BAYES, ORACLE BAYES, AND EMPIRICAL BAYES

 

BRADLEY EFRON – STANFORD UNIVERSITY

This talk concerns the relation of empirical Bayes methods to more familiar Bayesian and frequentist ideas. To this end, an intermediate framework, “Oracle Bayes”, is introduced. The goal here is to separate the empirical (i.e., frequentist) part of empirical Bayes from its Bayesian interpretations. The basic ideas are mostly familiar ones from Robbins and his students, but modern developments, in theory and especially in computation, allow a clearer picture of what’s at stake.