Kachiashvili, K. J.; Hashmi, M. A.; Mueed, A. Quasi-optimal Bayesian procedures of many hypotheses testing. (English) Zbl 1514.62648 J. Appl. Stat. 40, No. 1, 103-122 (2013). Summary: Quasi-optimal procedures of testing many hypotheses are described in this paper. They significantly simplify the Bayesian algorithms of hypothesis testing and computation of the risk function. The relations allowing for obtaining the estimations for the values of average risks in optimum tasks are given. The obtained general solutions are reduced to concrete formulae for a multivariate normal distribution of probabilities. The methods of approximate computation of the risk functions in Bayesian tasks of testing many hypotheses are offered. The properties and interrelations of the developed methods and algorithms are investigated. On the basis of a simulation, the validity of the obtained results and conclusions drawn is presented. MSC: 62-XX Statistics Keywords:approximation; average risk; decision rule; quasi-optimal decision rule; unconstrained and constrained Bayesian tasks PDFBibTeX XMLCite \textit{K. J. Kachiashvili} et al., J. Appl. Stat. 40, No. 1, 103--122 (2013; Zbl 1514.62648) Full Text: DOI References: [1] Bagui, S. and Datta, S. 1998. Some useful properties of the Bayes risk in classification. Calcutta Statist. Assoc. Bull., 48(1): 83-91. · Zbl 0912.62071 [2] Balasanova, E. V. 1995. Asymptotic expansions for the statistic and risk function of a Bayesian classification rule. J. Math. Sci., 75(2): 1552-1556. (doi:10.1007/BF02368741) · Zbl 0789.62049 · doi:10.1007/BF02368741 [3] Berger, J. O. 1985. Statistical Decision Theory and Bayesian Analysis, New York: Springer. · Zbl 0572.62008 · doi:10.1007/978-1-4757-4286-2 [4] Berger, J. O. The frequentist viewpoint and conditioning. Proceedings of the Berkeley Conference in Honor of J. Neyman and J. Kiefer. Edited by: Le Cam, L. and Olshen, R. pp.15-44. 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