Joint Specification of Model Space and Parameter Space Prior Distributions

TL;DR

This paper introduces a joint prior specification for Bayesian model comparison that reduces sensitivity to prior dispersion, improving inference stability in regression models.

Contribution

It proposes a novel joint prior approach across models to mitigate Lindley's paradox effects in Bayesian regression analysis.

Findings

Reduced sensitivity of posterior model probabilities to prior dispersion.

Improved stability of inferential and predictive quantities.

Validated with simulated and real data examples.

Abstract

We consider the specification of prior distributions for Bayesian model comparison, focusing on regression-type models. We propose a particular joint specification of the prior distribution across models so that sensitivity of posterior model probabilities to the dispersion of prior distributions for the parameters of individual models (Lindley's paradox) is diminished. We illustrate the behavior of inferential and predictive posterior quantities in linear and log-linear regressions under our proposed prior densities with a series of simulated and real data examples.