Constrained Bayesian method for testing composite hypotheses concerning normal distribution with equal parameters.

The problem of testing composite hypotheses with respect to the equal parameters of a normal distribution using the constrained Bayesian method is discussed. Hypotheses are tested using the maximum likelihood and Stein's methods. The optimality of our decision rule is shown by the following criteria: the mixed directional false discovery rate, the false discovery rate, and the Type I and Type II errors, under the conditions of providing a desired level of constraint. The algorithms for implementing the proposed methods and the computational tools for their application are included. Simulation results show validity of the theoretical results along with their superiority over the classical Bayesian method. [ABSTRACT FROM AUTHOR]