Power-Conditional-Expected Priors: Using g-priors with Random Imaginary Data for Variable Selection

TL;DR

This paper introduces the power-conditional-expected-posterior (PCEP) prior, a hierarchical extension of g-priors that accounts for imaginary data uncertainty, improving Bayesian variable selection in normal regression models.

Contribution

It develops the PCEP prior, a conjugate hierarchical prior that enhances variable selection by incorporating imaginary data uncertainty within the g-prior framework.

Findings

PCEP supports more parsimonious models than g-prior and hyper-g prior.

The method shows consistent variable selection in finite samples.

Empirical results demonstrate improved model selection accuracy.

Abstract

The Zellner's g-prior and its recent hierarchical extensions are the most popular default prior choices in the Bayesian variable selection context. These prior set-ups can be expressed power-priors with fixed set of imaginary data. In this paper, we borrow ideas from the power-expected-posterior (PEP) priors in order to introduce, under the g-prior approach, an extra hierarchical level that accounts for the imaginary data uncertainty. For normal regression variable selection problems, the resulting power-conditional-expected-posterior (PCEP) prior is a conjugate normal-inverse gamma prior which provides a consistent variable selection procedure and gives support to more parsimonious models than the ones supported using the g-prior and the hyper-g prior for finite samples. Detailed illustrations and comparisons of the variable selection procedures using the proposed method, the g-prior and the hyper-g prior are provided using both simulated and real data examples.