Groupe d’études et de recherche en analyse des décisions

Fifty Years of Empirical Bayes

Brad Efron

Scientific inference is the process of reasoning from observed data back to its underlying mechanism. The two great schools of statistical inference, Bayesian and frequentist, have competed over the past twocenturies, often bitterly, for scientific supremacy. Empirical Bayes, a novel hybrid, appreared in the early 1950's, showing promise of immense possible gains in inferential accuracy. Nevertheless it has languished in the statistics literature, with its gains viewed as suspicious and even paradoxical by Bayesians and frequentists alike. New scientific technology, exemplified by dna microarrays, has suddenly revived interest in empirical Bayes methods. This talk, which is aimed at a general scientific audience, examines the ideas involved through a series of real examples, and proceeds with a minimum of technical development.