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

Abstract

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.

Keywords:

• Bayesian method
• constrained Bayesian method
• maximum likelihood method
• Stein’s method
• Type I error rate
• Type II error rate

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62F15
• 62F03

ACKNOWLEDGMENTS

We are most grateful to the Editor, the Associate Editor, and the Reviewers for their constructive comments and suggestions. These have helped us to prepare this improved manuscript. We thank them all.

DISCLOSURE

The authors have no conflicts of interest to report.

Additional information

Funding

K. Kachiashvili’s and J. Kachiashvili’s researches were partially supported by European Commission HORIZON EUROPE WIDERA-2021-ACCESS-03 Grant Project GAIN (grant agreement no. 101078950).