An exact predictive recursion for Bayesian nonparametric analysis of incomplete data

This paper presents an original extension of the Bayesian predictive inferences to compound evidence. Does the idea that the predictive uncertainty can be encoded in a single measure, and that learning occurs by adding measure, holds also for missing data? The positive answer comes from the class of computationally efficient methods to approximate mixtures of Dirichlet processes, which involves order dependent recursive algorithms. In the present note, in the case where data are right-censored, we proof that there is a unique rational pattern which recursively produces the exact posterior predictive distributions for subsequent samples under a Dirichlet process prior. By "exact" we mean that our result coincides with the Susarla-Van Ryzin estimator under squared error loss.