Fully Bayes factors with a generalized g-prior

TL;DR

This paper introduces a fully Bayesian approach for variable selection in normal linear models using a generalized g-prior, enabling analysis when predictors outnumber observations, and provides new insights into model evaluation.

Contribution

It develops a generalized g-prior framework for Bayesian variable selection that is computationally tractable even when p > n, offering new model evaluation tools.

Findings

Closed-form expressions for marginal densities and Bayes factors.

New model evaluation characteristics revealed.

Applicable to high-dimensional variable selection.

Abstract

For the normal linear model variable selection problem, we propose selection criteria based on a fully Bayes formulation with a generalization of Zellner's $g$-prior which allows for $p>n$. A special case of the prior formulation is seen to yield tractable closed forms for marginal densities and Bayes factors which reveal new model evaluation characteristics of potential interest.