Quasi-optimal Bayesian procedures of many hypotheses testing

Kachiashvili, K. J.; Hashmi, Muntazim Abbas; Mueed, A.

doi:10.1080/02664763.2012.734797

Cited by 2 publications

(1 citation statement)

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“…It is a data-dependent measure like Fisher's test for making a decision, it uses a posteriori probabilities like the Jeffreys test and computes error probabilities Type I and Type II like the Neyman-Pearson's approach does [2]. The parallel and sequential methods for testing many (more than or equal to two) and multiple simple hypotheses are considered in the works [2,[3][4][5][6][7][8][9]. Also there are given the results of comparison of CBM with the Fisher, Jeffreys, Neyman-Pearson, Berger (parallel and sequential), Wald (sequential), Bonferroni and step-up and step-down methods of multiple hypotheses testing, which shows the unique properties of this method.…”

Section: Introductionmentioning

confidence: 99%

Constrained Bayesian Method of Composite Hypotheses Testing: Singularities and Capabilities

Kachiashvili¹

2016

ijsmr

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The paper deals with the constrained Bayesian Method (CBM) for testing composite hypotheses. It is shown that, similarly to the cases when CBM is optimal for testing simple and multiple hypotheses in parallel and sequential experiments, it keeps the optimal properties at testing composite hypotheses. In particular, it easily, without special efforts, overcomes the Lindley's paradox arising when testing a simple hypothesis versus a composite one. The CBM is compared with Bayesian test in the classical case and when the a priori probabilities are chosen in a special manner for overcoming the Lindley's paradox. Superiority of CBM against these tests is demonstrated by simulation. The justice of the theoretical judgment is supported by many computation results of different characteristics of the considered methods.

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