Invited discussion to the paper Using Stacking to Average Bayesian Predictive Distributions

Peter Grünwald and Rianne de Heide

What is this paper about?

This invited discussion responds to work on stacking Bayesian predictive distributions in the misspecified, or M-open, setting. It welcomes the move beyond ordinary Bayesian model averaging but argues that log-score stacking does not by itself resolve the hypercompression phenomenon.

Summary

Yao and coauthors propose stacking predictive distributions as an alternative to Bayesian model averaging in the M-open, or misspecified, case. We welcome the program of adapting Bayesian methods to misspecification and see merit in stacking. However, we argue that the log-score stacking method advocated in the paper does not address a central difficulty of Bayesian model averaging under misspecification: the hypercompression phenomenon, which can also occur on real data.

Topics

Bayesian learning and generalized Bayes · Foundations of statistics, probability and learning

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