Investigation and Computation of Unconditional and Conditional Bayesian Problems of Hypothesis Testing
|Issue Date||May 01, 2011|
|Publishing Date||May 01, 2011|
|Keywords||Bayesian problem, hypotheses testing, significance level, conditional problem, computation of Bayesian tasks. AMS 2000 Subject Classifications: 62F15; 62F03|
In Bayesian statement of hypotheses testing, instead of unconditional problem of minimization of average risk caused by the errors of the first and the second types, there is offered to solve the conditional optimization problem when restrictions are imposed on the errors of one type and, under such conditions, the errors of the second type are minimized. Depending on the type of restrictions, there are considered different conditional optimization problems. Properties of hypotheses acceptance regions for the stated problems are investigated and, finally, comparison of the properties of unconditional and conditional methods is realized. The results of the computed example confirm the validities of the theoretical judgments.