Power-expected-posterior prior Bayes factor consistency for nested linear models with increasing dimensions

Abstract

The power-expected-posterior prior is used in this paper for comparing nested linear models. The asymptotic behaviour of the method is investigated for different values of the power parameter of the prior. Focus is given on the consistency of the Bayes factor of comparing the full model $M_p$ versus a generic submodel $M_{\ell }$. In each case, we allow the true generating model to be either $M_p$ or $M_{\ell }$ and we keep the dimension of $M_{\ell }$ fixed, while the dimension of $M_p$ can be either fixed or (grow as) $O\left(n\right)$, with n denoting the sample size.

Keywords:

• Bayesian model selection
• Bayes factor
• consistency
• expected-posterior prior
• Gaussian linear models
• increasing dimension
• power-expected-posterior prior

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

D. Fouskakis

D. Fouskakis is an Associate Professor in the Department of Mathematics, at the National Technical University of Athens, in Greece. He is also the Director of the Stats Lab at the same University. His research mostly focuses on Bayesian model and variable selection, on objective priors and on stochastic optimization methods.

J. K. Innocent

J. K. Innocent received a Ph.D in Mathematics at the University of Puerto Rico, Puerto Rico, USA in 2016. He is currently back to Haiti, where he teaches mathematical and Statistical courses at a university level. His main research areas are on Bayesian Statistics, Statistical Analysis, Biostatistics and Epidemiology.

L. Pericchi

L. Pericchi is a Full Professor in the Department of Mathematics of the University of Puerto Rico Rio Piedras, USA. He is also the Director of the Center of Biostatistics and Bioinformatics of the College of Natural Sciences. His research is in the Theory and Applications of Statistics, with emphasis in the Bayesian Approach.