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1981•Journal of the American Statistical AssociationRequires access

Bayes Empirical Bayes

John Deely, D. V. Lindley

Open publisher page 61 citations

Abstract

A Bayesian approach is given for various kinds of empirical Bayes problems. In particular it is shown that empirical Bayes procedures are really non-Bayesian, asymptotically optimal, classical procedures for mixtures. In some situations these procedures are Bayes with respect to some prior and in other situations, there is no prior for which they are Bayes. Several examples of these concepts are given as well as a general theory showing the difference between an empirical Bayes model and a Bayes empirical Bayes model.

About this research paper

What this paper is about

A Bayesian approach is given for various kinds of empirical Bayes problems. In particular it is shown that empirical Bayes procedures are really non-Bayesian, asymptotically optimal, classical procedures for mixtures. In some situations these procedures are Bayes with respect to some prior and in other situations, there is no prior for which they are Bayes. Several examples of these concepts are given as well as a general theory showing the difference between an empirical Bayes model and a Bayes empirical Bayes model.

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OpenAlex reports 61 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

A Bayesian approach is given for various kinds of empirical Bayes problems. In particular it is shown that empirical Bayes procedures are really non-Bayesian, asymptotically optimal, classical procedures for mixtures. In some situations these procedures are Bayes with respect to some prior and in other situations, there is no prior for which they are Bayes. Several examples of these concepts are given as well as a general theory showing the difference between an empirical Bayes model and a Bayes empirical Bayes model.

Key concepts: Bayes' theorem, Bayes factor, Bayes' rule, Bayes error rate, Bayes estimator, Bayesian programming, Bayesian probability, Mathematics

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