Brazilian Journal of Probability and Statistics

Limiting behavior of the Jeffreys power-expected-posterior Bayes factor in Gaussian linear models

D. Fouskakis and I. Ntzoufras

Full-text: Open access

Abstract

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.

Article information

Source
Braz. J. Probab. Stat., Volume 30, Number 2 (2016), 299-320.

Dates
Received: May 2014
Accepted: January 2015
First available in Project Euclid: 31 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1459429714

Digital Object Identifier
doi:10.1214/15-BJPS281

Mathematical Reviews number (MathSciNet)
MR3481105

Zentralblatt MATH identifier
1381.62230

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

Citation

Fouskakis, D.; Ntzoufras, I. Limiting behavior of the Jeffreys power-expected-posterior Bayes factor in Gaussian linear models. Braz. J. Probab. Stat. 30 (2016), no. 2, 299--320. doi:10.1214/15-BJPS281. https://projecteuclid.org/euclid.bjps/1459429714


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