The Consistency of Posterior Distributions in Nonparametric Problems AOS

Authors: Andrew Barron, Mark J. Schervish, Larry Wasserman

Presenter: Ruobin Gong

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 Ž . mass near distributions with very rough densities and 2 a requirement Ž . 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.