Under the model of independent test statistics, we propose a two-parameter family of Bayes multiple testing procedures. The two parameters can be viewed as tuning parameters. Using the Benjamini--Hochberg step-up procedure for controlling false discovery rate as a baseline for conservativeness, we choose the tuning parameters to compromise between the operating characteristics of that procedure and a less conservative procedure that focuses on alternatives that a priori might be considered likely or meaningful. The Bayes procedures do not have the theoretical and practical shortcomings of the popular stepwise procedures. In terms of the number of mistakes, simulations for two examples indicate that over a large segment of the parameter space, the Bayes procedure is preferable to the step-up procedure. Another desirable feature of the procedures is that they are computationally feasible for any number of hypotheses. Copyright 2008, Oxford University Press.
