A comparison of learning rate selection methods in generalized Bayesian inference

TL;DR

This paper compares various data-driven learning rate selection methods for generalized Bayesian inference, evaluating their performance in misspecified models with a focus on credible region coverage.

Contribution

It provides a direct comparison of existing methods under different misspecification scenarios, highlighting the generalized posterior calibration algorithm's superior performance.

Findings

Generalized posterior calibration often outperforms other methods in credible region coverage.

Performance varies depending on the severity of model misspecification.

Some methods perform well in mild misspecification but fail under severe conditions.

Abstract

Generalized Bayes posterior distributions are formed by putting a fractional power on the likelihood before combining with the prior via Bayes's formula. This fractional power, which is often viewed as a remedy for potential model misspecification bias, is called the learning rate, and a number of data-driven learning rate selection methods have been proposed in the recent literature. Each of these proposals has a different focus, a different target they aim to achieve, which makes them difficult to compare. In this paper, we provide a direct head-to-head comparison of these learning rate selection methods in various misspecified model scenarios, in terms of several relevant metrics, in particular, coverage probability of the generalized Bayes credible regions. In some examples all the methods perform well, while in others the misspecification is too severe to be overcome, but we find that the so-called generalized posterior calibration algorithm tends to outperform the others in terms of credible region coverage probability.