Two groups and one group model for multiple tests for microarrays and other examples - a survey and new results

I will first present a brief survey based on recent papers of Efron, Storey, Genovese and Wasserman, Scott and Berger, our papers and the classic paper of Bengamini and Hochberg (1995). I will then explore briefly the Full Bayes, Empirical Bayes and the classical BH rule, indicating some similarities.
In the second part of the talk, I will introduce a Bayes Oracle for misclassification probability in sparse mixtures with proportion of signals tending to zero at (almost) arbitrary rates, and show that the BH rule attains the Oracle asymptotically. Such results for Full Bayes and Empirical Bayes are still out of bounds.
This is joint work with Malgorzata Bogdan, Arijit Chakrabarti, and Florian Frommlet.