Comment on "Bayesian Nonparametric Inference - Why and How" by Mueller and Mitra

TL;DR

This paper critically examines the assumptions and interpretations of nonparametric Bayesian methods, arguing that many default procedures are only weakly Bayesian and may not provide honest uncertainty assessments, urging for more careful application and modification.

Contribution

It challenges the common perception of nonparametric Bayes methods as assumption-free and fully Bayesian, highlighting the need for modifications to incorporate true prior information.

Findings

Default nonparametric Bayes procedures are often only weakly Bayesian.

Many such procedures do not provide honest uncertainty assessments.

Careful evaluation of hyperparameters is necessary for valid Bayesian interpretation.

Abstract

Due to their great flexibility, nonparametric Bayes methods have proven to be a valuable tool for discovering complicated patterns in data. The term "nonparametric Bayes" suggests that these methods inherit model-free operating characteristics of classical nonparametric methods, as well as coherent uncertainty assessments provided by Bayesian procedures. However, as the authors say in the conclusion to their article, nonparametric Bayesian methods may be more aptly described as "massively parametric." Furthermore, I argue that many of the default nonparametric Bayes procedures are only Bayesian in the weakest sense of the term, and cannot be assumed to provide honest assessments of uncertainty merely because they carry the Bayesian label. However useful such procedures may be, we should be cautious about advertising default nonparametric Bayes procedures as either being "assumption free" or providing descriptions of our uncertainty. If we want our nonparametric Bayes procedures to have a Bayesian interpretation, we should modify default NP Bayes methods to accommodate real prior information, or at the very least, carefully evaluate the effects of hyperparameters on posterior quantities of interest.