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Biometrika 1999 86(1):15-26; doi:10.1093/biomet/86.1.15
© 1999 by Biometrika Trust
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A recursive algorithm for nonparametric analysis with missing data

MA NewtonA1 and Y ZhangA

A1 Department of Statistics, University of Wisconsin-Madison, 1210 West Dayton Street, Madison, Wisconsin 53706-1685, USA newton@stat.wisc.edu A Cendant Corporation, Connecticut, USA bzhang@corp.cuc.com

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.


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