Specific features of regions of acceptance of hypotheses in conditional Bayesian problems of statistical hypotheses testing Article

First Online: 13 November 2012 Received: 26 October 2010 Revised: 09 August 2011 DOI :
10.1007/s13171-012-0014-8

Cite this article as: Kachiashvili, G.K., Kachiashvili, K.J. & Mueed, A. Sankhya A (2012) 74: 112. doi:10.1007/s13171-012-0014-8
Abstract Specific features of the regions of acceptance of hypotheses in conditional Bayesian problems of statistical hypotheses testing are discussed. It is shown that the classical Bayesian statement of the problem of statistical hypotheses testing in the form of an unconditional optimizing problem is a special case of conditional Bayesian problems of hypotheses testing set in the form of conditional optimizing problems. It is also shown that, at acceptance of hypotheses in conditional problems of hypotheses testing, the situation is similar to the sequential analysis. It is possible an occurrence of the situation when the acceptance of a hypothesis with specified validity on the basis of the available information is impossible. In such a situation, the actions are similar to the sequential analysis, i.e. it is necessary to obtain additional information in the form of new observation results or to change the significance level of a test.

Keywords and phrases Bayesian problem hypotheses testing significance level conditional problem unconditional problem

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© Indian Statistical Institute 2012

Authors and Affiliations 1. Georgian Technical University Tbilisi Georgia 2. I. Vekua Institute of Applied Mathematics of Tbilisi State University Tbilisi Georgia 3. Abdus Salam School of Mathematical Sciences of GC University Lahore Pakistan 4. Air University Multan Campus Multan Pakistan