## Brazilian Journal of Probability and Statistics

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

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

#### 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