Journal of Mathematics and System Science
The paper discusses the generalization of constrained Bayesian method (CBM) for arbitrary loss functions and its application for testing the directional hypotheses. The problem is stated in terms of false and true discovery rates. One more criterion of estimation of directional hypotheses tests quality, the Type III errors rate, is considered. The ratio among discovery rates and the Type III errors rate in CBM is considered. The advantage of CBM in comparison with Bayes and frequentist methods is theoretically proved and demonstrated by an example.
Kachiashvili, Kartlos J.; Bansal, Naveen K.; and Prangishvili, I. A., "Constrained Bayesian Method for Testing the Directional Hypotheses" (2018). Mathematical and Statistical Science Faculty Research and Publications. 23.