A Bayesian Review of the Poisson-Dirichlet Process

The two parameter Poisson-Dirichlet process is also known as the PitmanYor Process and related to the Chinese Restaurant Process, is a generalisation of the Dirichlet Process, and is increasingly being used for probabilistic modelling in discrete areas such as language and images. This article reviews the theory of the Poisson-Dirichlet process in terms of its consistency for estimation, the convergence rates and the posteriors of data. This theory has been well developed for continuous distributions (more generally referred to as nonatomic distributions). This article then presents a Bayesian interpretation of the Poisson-Dirichlet process: it is a mixture using an improper and infinite dimensional Dirichlet distribution. This interpretation requires technicalities of priors, posteriors and Hilbert spaces, but conceptually, this means we can understand the process as just another Dirichlet and thus all its sampling properties fit naturally. Finally, this article also presents results...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Wray L. Buntine, Marcus Hutter
• Keywords: Chinese Restaurant Process, CORR 2010, Education, Parameter Poisson-dirichlet Process, Poisson-Dirichlet Process