A recursive algorithm for nonparametric analysis with missing data
Michael A. Newton · Biometrika · 1999
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.