes factors , Bayesian variable selection , consistency , expected-posterior priors , Gaussian linear models , objective model selection methods , power prior , power-expected-posterior priors , training sample , unit-information prior

Rights: Copyright © 2016 Brazilian Statistical Association


Vol.30 • No. 2 • May 2016
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