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.
@article{1018031206,
author = {Barron, Andrew and Schervish, Mark J. and Wasserman, Larry},
title = {The consistency of posterior distributions in nonparametric
problems},
journal = {Ann. Statist.},
volume = {27},
number = {4},
year = {1999},
pages = { 536-561},
language = {en},
url = {http://dml.mathdoc.fr/item/1018031206}
}
Barron, Andrew; Schervish, Mark J.; Wasserman, Larry. The consistency of posterior distributions in nonparametric
problems. Ann. Statist., Tome 27 (1999) no. 4, pp. 536-561. http://gdmltest.u-ga.fr/item/1018031206/