Slice Sampling σ-Stable Poisson-Kingman Mixture Models

Abstract

The article is concerned with the use of Markov chain Monte Carlo methods for posterior sampling in Bayesian nonparametric mixture models.In particular, we consider the problem of slice sampling mixture models for a large class of mixing measures generalizing the celebrated Dirichlet process. Such a class of measures, known in the literature as σ-stable Poisson-Kingman models, includes as special cases most of the discrete priors currently known in Bayesian nonparametrics, for example, the two-parameter Poisson-Dirichlet process and the normalized generalized Gamma process. The proposed approach is illustrated on some simulated data examples. This article has online supplementary material.

Key Words:

• Bayesian nonparametrics
• MCMC posterior sampling
• Normalized random measures
• Size-biased random permutation
• Stick-breaking representation for the σ-Stable Poisson-Kingman models

ACKNOWLEDGMENT

Detailed comments and suggestions by an Associate Editor and two Referees are gratefully acknowledged. Stefano Favaro is supported by grants from the Italian Ministry of University and Research and Regione Piemonte.