Computing Nonparametric Hierarchical Models
Michael D. Escobar and Mike West
Abstract
Bayesian models involving Dirichlet process mixtures are at the heart of
the modern nonparametric Bayesian movement. Much of the rapid
development of these models in the last decade has been a direct result
of advances in simulation-based computational methods. Some of the very
early work in this area, circa 1988-1991, focused on the use of such
nonparametric ideas and models in applications of otherwise standard
hierarchical models. This chapter provides some historical review and
perspective on these developments, with a prime focus on the use and
integration of such nonparametric ideas in hierarchical models. We
illustrate the ease with which the strict parametric assumptions common
to most standard Bayesian hierarchical models can be relaxed to
incorporate uncertainties about functional forms using Dirichlet process
components, partly enabled by the approach to computation using MCMC
methods. The resulting methodology is illustrated with two examples taken
from an unpublished 1992 report on the topic.
This is a revision of Escobar, M.D., and West, M.
(1992), ``Computing Bayesian Nonparametric Hierarchical Models,'' Discussion
Paper 92-A20, Duke University, ISDS.}