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.

中文翻译：

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CBM 用于在连续实验中测试具有定向替代方案的多个假设

摘要 本文考虑了用于测试定向假设的约束贝叶斯方法 (CBM) 和错误发现率 (FDR) 的概念。结果表明，当我们考虑 () 组方向假设时，CBM 的直接应用允许我们将 FDR 控制在一组方向假设和多个情况的所需水平上。当保证对期望水平的限制时，可以应用贝叶斯序列方法，其停止规则是适当的，并且用于做出决策的序列方案强烈地控制了混合定向FDR。具体实例的计算结果证实了理论结果的正确性。