On Bayesian consistency
Stephen Walker, Nils Lid Hjort
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2001 · Volume 63 · Issue 4
Abstract
We consider a sequence of posterior distributions based on a data-dependent prior (which we shall refer to as a pseudoposterior distribution) and establish simple conditions under which the sequence is Hellinger consistent. It is shown how investigations into these pseudo posteriors assist with the understanding of some true posterior distributions, including Pólya trees, the infinite dimensional exponential family and mixture models.
Keywords
Asymptotics, Bayesian sieve, Bayes nonparametrics, Consistency
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