Charles Lewis Undesirable Optimality Results in Multiple Testing?
Several optimality results have been obtained that are related to multiple testing procedures designed to control some version of the FDR. These results have been obtained using Bayesian and semi-Bayesian approaches to the problem. However, some of the results conflict with the basic intuition that taking multiplicity into account should lead to more conservative tests (i.e., rejecting fewer hypotheses), compared to treating each test individually. This conflict leads to several questions: Is a Bayesian approach always appropriate for multiple testing problems? Is some version of the FDR always an appropriate choice of error rate? Or do our intuitions need to be updated?