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Computing nonparametric hierarchical models. (English) Zbl 0918.62028

Dey, Dipak (ed.) et al., Practical nonparametric and semiparametric Bayesian statistics. New York, NY: Springer. Lect. Notes Stat., Springer-Verlag. 133, 1-22 (1998).
Summary: 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 The resulting methodology is illustrated with two examples taken from an unpublished 1992 report on the topic.
For the entire collection see [Zbl 0893.00018].

MSC:

62G05 Nonparametric estimation
65C99 Probabilistic methods, stochastic differential equations