651
The Consistency of Posterior Distribtions in Nonparametric Problems
Andrew Barron, Mark J. Schervish and Larry Wasserman
Abstract:
We give conditions that guarantee that the posterior probability of
every Hellinger neighborhood of the true density tends to 1 almost
surely. The conditions are (i) a smoothness condition on the prior and
(ii) a requirement that the prior put positive mass in appropriate
neighborhoods of the true density. The results are based on the idea
of approximating the set of densities with a finite dimensional set of
densities and then computing the Hellinger bracketing metric entropy
of the approximating set. We apply the results to some examples.
Keywords: Exponential families, Hellinger distance,
Nonparametric Bayesian inference, Polya trees.
Here is the full postscript text for this
technical report. It is 293889 bytes long.