Bridge Sampling Diagnostics

TL;DR

This paper introduces methods to estimate the Monte Carlo standard error and diagnose the reliability of bridge sampling estimates in Bayesian model selection, improving accuracy and trustworthiness without repeated computations.

Contribution

It presents novel diagnostics and estimation techniques for assessing the reliability of bridge sampling in Bayesian inference, addressing high variability issues.

Findings

MCSE estimation for bridge sampling is feasible and effective.

Pareto-$k$ and block reshuffling diagnostics improve reliability assessment.

Demonstrated on simulated and real posteriors from posteriordb.

Abstract

In Bayesian statistics, the marginal likelihood is used for model selection and averaging, yet it is often challenging to compute accurately for complex models. Approaches such as bridge sampling, while effective, may suffer from issues of high variability of the estimates. We present how to estimate Monte Carlo standard error (MCSE) for bridge sampling, and how to diagnose the reliability of MCSE estimates using Pareto-$\hat{k}$ and block reshuffling diagnostics without the need to repeatedly re-run full posterior inference. We demonstrate the behavior with increasingly more difficult simulated posteriors and many real posteriors from the posteriordb database.