The Methods of Sequential Analysis of Bayesian Type for the Multiple Testing Problem

Abstract

New sequential methods of multiple testing problems based on special properties of hypotheses acceptance regions in the constrained Bayesian tasks of testing hypotheses are offered. Results of an investigation on the properties of one of these methods are given. They show the consistency, simplicity, and optimality of the results obtained in the sense of the chosen criterion. The essence of the criterion is to restrict from above the probability of the error of one type and to minimize the probability of the error of the second type. The facts of the validity of the suitable properties of the method are proved. Examples of testing of hypotheses for the sequentially obtained independent samples from the multivariate normal distribution with correlated components are cited. They show the high quality of the proffered methods. The results of the Wald sequential method are given for the examples with two hypotheses and compared with the results obtained by the proffered method.

Keywords:

• Constrained Bayesian tasks
• Decision rule
• Hypothesis acceptance errors
• Hypotheses testing
• Sequential analysis

Subject Classifications:

• 62F15
• 62F03

ACKNOWLEDGMENT

I thank the Editor, the Associate Editor, and the referee(s) for their substantial help in revising this article.

Notes

Recommended by Wolfgang Schmid