Bayesian Analysis

Local-Mass Preserving Prior Distributions for Nonparametric Bayesian Models

Juhee Lee, Steven N. MacEachern, Yiling Lu, and Gordon B. Mills

Full-text: Open access

Abstract

We address the problem of prior specification for models involving the two-parameter Poisson-Dirichlet process. These models are sometimes partially subjectively specified and are always partially (or fully) specified by a rule. We develop prior distributions based on local mass preservation. The robustness of posterior inference to an arbitrary choice of overdispersion under the proposed and current priors is investigated. Two examples are provided to demonstrate the properties of the proposed priors. We focus on the three major types of inference: clustering of the parameters of interest, estimation and prediction. The new priors are found to provide more stable inference about clustering than traditional priors while showing few drawbacks. Furthermore, it is shown that more stable clustering results in more stable inference for estimation and prediction. We recommend the local-mass preserving priors as a replacement for the traditional priors.

Article information

Source
Bayesian Anal., Volume 9, Number 2 (2014), 307-330.

Dates
First available in Project Euclid: 26 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.ba/1401148311

Digital Object Identifier
doi:10.1214/13-BA857

Mathematical Reviews number (MathSciNet)
MR3216998

Zentralblatt MATH identifier
1327.62149

Keywords
nonparametric Bayes Dirichlet process two-parameter Poisson-Dirichlet process local mass prior misspecification clustering

Citation

Lee, Juhee; MacEachern, Steven N.; Lu, Yiling; Mills, Gordon B. Local-Mass Preserving Prior Distributions for Nonparametric Bayesian Models. Bayesian Anal. 9 (2014), no. 2, 307--330. doi:10.1214/13-BA857. https://projecteuclid.org/euclid.ba/1401148311


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