Asymptotics for posterior hazards

TL;DR

This paper analyzes the asymptotic behavior of Bayesian nonparametric models for hazard rates in survival analysis, focusing on posterior consistency and distributional limits of functionals.

Contribution

It provides a comprehensive asymptotic analysis of kernel mixture hazard models, including consistency results and central limit theorems for functionals.

Findings

Posterior distribution is consistent under minimal conditions.

Central limit theorems are derived for linear and quadratic functionals.

Results are specialized to various kernels and mixing measures.

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.