Asymptotics for posterior hazards

Abstract

An important issue in survival analysis is the investigation and the modeling of hazard rates. Within a Bayesian nonparametric framework, a natural and popular approach is to model hazard rates as kernel mixtures with respect to a completely random measure. In this paper we provide a comprehensive analysis of the asymptotic behavior of such models. We investigate consistency of the posterior distribution and derive fixed sample size central limit theorems for both linear and quadratic functionals of the posterior hazard rate. The general results are then specialized to various specific kernels and mixing measures yielding consistency under minimal conditions and neat central limit theorems for the distribution of functionals.

Published in at http://dx.doi.org/10.1214/08-AOS631 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (5)

• New approaches to Bayesian consistency
• Kullback Leibler property of kernel mixture priors in Bayesian density estimation
• Bayesian Poisson process partition calculus with an application to Bayesian Lévy moving averages
• Central limit theorems for double Poisson integrals
• A Bayes method for a monotone hazard rate via S-paths

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