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

Through his various examples, Professor Efron makes a convincing case that cutting-edge science requires methods for detecting multiple "non-nulls." These methods must be straightforward to implement, but perhaps more importantly statisticians need to be able to justify them unambiguously. Efron's Empirical Bayes approach is certainly computationally efficient, but we feel the rationale for making each of his steps is unattractively ad hoc. This concern is practical, not philosophical; Efron's criterion for choice of tuning parameters seems to be that they look "believable." In less expert hands, this approach seems to introduce a lot of leeway for practitioners to simply "tune" away until they get the results they want. In an attempt to address this problem, we will de scribe an approach developed in a fully model-based framework. As with locfdr, the calculations are fast, but our whole analysis derives from clear up-front statements about what the analysis is trying to achieve, and the modeling assumptions made. The results look reassuringly similar to Professor Efron's. We hope this will be helpful for understanding the current paper, and in making a contribution to this general field. We begin by following Efron in placing the local false discovery rate, fdr(z), as the primary focus of the analysis, and exploit the fact that it can offer a neat pa rameterization of the two-part model. If the marginal, "mixture" density for the z-values is