Compound decision theory and empirical Bayes methods: invited paper

Invited Paper Compound Decision Theory and Empirical Bayes Methods

1. Introduction. Compound decision theory and empirical Bayes methodology , acclaimed as " two breakthroughs " by Neyman (1962), are the most important contributions of Herbert Robbins to statistics. The purpose of this paper is to provide a brief description of his work in these two intimately connected fields, its impact and a number of important related developments. Robbins introduced compo...

Empirical Bayes Ranking Methods

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Semi-Bayes and empirical Bayes adjustment methods for multiple comparisons.

Epidemiological studies often involve multiple comparisons, and may therefore report many "false positive" statistically significant findings simply because of the large number of statistical tests involved. Traditional methods ofadjustment for multiple comparisons, such as the Bonferroni method, may induce investigators to ignore potentially important findings, because they do not take account...

Bayes and Empirical Bayes Methods for Data Analysis

Convex Optimization, Shape Constraints, Compound Decisions, and Empirical Bayes Rules

Estimation of mixture densities for the classical Gaussian compound decision problem and their associated (empirical) Bayes rules is considered from two new perspectives. The first, motivated by Brown and Greenshtein (2009), introduces a nonparametric maximum likelihood estimator of the mixture density subject to a monotonicity constraint on the resulting Bayes rule. The second, motivated by Ji...