Prior-predictive value from fast growth simulations

TL;DR

This paper introduces a novel, efficient method based on a variant of the Jarzynski equation for calculating the prior-predictive value in Bayesian inference, outperforming thermodynamic integration especially with multi-modal posteriors.

Contribution

It generalizes thermodynamic integration using a Jarzynski-based approach, avoiding equilibration issues in Bayesian prior-predictive calculations.

Findings

Method works well on simple examples

Outperforms thermodynamic integration on multi-modal distributions

Not hampered by equilibration problems

Abstract

Building on a variant of the Jarzynski equation we propose a new method to numerically determine the prior-predictive value in a Bayesian inference problem. The method generalizes thermodynamic integration and is not hampered by equilibration problems. We demonstrate its operation by applying it to two simple examples and elucidate its performance. In the case of multi-modal posterior distributions the performance is superior to thermodynamic integration.