CBM for testing multiple hypotheses with directional alternatives in sequential experiments. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Kachiashvili, K. J.; Kachiashvili, J. K.; Prangishvili, I. A.
• Is Part Of: Sequential analysis. Volume 39:Issue 1(2020)
• Page Start: 115
• Page End: 131
• Publication Date: 2020-01-02
• Subjects: Constrained Bayesian method -- directional hypotheses -- false discovery rate -- mixed directional false discovery rate -- multiple hypotheses -- sequential method of Bayesian type; 62F15 -- 62F03; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2020.1727166
• Languages: English
• ISSNs: 0747-4946

Abstract

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 m ( m > 1 ) 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.