Bayesian nonparametric inference – why and how. (English) Zbl 1329.62171

Müller, Peter; Mitra, Riten

Bayesian Anal. 8, No. 2, 269-302 (2013).

Summary: We review inference under models with nonparametric Bayesian (BNP) priors. The discussion follows a set of examples for some common inference problems. The examples are chosen to highlight problems that are challenging for standard parametric inference. We discuss inference for density estimation, clustering, regression and for mixed effects models with random effects distributions. While we focus on arguing for the need for the flexibility of BNP models, we also review some of the more commonly used BNP models, thus hopefully answering a bit of both questions, why and how to use BNP. {
} This review was sponsored by the Bayesian Nonparametrics Section of ISBA (ISBA/BNP). The authors thank the section officers for the support and encouragement.

MSC:

62G05	Nonparametric estimation
62F15	Bayesian inference
62A01	Foundations and philosophical topics in statistics
62H30	Classification and discrimination; cluster analysis (statistical aspects)
62J05	Linear regression; mixed models
62-02	Research exposition (monographs, survey articles) pertaining to statistics

Keywords:

nonparametric models; Dirichlet process; Polya tree; dependent Dirichlet process