MCMC for normalized random measure mixture models

Journal article

This paper concerns the use of Markov chain Monte Carlo methods for posterior sampling in Bayesian nonparametric mixture models with normalized random measure priors. Making use of some recent posterior characterizations for the class of normalized random measures, we propose novel Markov chain Monte Carlo methods of both marginal type and conditional type. The proposed marginal samplers are generalizations of Neal’s well-regarded Algorithm 8 for Dirichlet process mixture models, whereas the conditional sampler is a variation of those recently introduced in the literature. For both the marginal and conditional methods, we consider as a running example a mixture model with an underlying normalized generalized Gamma process prior, and describe comparative simulation results demonstrating the efficacies of the proposed methods.

Authors: Favaro, S; Teh, Y

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Institute of Mathematical Statistics
• Journal: Statistical Science
• Volume: 28
• Issue: 3
• Pages: 335-359
• Publication date: 2013-01-01
• DOI: 10.1214/13-STS422
• ISSN: 0883-4237
• Keywords: MCMC posterior sampling method; normalized random measure; Dirichlet process; completely random measure; Algorithm 8; marginalized sampler; normalized generalized Gamma process; Bayesian nonparametrics; conditional sampler; slice sampling; hierarchical mixture model