Graphically Dependent and Spatially Varying Dirichlet Process Mixtures

• Activity Number: 222
• Type: Topic Contributed
• Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Long Nguyen*+
• Companies: University of Michigan
• Keywords: local clustering ; global clustering ; mixture models ; nonparametric Bayes ; spatial model ; graphical model

Abstract

We consider the problem of clustering grouped and functional data, which are indexed by a covariate, and assessing the dependency of the clustered groups on the covariate. In addition to learning the ``local'' clusters within each group we also assume the existence of ``global clusters'' indexed over the covariate domain when the observations across the groups are jointly analyzed. We propose a nonparametric Bayesian solution to this problem, reposing on the theory of dependent Dirichlet processes, where the dependency among the Dirichlet processes is regulated by a spatial or a graphical model distribution. We provide an analysis of the model properties, including the spatial and graphical dependency underlying the model, and the issues of identifiability. We also present an efficient MCMC sampling method. The model and inference method are illustrated by several data examples.