Speaker: Ben Bloem-Reddy, Department of Statistics, University of Oxford
Date: Thursday 15th February, 3.30 pm, Small Lecture Theatre, Department of Statistics
Title: An introduction to exchangeable random partitions and random discrete probability measures
Abstract: Random partition processes underly many constructions for Bayesian models of clustered data; the Chinese Restaurant Process (CRP) is the prototypical example. They are also perhaps the simplest type of combinatorial stochastic process, and are a starting point for studying processes with more complex structure. In the first part of the lecture, I will give an introduction to exchangeable random partitions and their connection to random discrete probability measures via Kingman’s paintbox, with special focus on the CRP. In the second part, I will focus on the properties of the Dirichlet Process (DP), and how different constructions of the DP lead to various classes of random probability measures that appear in the probability and Bayesian nonparametrics literature. Some of these properties will be used in the subsequent week’s grad lecture by Jessie Wu on applications of and inference with models that use the DP as a building block.