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May, 1980 On Approximating Parametric Bayes Models by Nonparametric Bayes Models
S. R. Dalal, Gaineford J. Hall Jr.
Ann. Statist. 8(3): 664-672 (May, 1980). DOI: 10.1214/aos/1176345016


Let $\tau$ be a prior distribution over the parameter space $\Theta$ for a given parametric model $P_\theta, \theta \in \Theta$. For the sample space $\mathscr{X}$ (over which $P_\theta$'s are probability measures) belonging to a general class of topological spaces, which include the usual Euclidean spaces, it is shown that this parametric Bayes model can be approximated by a nonparametric Bayes model of the form of a mixture of Dirichlet processes prior, so that (i) the nonparametric prior assigns most of its weight to neighborhoods of the parametric model, and (ii) the Bayes rule for the nonparametric model is close to the Bayes rule for the parametric model in the no-sample case. Moreover, any prior parametric or nonparametric, may be approximated arbitrarily closely by a prior which is a mixture of Dirichlet processes. These results have implications in Bayesian inference.


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S. R. Dalal. Gaineford J. Hall Jr.. "On Approximating Parametric Bayes Models by Nonparametric Bayes Models." Ann. Statist. 8 (3) 664 - 672, May, 1980.


Published: May, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0438.62042
MathSciNet: MR568728
Digital Object Identifier: 10.1214/aos/1176345016

Primary: 62G99
Secondary: 60K99

Rights: Copyright © 1980 Institute of Mathematical Statistics


Vol.8 • No. 3 • May, 1980
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