Prior-predictive value from fast-growth simulations: Error analysis and bias estimation

TL;DR

This paper analyzes the statistical errors and biases in using fluctuation theorem variants for high-dimensional Bayesian integrals, validated through simulations of bimodal systems.

Contribution

It provides a comprehensive error and bias analysis for prior-predictive value estimation using fluctuation theorems in Bayesian inference.

Findings

Error analysis and bias estimation methods are developed.

Numerical simulations confirm the theoretical findings.

Approach is effective for multimodal posterior distributions.

Abstract

Variants of fluctuation theorems recently discovered in the statistical mechanics of non-equilibrium processes may be used for the efficient determination of high-dimensional integrals as typically occurring in Bayesian data analysis. In particular for multimodal distributions, Monte-Carlo procedures not relying on perfect equilibration are advantageous. We provide a comprehensive statistical error analysis for the determination of the prior-predictive value in a Bayes problem building on a variant of the Jarzynski equation. Special care is devoted to the characterization of the bias intrinsic to the method. We also discuss the determination of averages over multimodal posterior distributions with the help of a variant of the Crooks theorem. All our findings are verified by extensive numerical simulations of two model systems with bimodal likelihoods.