A Bernstein-von Mises theorem in the nonparametric right-censoring model
Abstract
Description
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\leq 1/2, a prior process neutral to the right can be chosen so that its posterior distribution achieves the convergence rate n^{-α}.
Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/009053604000000526
Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/009053604000000526