A Bayesian Review of the Poisson-Dirichlet Process

9 years 11 months ago
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...
Wray L. Buntine, Marcus Hutter
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where CORR
Authors Wray L. Buntine, Marcus Hutter
Comments (0)