Bayesian Analysis

Comment on Article by Müller and Mitra

Peter D. Hoff

Full-text: Open access

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.

Article information

Source
Bayesian Anal., Volume 8, Number 2 (2013), 311-318.

Dates
First available in Project Euclid: 24 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.ba/1369407552

Digital Object Identifier
doi:10.1214/13-BA811B

Mathematical Reviews number (MathSciNet)
MR3066941

Zentralblatt MATH identifier
1329.62168

Keywords
marginal likelihood model misspecification prior specification sandwich estimation

Citation

Hoff, Peter D. Comment on Article by Müller and Mitra. Bayesian Anal. 8 (2013), no. 2, 311--318. doi:10.1214/13-BA811B. https://projecteuclid.org/euclid.ba/1369407552


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See also

  • Related item: Peter Müller, Riten Mitra. Bayesian Nonparametric Inference – Why and How. Bayesian Anal., Vol. 8, Iss. 2 (2013) 269–302.