Abstract
Nonparametric Bayesian methods make use of infinite-dimensional mathematical structures to allow the practitioner to learn more from their data as the size of their data set grows. The underlying mathematics is the theory of stochastic processes, with fascinating connections to combinatorics, graph theory, functional analysis and convex analysis. In this tutorial, we'll introduce such foundational nonparametric Bayesian models as the Dirichlet process and Chinese restaurant process and we will discuss the wide range of models captured by the formalism of completely random measures. We'll present some of the algorithms used for posterior inference in nonparametric Bayes, and we will discuss some open theoretical problems.