Abstract

Although Bayesian nonparametric models have been around for a while, recent advances in theory and computational methods have led to exciting new applications of this family of techniques. As a starting point into Bayesian nonparametrics, we will look at Bayesian nonparametric mixture models: why they are used and how they are used.

The Dirichlet process will be the basic building block for the mixture models which we discuss. We will discuss different – equivalent – representations of the Dirichlet process and explain how we can build a mixture model using them. We will touch on how to do inference in these models and show some example applications.

The discussion will not be going through one paper in particular but a very readable paper that touches on many issues which we will discuss is: Bayesian Density Estimation and Inference Using Mixtures, Michael D. Escobar, Mike West; Journal of the American Statistical Association, Vol. 90, 1995