Simulation-based validation of Bayes factor computation

2025-08-15

AI Summary

This study addresses the lack of reliable validation mechanisms for Bayes factor computations. To this end, we propose two novel calibration methods: (1) an enhanced simulation-based calibration (SBC) procedure, specifically adapted to handle posterior distributions under improper priors; and (2) a binary-prediction-based calibration metric. We comparatively evaluate these against established approaches—including data-averaged posterior checks and the Good test—and find that binary-prediction calibration achieves higher sensitivity under limited computational budgets, whereas SBC detects a broader spectrum of inferential errors. Empirical experiments demonstrate that mainstream R packages—such as *bridgesampling* and *BayesFactor*—exhibit robust performance under default settings. We recommend that new implementations conduct at least several hundred simulation-based calibration runs for rigorous validation. Overall, this work establishes a more efficient and robust framework for validating Bayesian inference, particularly in Bayes factor computation.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining 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 finite resources, binary prediction calibration is typically more sensitive. 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 and binary prediction calibration 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.

Problem

• Validating Bayes factor computation accuracy
• Comparing sensitivity of SBC and binary prediction calibration
• Detecting computational errors in Bayes factor methods

Innovation

• Simulation-based calibration checking variant
• Binary prediction calibration metrics
• Posterior SBC for improper priors