, Volume 74, Issue 1, pp 112125
First online:
Specific features of regions of acceptance of hypotheses in conditional Bayesian problems of statistical hypotheses testing
 G. K. KachiashviliAffiliated withGeorgian Technical University
 , K. J. KachiashviliAffiliated withI. Vekua Institute of Applied Mathematics of Tbilisi State UniversityAbdus Salam School of Mathematical Sciences of GC University Email author
 , A. MueedAffiliated withAir University Multan Campus
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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 problemAMS (2000) subject classification
Primary 62F03; Secondary 62F15 Title
 Specific features of regions of acceptance of hypotheses in conditional Bayesian problems of statistical hypotheses testing
 Journal

Sankhya A
Volume 74, Issue 1 , pp 112125
 Cover Date
 201202
 DOI
 10.1007/s1317101200148
 Print ISSN
 0976836X
 Online ISSN
 09768378
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Primary 62F03; Secondary 62F15
 Bayesian problem
 hypotheses testing
 significance level
 conditional problem
 unconditional problem
 Authors

 G. K. Kachiashvili ^{(1)}
 K. J. Kachiashvili ^{(2)} ^{(3)}
 A. Mueed ^{(4)}
 Author Affiliations

 1. Georgian Technical University, 77 Kostava St., Tbilisi, 380078, Georgia
 2. I. Vekua Institute of Applied Mathematics of Tbilisi State University, 2 University St, Tbilisi, 380043, Georgia
 3. Abdus Salam School of Mathematical Sciences of GC University, 68B, New Muslim Town, Lahore, Pakistan
 4. Air University Multan Campus, Khan Centre Abdali Road, Multan, Pakistan