An Example of Application of CBM to Intersection- Union Hypotheses Testing
Journal Title: Biomedical Journal of Scientific & Technical Research (BJSTR) - Year 2019, Vol 19, Issue 3
Abstract
Application of CBM to the testing of the intersection of a sub-set of basic hypotheses against an alternative one is considered. Optimal decision rule allows us to restrict the Type-I and Type-II errors rates on the desired levels.In many applications, there arise the problems when basic or/and alternative hypotheses can be represented as the union or intersection of several sub-hypotheses Sen Gupta [1], Roy [2]. The general methodology of testing union-intersection hypotheses was offered in Roy [2]. An idea of this methodology consists in consideration in pairs of sub-hypotheses from basic and alternative hypotheses. Each pair of hypotheses is chosen one by one from basic and alternative hypotheses sub-sets accordingly. Final regions, for acceptance of basic and alternative hypotheses, are defined as intersection of the appropriate sub-regions. The reverse scenario, when basic and/or alternative hypotheses are presented as intersection of the appropriate sub-sets of hypotheses, is considered in Sen Gupta [1]. The special methodology, giving the powerful decision rule, based on Pivotal Parametric Product (P3), is offered there. Application of constrained Bayesian method (CBM), developed by author Kachiashvili [3], to the considered type of hypotheses in one concrete case, is offered below. Here is shown that obtained decision rule allows us to restrict the Type-I and Type-II error rates on the desired level, in this case.
Authors and Affiliations
Kachiashvili KJ
Keywords
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- EP ID EP621787
- DOI 10.26717/BJSTR.2019.19.003304
- Views 184
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