A Marginal Sampler for sigma-Stable Poisson-Kingman MixtureModels

作者：Lomeli Maria; Favaro Stefano; Teh Yee Whye

来源：Journal of Computational and Graphical Statistics, 2017, 26(1): 44-53.

DOI：10.1080/10618600.2015.111026

• Bayesian nonparametrics
• MCMC posterior sampling
• Mixture models
• Normalized generalized gamma process
• Pitman-Yor process
• sigma-stable Poisson-Kingman random probability measures

We investigate the class of sigma-stable Poisson-Kingman random probability measures (RPMs) in the context of Bayesian nonparametric mixture modeling. This is a large class of discrete RPMs, which encompasses most of the popular discrete RPMs used in Bayesian nonparametrics, such as the Dirichlet process, PitmanYor process, the normalized inverse Gaussian process, and the normalized generalized Gamma process. We show how certain sampling properties and marginal characterizations of sigma-stable Poisson-Kingman RPMs can be usefully exploited for devising aMarkov chainMonte Carlo (MCMC) algorithm for performing posterior inferencewith a Bayesian nonparametric mixture model. Specifically, we introduce a novel and efficient MCMC sampling scheme in an augmented space that has a small number of auxiliary variables per iteration. We apply our sampling scheme to a density estimation and clustering tasks with unidimensional and multidimensional datasets, and compare it against competing MCMC sampling schemes. Supplementary materials for this article are available online.

• 出版日期2017