Robust Bayesian Predictive Model Selection using Bregman Divergence

2026-06-09

AI Summary

Traditional Bayesian model comparison methods based on log scoring, such as the expected log predictive density (ELPD), are highly sensitive to outliers and tail mismatches, often leading to unstable model selection. This work proposes a generalized ELPD framework grounded in Bregman divergences, replacing the log score with the β-divergence family to construct generalized posteriors and employing leave-one-out cross-validation to assess predictive utility. The approach asymptotically selects the predictive distribution closest to the true data-generating mechanism even under model misspecification, substantially reducing sensitivity to low-density observations. Simulation studies and analyses of microbiome and forensic data demonstrate that the proposed method enhances the robustness of model selection and can lead to substantively different final model choices compared to conventional approaches.

Abstract

Predictive Bayesian model comparison often relies on leave-one-out (LOO) cross-validation criteria such as the expected log predictive density (ELPD). However, model rankings can be overly sensitive to outliers and tail mismatch because ELPD is based on the log score. We propose a score-matched generalized ELPD framework that replaces the log score by a Bregman scoring rule to update model parameters through a generalized posterior and to evaluate LOO predictive utility. Candidate posterior predictive distributions are ranked by out-of-sample utility under the chosen scoring rule, yielding a direct proper-score generalization of standard ELPD. We focus especially on the $β$-divergence family, where $β$ controls the sensitivity of predictive comparison to low-density observations. Under model misspecification, the procedure asymptotically selects the model whose predictive distribution is closest to the data-generating process under the chosen Bregman divergence. A simulation study and applications to microbial and forensic data show that the generalized ELPD can change the selected model through reduced sensitivity to low-density observations.

Problem

• Bayesian model selection
• outliers
• expected log predictive density
• model misspecification
• predictive comparison

Innovation

• Bregman divergence
• Bayesian model selection
• generalized ELPD
• β-divergence
• robust prediction