Asymptotics for posterior hazards

Pierpaolo De Blasi, Giovanni Peccati, Igor Prünster
2009 Annals of Statistics  
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
more » ... s 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.
doi:10.1214/08-aos631 fatcat:hgoxdkria5frhlw2jwi5e2znhe