A recursive algorithm for nonparametric analysis with missing data.

A recursive algorithm for nonparametric analysis with missing data. (Formerly, ``A partial predictive recursion'')

Michael A. Newton , and Yunlei Zhang

Biometrika , 86 , 15-26, 1999.

Formerly Technical Report 965, Department of Statistics, University of Wisconsin, Madison. First issued, August 1996.


Nonparametric Bayesian analysis has proved to be computationally demanding when data are arbitrarily censored, truncated, or otherwise degraded prior to observation. The mixture of Dirichlet processes posterior that arises in such problems has been analyzed 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 behavior in several numerical examples. The method overcomes a diffuse prior defect inherent in the exact Bayes estimate from interval censored data. From a non-Bayesian perspective, this new recursion may be used to obtain solutions of the self-consistency equation.

Key words: Dirichlet process, interval censoring, nonparametric mixtures, nonparametric maximum likelihood, Polya urn, prior feedback, random effects, self-consistency, truncation.
Data sets analysed