Calibrated Generalized Bayesian Inference

TL;DR

This paper introduces a simple, effective method for accurate uncertainty quantification in Bayesian inference under model misspecification and for generalized posteriors, applicable to various models including generalized linear and doubly intractable models.

Contribution

The authors propose replacing the standard posterior with an alternative that reliably captures uncertainty, improving inference in misspecified or approximate models.

Findings

Accurately quantifies uncertainty in misspecified models

Applicable to likelihood-based and loss-based posteriors

Demonstrated on generalized linear and doubly intractable models

Abstract

We propose a simple approach that provides accurate uncertainty quantification for Bayesian inference in misspecified or approximate models, and for generalized (Gibbs) posteriors. While existing solutions in this context are based on explicit Gaussian approximations or post-processing procedures, we demonstrate that correct uncertainty quantification can be achieved by substituting the usual posterior with an intuitively appealing alternative that conveys the same information. This solution applies to both likelihood-based and loss-based posteriors, and is formally demonstrated to reliably quantify uncertainty. This new approach is demonstrated through a range of examples, including generalized linear models, and doubly intractable models.