The article discusses the special properties and features of the methodology created by the author for testing statistical hypotheses – the constrained Bayesian method, which allows its use in solving modern problems of machine learning and artificial intelligence. Examples of the use of this method in solving medical problems are given. In particular, for making decisions on the diagnosis of pulmonary pneumonia and cancer at a desired level of authenticity; as well as for making decisions on the uniformity of experimental results. For example, for making decisions related to treatment methods, drug dosage effectiveness, etc. at a predetermined level of reliability.