Review of the Problems Solved Using the Constrained Bayesian Methods

A new philosophy of hypothesis testing - the constrained Bayesian method (CBM) and its application for testing different types of statistical hypotheses such as: simple, composite, asymmetric, multiple hypotheses, are considered in the work. The advantage of the CBM over existing classical methods is theoretically proven in the form of theorems and practi-cally demonstrated by the results of numerous example computations. Examples of the use of CBM to solve some practically important problems are presented, which confirm the flexibility of the method and its great ability to deal with difficult problems.