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

Efron has given us a comprehensive and thoughtful review of his approach to large-scale testing stemming from the challenges of analyzing microarray data. Addressing the microarray challenge right from the emergence of the technology, and adapting the point of view on multiple testing that emphasizes the false discovery rate, Efron’s contributions in both fields have been immense. In the discussed paper he reviews philosophy, motivation, methodologies and even practicalities, and along this process gives us a view of the field of statistics from an eagle’s eye. A thorough discussion of such a work is a major undertaking. Instead, I shall first comment on five issues and then discuss new directions for research on largescale multiple inference that bear on Efron’s review. The scope of the review challenges a discussant to try and address some of the issues raised from a broader point of view. I shall give it a try.

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