MCMC for Normalized Random Measure Mixture Models

Abstract

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.

Published in at http://dx.doi.org/10.1214/13-STS422 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Poisson Process Partition Calculus with applications to Exchangeable models and Bayesian Nonparametrics
• Modeling with Normalized Random Measure Mixture Models
• Bayesian nonparametric estimators derived from conditional Gibbs structures
• On the posterior distribution of classes of random means

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