A Marginal Sampler for σ-Stable Poisson–Kingman Mixture Models. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Lomelí, María; Favaro, Stefano; Teh, Yee Whye
• Is Part Of: Journal of computational and graphical statistics. Volume 26:Issue 1(2017)
• Page Start: 44
• Page End: 53
• Publication Date: 2017-01-02
• Subjects: Bayesian nonparametrics -- MCMC posterior sampling -- Mixture models -- Normalized generalized gamma process -- Pitman–Yor process -- σ-stable Poisson–Kingman random probability measures; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2015.1110526
• Languages: English
• ISSNs: 1061-8600

Abstract

ABSTRACT: We investigate the class of σ-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, Pitman–Yor process, the normalized inverse Gaussian process, and the normalized generalized Gamma process. We show how certain sampling properties and marginal characterizations of σ-stable Poisson–Kingman RPMs can be usefully exploited for devising a Markov chain Monte Carlo (MCMC) algorithm for performing posterior inference with 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.