Fast Bayesian Inference in Dirichlet Process Mixture Models

• Published in: Journal of computational and graphical statistics Vol. 20; no. 1; pp. 196 - 216
• Main Authors: Wang, Lianming, Dunson, David B.
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis 01.01.2011; JCGS Management Committee of the American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America; Taylor & Francis Ltd
• Subjects: Algorithms; Bayes estimators; Bayesian analysis; Bayesian Nonparametrics; Clustering; Data analysis; Datasets; Density; Density estimation; Efficient computation; Inference; Large samples; Markov analysis; Modeling; Monte Carlo simulation; Nonparametric Bayes; Nonparametric models; Nonparametric statistics; Optimization algorithms; Parametric models; Predictive modeling; Probability distribution; Pólya urn scheme; Sequential analysis; Statistical inference; Studies; Density estimation; Sequential analysis; Large samples; Efficient computation; Nonparametric Bayes; Pólya urn scheme; Clustering
• ISSN: 1061-8600; 1537-2715
• DOI: 10.1198/jcgs.2010.07081

There has been increasing interest in applying Bayesian nonparametric methods in large samples and high dimensions. As Markov chain Monte Carlo (MCMC) algorithms are often infeasible, there is a pressing need for much faster algorithms. This article proposes a fast approach for inference in Dirichlet process mixture (DPM) models. Viewing the partitioning of subjects into clusters as a model selection problem, we propose a sequential greedy search algorithm for selecting the partition. Then, when conjugate priors are chosen, the resulting posterior conditionally on the selected partition is available in closed form. This approach allows testing of parametric models versus nonparametric alternatives based on Bayes factors. We evaluate the approach using simulation studies and compare it with four other fast nonparametric methods in the literature. We apply the proposed approach to three datasets including one from a large epidemiologic study. Matlab codes for the simulation and data analyses using the proposed approach are available online in the supplemental materials.