Investigation of the method of sequential analysis of Bayesian type

Abstract

The results of investigation of the properties of new sequential methods of testing many hypotheses based on special properties of hypotheses acceptance regions in the constrained Bayesian tasks of testing many hypotheses are offered. In particular, some relations between the errors of the first and the second kinds in constrained Bayesian task and in sequential method of Bayesian type depending on the divergence between the tested hypotheses are given. Also dependences of the Lagrange multiplier and the risk function on the probability of incorrectly accepted hypotheses are presented. Theses results are necessary for computation of errors of made decisions at testing multiple hypotheses using offered new sequential methods of testing hypotheses. Computation results of some examples confirm the rightness of theoretical researches.