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Abstract:
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The different kinds of mixture models, such as finite mixtures, hidden Markov models and Dirichlet processes, have traditionally been motivated and analyzed from very different perspectives. Furthermore, their inferential techniques usually involve heavy computational burdens that make them difficult, if not impossible, to apply to the massive data sets increasingly encountered in real world studies. We introduce a flexible class of models called generalized Polya urn schemes. Many common mixture models are obtained as its special cases. An investigation of their asymptotic properties suggests universally applicable and cost-effective MCMC strategies for very large data sets. The versatility and impressive gains of the technique are demonstrated by simulation studies and by a nonparametric Bayesian analysis of survival data on pancreatic cancer consisting of 10,459 individuals.
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