Bayesian variable selection with spherically symmetric priors

TL;DR

This paper introduces a Bayesian variable selection method leveraging spherical symmetry of the parameter space, providing closed-form evidence calculations and demonstrating improved model comparison performance.

Contribution

It presents a novel r-prior framework that unifies existing priors and offers analytical evidence formulas for Bayesian variable selection.

Findings

Closed-form evidence for multiple priors including hyper-g and Zellner-Siow

Asymptotic forms similar to information criteria

Simulation results show improved model comparison accuracy

Abstract

We propose that Bayesian variable selection for linear parametrisations with Gaussian iid likelihoods be based on the spherical symmetry of the diagonalised parameter space. Our r-prior results in closed forms for the evidence for four examples, including the hyper-g prior and the Zellner-Siow prior, which are shown to be special cases. Scenarios of a single variable dispersion parameter and of fixed dispersion are studied, and asymptotic forms comparable to the traditional information criteria are derived. A simulation exercise shows that model comparison based on our r-prior gives good results comparable to or better than current model comparison schemes.