Introduction to Dirichlet Processes and their use

Wray Buntine - Professor, Monash University, Melbourne, Australia Assuming the attendee has knowledge of the Poisson, Gamma, multinomial and Dirichlet distributions, this talk will present the basic ideas and theory to understand and use the Dirichlet process and its close relatives, the Pitman-Yor process and the gamma process. We will first look at some motivating examples. Then we will look at the non-hierarchical versions of the processes, which are basically infinite parameter vectors. These have a number of handy properties and have simple, elegant marginal and posterior inference. Finally, we will look at the hierarchical versions of these processes. These are fundamentally different. To understand the hierarchical version we will briefly review some aspects of stochastic process theory and additive distributions. The hierarchical versions becomes Dirichlet and Gamma distributions (the process part disappears) but the techniques developed for the non-hierarchical process models can be borrowed to develop good algorithms, since the Dirichlet and Gamma are challenging when placed hierarchically.