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Fdr And Bayesian Multiple Comparisons Rules, Peter Muller, Giovanni Parmigiani, Kenneth Rice

Johns Hopkins University, Dept. of Biostatistics Working Papers

We discuss Bayesian approaches to multiple comparison problems, using a decision theoretic perspective to critically compare competing approaches. We set up decision problems that lead to the use of FDR-based rules and generalizations. Alternative definitions of the probability model and the utility function lead to different rules and problem-specific adjustments. Using a loss function that controls realized FDR we derive an optimal Bayes rule that is a variation of the Benjamini and Hochberg (1995) procedure. The cutoff is based on increments in ordered posterior probabilities instead of ordered p- values. Throughout the discussion we take a Bayesian perspective. In particular, …