Year: 2004
Type: article
Abstract: In the recent Bayesian nonparametric literature, many examples have been reported in which Bayesian estimators and posterior distributions do not achieve the optimal convergence rate, indicating that the Bernstein–von Mises theorem does not hold. In this article, we give a positive result in this direction by showing that the Bernstein–von Mises theorem holds in survival models for a large class of prior processes neutral to the right. We also show that, for an arbitrarily given convergence rate n−α with 0<α≤1/2, a prior process neutral to the right can be chosen so that its posterior distribution achieves the convergence rate n−α.
Source: The Annals of Statistics
Authors: Yongdai Kim, Jaeyong Lee
Institution: Seoul National University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: Seoul National University
OpenAlex ID: W2071820122