Sensitivity Analysis of Classical and Conditional Bayesian Problems of Many Hypotheses Testing

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

doi:10.1080/03610926.2010.510255

Cited by 16 publications

(22 citation statements)

References 8 publications

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“…i , i = 1,..., S . When testing composite hypotheses (1) using CBM, we can use one of the possible decision rules of different statements of CBM depending on the final aim [1,4,9]. In these decision rules, one must use densities f !…”

Section: Cbm For Testing Composite Hypothesesmentioning

confidence: 99%

“…Let us apply one of CBM, for example, task 1 with restrictions on the averaged probability of acceptance of true hypotheses for testing hypotheses [1,4,9]. For two hypotheses, it has the following form…”

Section: Lindley's Paradox and Cbmmentioning

confidence: 99%

“…Constrained Bayesian methods of hypotheses testing have the following specificity [1,9]: when the Lagrange multiplier ! differs from the one in the observation space there appears the region of no acceptance of the simple hypothesis and the region of supposition of the validity of both hypotheses.…”

Section: Examplementioning

confidence: 99%

“…As was investigated in [1], the change of a priori probability affects the decision made. This influence is not so significant as in the classical Bayesian test, but still it is present in the constrained test too, especially, when p is very small ( < 0.1 ) or very big ( > 0.8 ) (see Table 3 and Figure 3a).…”

Section: Examplementioning

confidence: 99%

“…In [1] was offered Constrained Bayesian Methods (CBM) of statistical hypotheses testing. The CBM have all positive characteristics of well-known classical approaches.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Cbm For Testing Composite Hypothesesmentioning

confidence: 99%

Section: Lindley's Paradox and Cbmmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Section: Examplementioning

confidence: 99%

“…In [1] was offered Constrained Bayesian Methods (CBM) of statistical hypotheses testing. The CBM have all positive characteristics of well-known classical approaches.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations