BRANCHING PROCESS REPRESENTATION OF POISSONIZED CHINESE-RESTAURANT PROCESS [OCRP(α, 0)]

Abstract

The Chinese Restaurant Process (CRP) is a stochastic process on partitions. One of its importance lies in Markov chain Monte Carlo algorithm for Bayesian non parametric clustering. This thesis is built in the realm of a special type of CRP called Poissonized up-down CRP. Inspired by Roger’s work to recover CRPs from a continuous-time stochastic process called a Lévy process, we study a branching process construction that we show is equivalent to Poissonized up down CRP. This study touches on discrete trees, continuous trees namely chronological trees, Jumping Chronological Contour Process (JCCP) and Skewer process. In the course of this study we explored interesting identities involving conditional exponential distribution.