The consistency of posterior distributions in nonparametric problems
Open Access
- 1 April 1999
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 27 (2) , 536-561
- https://doi.org/10.1214/aos/1018031206
Abstract
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.Keywords
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