Approximate posterior recalibration

TL;DR

This paper introduces two methods to recalibrate approximate Bayesian posteriors, ensuring they better reflect true uncertainty, demonstrated through various experiments and applicable to hierarchical models.

Contribution

The paper presents novel methods extending simulation-based calibration to improve the uncertainty quantification of approximate posteriors.

Findings

Methods successfully widen credible intervals for better calibration.

Experimental results show improved posterior uncertainty estimation.

Applicable to hierarchical Bayesian models.

Abstract

Bayesian inference is often implemented using approximations, which can yield interval estimates that are too narrow, not fully capturing the uncertainty in the posterior distribution. We address the question of how to adjust these approximate posteriors so that they appropriately capture uncertainty. vWe introduce two methods that extend simulation-based calibration checking (SBC) to widen approximate posterior uncertainty intervals to aim for marginal calibration. We demonstrate these methods in several experimental settings, and we discuss the challenge of calibration using posterior inferences and the potential for posterior recalibration of hierarchical models.