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Alpha-Stable Poisson-Kingman Processes: Some Applications and Methodologies

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Poisson-Kingman partitions reposed on alpha-stable processes have been well-studied, e.g. by Pitman (2003) who first introduced them, and Gnedin and Pitman (2006) who characterized them as a particular class of Gibbs-type exchangeable random partitions. They have recently enjoyed increasing interest in the Bayesian nonparametrics community for being the largest known class of random probability measures that have significant advantages in terms of mathematical and computational tractability.

In this talk I will give an overview to alpha-stable Poisson-Kingman processes from the perspective of using them in statistical modelling applications. Specifically I will describe their use in Bayesian nonparametric mixture models for clustering and density estimation problems, and in estimating discovery probabilities in special sampling problems. I will also describe computational techniques which allow us to perform efficient Markov chain Monte Carlo inference for these processes.

Joint work with Stefano Favaro and Maria Lomeli.

This talk is part of the Statistics series.

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