An Introduction to Bayesian Nonparametric Statistics via the Dirichlet Process
Myles Hollander, Douglas A. Wolfe, Eric Chicken · Wiley series in probability and statistics · 2015
A challenging problem for statisticians who wish to pursue a Bayesian nonparametric approach is to put a prior distribution on F and then compute the posterior distribution of F, given the data. The Dirichlet process has proved to have staying power and is frequently used. It is surprisingly tractable because, in the simplest problems, the posterior distribution, given the data, is also a Dirichlet process prior. The chapter describes that the Dirichlet process priors are a conjugate family, and the posterior distribution, given the data, is readily obtained. It considers Ferguson's Bayesian nonparametric estimator of the distribution function F. Next, the chapter treats a rank order estimation problem and the Bayesian nonparametric rank order estimator of Campbell and Hollander. Then, it treats the censored data and gives the Susarla-van Ryzin Bayesian non-parametric estimator of F for the case where the data are right censored.