Simulation-based validation of Bayes factor computation

TL;DR

This paper introduces and evaluates two validation methods for Bayes factor computation, demonstrating their effectiveness over previous checks and providing guidelines for reliable validation in Bayesian analysis.

Contribution

The paper presents two novel validation methods for Bayes factors, improving detection of computational issues and extending validation to models with improper priors.

Findings

SBC can detect all problems in Bayes factor computation with well-designed tests.

Binary prediction calibration is more sensitive than SBC with limited resources.

Existing checks like the Good check miss many issues detectable by proposed methods.

Abstract

We propose and evaluate two methods that validate the computation of Bayes factors: one based on an improved variant of simulation-based calibration checking (SBC) and one based on calibration metrics for binary predictions. We show that in theory, binary prediction calibration is equivalent to a special case of SBC, but with limited resources, binary prediction calibration is typically more sensitive to the problems we investigated. With well-designed test quantities, SBC can however detect all possible problems in computation, including some that cannot be uncovered by binary prediction calibration. Previous work on Bayes factor validation includes checks based on the data-averaged posterior and the Good check method. We demonstrate that both checks miss many problems in Bayes factor computation detectable with SBC and binary prediction calibration. Moreover, we find that the Good check as originally described fails to control its error rates. Our proposed checks also typically use simulation results more efficiently than data-averaged posterior checks. Finally, we show that a special approach based on posterior SBC is necessary when checking Bayes factor computation under improper priors and we validate several models with such priors. We recommend that novel methods for Bayes factor computation be validated with SBC, binary prediction calibration and data-averaged posterior with at least several hundred simulations. For all the models we tested, the bridgesampling and BayesFactor R packages satisfy all available checks and thus are likely safe to use in standard scenarios.