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Nonparametric Bayesian approaches to clustering, information retrieval,language modeling and object recognition have recently shown great promise as anew paradigm for unsupervised data analysis. Most contributions have focused onthe Dirichlet process mixture models or extensions thereof for which efficientGibbs samplers exist. In this paper we explore Gibbs samplers for infinitecomplexity mixture models in the stick breaking representation. The advantageof this representation is improved modeling flexibility. For instance, one candesign the prior distribution over cluster sizes or couple multiple infinitemixture models (e.g. over time) at the level of their parameters (i.e. thedependent Dirichlet process model). However, Gibbs samplers for infinitemixture models (as recently introduced in the statistics literature) seem tomix poorly over cluster labels. Among others issues, this can have the adverseeffect that labels for the same cluster in coupled mixture models are mixed up.We introduce additional moves in these samplers to improve mixing over clusterlabels and to bring clusters into correspondence. An application to modeling ofstorm trajectories is used to illustrate these ideas.

Gibbs Sampling for (Coupled) Infinite Mixture Models in the Stick Breaking Representation