Nonparametric Bayesian Methods

. Most of this book emphasizes frequentist methods, especially for nonparametric problems. However, there are Bayesian approaches to many nonparametric problems. In this chapter we present some of the most commonly used nonparametric Bayesian methods. These methods place priors on infinite dimensional spaces. The priors are based on certain stochastic processes called Dirichlet processes and Gaussian processes. In many cases, we cannot write down explicit formulas for the priors. Instead, we give explicit algorithms for drawing from the prior and the posterior.