CBM for testing multiple hypotheses with directional alternatives in sequential experiments

Abstract Constrained Bayesian methods (CBMs) and the concept of false discovery rates (FDRs) for testing directional hypotheses are considered in this article. It is shown that the direct application of CBM allows us to control FDR on the desired level for both one set of directional hypotheses and a multiple case when we consider () sets of directional hypotheses. When guaranteeing restriction on the desired level, a Bayesian sequential method can be applied, the stopping rules of which are proper and the sequential scheme for making a decision strongly controls the mixed directional FDR. Computational results of concrete examples confirm the correctness of the theoretical outcomes.