Estimating normal means with a Dirichlet process prior. (English) Zbl 0791.62039

Summary: The Dirichlet process prior is used to provide a nonparametric Bayesian estimate of a vector of normal means. In the past there have been computational difficulties with this model. This article solves the computational difficulties by developing a “Gibbs sampler” algorithm. The estimator developed in this article is then compared to parametric empirical Bayes estimators (PEB) and nonparametric empirical Bayes estimators (NPEB) in a Monte Carlo study. The Monte Carlo study demonstrates that in some conditions the PEB is better than NPEB and in other conditions the NPEB is better than the PEB. The Monte Carlo study also shows that the estimator developed in this article produces estimates that are about as good as the PEB when the PEB is better and produces estimates that are as good as the NPEB estimator when that method is better.


62G05 Nonparametric estimation
62C10 Bayesian problems; characterization of Bayes procedures
65C99 Probabilistic methods, stochastic differential equations
62C12 Empirical decision procedures; empirical Bayes procedures
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