A Computational Approach for Full Nonparametric Bayesian Inference Under Dirichlet Process Mixture Models
نویسندگان
چکیده
Widely used parametricgeneralizedlinearmodels are, unfortunately,a somewhat limited class of speci cations. Nonparametric aspects are often introduced to enrich this class, resulting in semiparametricmodels. Focusingon single or k-sample problems,many classical nonparametricapproachesare limited to hypothesis testing.Those that allow estimation are limited to certain functionals of the underlying distributions.Moreover, the associated inference often relies upon asymptotics when nonparametric speci cations are often most appealing for smaller sample sizes. Bayesian nonparametricapproachesavoid asymptotics but have, to date, been limited in the range of inference. Working with Dirichlet process priors, we overcome the limitations of existing simulation-basedmodel tting approaches which yield inference that is con ned to posterior moments of linear functionals of the populationdistribution.This article provides a computationalapproach to obtain the entire posterior distribution for more general functionals. We illustrate with three applications: investigation of extreme value distributions associated with a single population, comparison of medians in a k-sample problem, and comparison of survival times from different populations under fairly heavy censoring.
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