An exact predictive recursion for Bayesian nonparametric analysis of incomplete data

Abstract

This paper presents a new derivation of nonparametric distribution estimation with right-censored data. It is based on an extension of the predictive inferences to compound evidence. The estimate is recursive and exact, and no stochastic approximation is needed: it simply requires that the censored data are processed in decreasing order. Only in this case the recursion provides exact posterior predictive distributions for subsequent samples under a Dirichlet process prior. The resulting estimate is equivalent to the Susarla-VanRyzin estimator and to the beta-Stacy process.