A recursive algorithm for nonparametric analysis with missing data

Abstract

The mixture of Dirichlet processes posterior that arises in nonparametric Bayesian analysis has been analysed most effectively using Markov chain Monte Carlo. As a computationally simple alternative, we introduce a recursive approximation based on one-step posterior predictive distributions. Asymptotic calculations provide theoretical support for this approximation, and we investigate its actual behaviour in several numerical examples. From a non-Bayesian perspective, this new recursion may be used to obtain solutions of the self-consistency equations. Keywords: Dirichlet process; Interval censoring; Nonparametric Bayesian analysis; Nonparametric mixture; Nonparametric maximum likelihood; Polya urn; Prior feedback; Quasi-Bayes; Self-consistency; Stochastic approximation; Truncation.