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(n) $, 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