Comment: Microarrays, Empirical Bayes and the Two-Groups Model

Abstract

Abstract. Brad Efron’s paper has inspired a return to the ideas be-hind Bayes, frequency and empirical Bayes. The latter preferably wouldnot be limited to exchangeable models for the data and hyperparam-eters. Parallels are revealed between microarray analyses and profilingof hospitals, with advances suggesting more decision modeling for geneidentification also. Then good multilevel and empirical Bayes modelsfor random effects should be sought when regression toward the meanis anticipated. Key words and phrases: Bayes, frequency, interval estimation, ex-changeable, general model, random effects.1. FREQUENCY, BAYES, EMPIRICAL BAYESAND A GENERAL MODELBrad Efron’s two-groups approach and the empir-ical null (“null” refers to a distribution, not to ahypothesis) extension of his local fdr addresses test-ing many hypotheses simultaneously, with model-ing enabled by the repeated presence of many simi-lar problems. He assumes two-level models for ran-dom effects, developing theory by drawing on andcombining ideas from frequency, Bayesian and em-pirical Bayesian perspectives. The last half-centuryin statistics has seen exciting developments frommany perspectives for simultaneous estimation ofrandom effects, but there has been little explicit par-allel work on the complementary problem of hypoth-esis testing. That changes in Brad’s paper,especiallyfor testing many hypotheses when exchangeabilityrestrictions are plausible.“Empirical Bayes” is in the paper’s title, said inSection 3 to be a “bipolar” methodology that draws