Calibrating general posterior credible regions

TL;DR

This paper proposes a method to calibrate Bayesian credible regions by introducing a tuning parameter that ensures these regions achieve the desired frequentist coverage, improving their reliability in practice.

Contribution

It introduces a general calibration strategy with an algorithm to adjust posterior spread, ensuring credible regions attain nominal coverage probabilities.

Findings

The calibration method effectively improves coverage accuracy.

The algorithm reliably selects the tuning parameter.

Credible regions become more aligned with frequentist confidence regions.

Abstract

An advantage of methods that base inference on a posterior distribution is that credible regions are readily obtained. Except in well-specified situations, however, there is no guarantee that such regions will achieve the nominal frequentist coverage probability, even approximately. To overcome this difficulty, we propose a general strategy that introduces an additional scalar tuning parameter to control the posterior spread, and we develop an algorithm that chooses this parameter so that the corresponding credible region achieves the nominal coverage probability.