2003, Volume 65, Pt. 3, 577-592

Some Further Developments For Stick-Breaking Priors: Finite And Infinite Clustering And Classification

By

HEMANT ISHWARAN, Cleveland Clinic Foundation, Cleveland, USA and

LANCELOT F. JAMES, Hong Kong University of Science and Technology, Hong Kong

SUMMARY. The class of stick-breaking priors and their extensions are considered in classification and clustering problems in which the complexity, the number of possible models or clusters, can be either bounded or unbounded.  A conjugacy property for the extended stick-breaking prior is established which allows for informative characterizations of the priors under i.i.d. sampling, and which further enables an informative characterization of the posterior in the classification model.  Such characterizations show how to develop Monte Carlo algorithms for efficient posterior computing.  One implication is that it is possible to estimate infinite complexity mixture models subject to arbitrary stick-breaking priors.

AMS (1991) subject classification. 62G99, 62G09.

Key words and phrases. Classification variables, Collapsed Gibbs sampling, Dirichlet process, Finite and infinite dimensional Dirichlet priors, Two-parameter Poisson-Dirichlet process, sequential importance sampling.

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