The Annals of Statistics
- Ann. Statist.
- Volume 27, Number 2 (1999), 536-561.
The consistency of posterior distributions in nonparametric problems
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.
Ann. Statist., Volume 27, Number 2 (1999), 536-561.
First available in Project Euclid: 5 April 2002
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G20: Asymptotic properties
Barron, Andrew; Schervish, Mark J.; Wasserman, Larry. The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27 (1999), no. 2, 536--561. doi:10.1214/aos/1018031206. https://projecteuclid.org/euclid.aos/1018031206