  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.
