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April 1999 The consistency of posterior distributions in nonparametric problems
Andrew Barron, Mark J. Schervish, Larry Wasserman
Ann. Statist. 27(2): 536-561 (April 1999). DOI: 10.1214/aos/1018031206


We give conditions that guarantee that the posterior probability of every Hellinger neighborhood of the true distribution tends to 1 almost surely. The conditions are (1) a requirement that the prior not put high mass near distributions with very rough densities and (2) a requirement that the prior put positive mass in Kullback-Leibler neighborhoods of the true distribution. The results are based on the idea of approximating the set of distributions with a finite-dimensional set of distributions with sufficiently small Hellinger bracketing metric entropy. We apply the results to some examples.


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Andrew Barron. Mark J. Schervish. Larry Wasserman. "The consistency of posterior distributions in nonparametric problems." Ann. Statist. 27 (2) 536 - 561, April 1999.


Published: April 1999
First available in Project Euclid: 5 April 2002

zbMATH: 0980.62039
MathSciNet: MR1714718
Digital Object Identifier: 10.1214/aos/1018031206

Primary: 62G20

Keywords: exponential families , Hellinger distance , nonparametric Bayesian inference , Pólya trees.

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 2 • April 1999
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