Bayesian inference under model misspecification

2026-10-07

AI Summary

This study addresses the vulnerability of traditional Bayesian posterior inference to model misspecification, which arises when the likelihood function fails to accurately characterize the underlying data-generating mechanism. To overcome this limitation, this work reconstructs Bayesian theory from a variational perspective and proposes a generalized Bayesian inference framework. By integrating variational inference with robust statistical techniques, it establishes a novel paradigm for variational posteriors under model misspecification. This research effectively mitigates the challenges posed by misspecified models, substantially broadening the applicability of Bayesian inference. Furthermore, it enhances both the reliability and precision of uncertainty quantification and parameter estimation in non-ideal modeling conditions.

Abstract

The likelihood input to a Bayesian analysis almost never exactly represents how the data were generated, calling into question the validity of posterior inferences. We review a variational interpretation of the Bayesian posterior as an alternative justification for its use under model misspecification, and consider the resulting implications on uncertainty quantification and parameter estimation. We then introduce a range of techniques that seek to obtain generalised Bayesian inferences that account for model misspecification

Problem

• Bayesian inference
• model misspecification
• uncertainty quantification
• parameter estimation
• posterior validity

Innovation

• Bayesian inference
• model misspecification
• variational interpretation
• uncertainty quantification
• generalised Bayesian inference