Mathematical Sciences: Research in Sequential Analysis

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The principal investigator will continue his work on two topics. The first one called multistage testing can be seen as the practical compromise between the standard fixed sample size methods and the optimal sequential methods. Sequential one-at-a- time testing procedures have significant practical problems. Previous work of the investigator has shown that asymptotic optimality can be achieved by a three stage procedure where the size of the sample may depend on the previous stage. Multistage procedures change the error probabilities of the problem in complex ways. Dr. Lorden will study the error probabilities and the choice of successive sample sizes. The second problem is detecting the change in the underlying distribution as soon after it occurs, as possible. The new method will employ Bayes procedures to utilize the prior information on the location of the change point. In sequential tests, both the standard Neyman-type approach and the Bayesian approach have proved to be valuable. Dr. Lorden investigates a partial-Bayes method in which a weighted average of the expected sample size is minimized subjected to the required error probabilities.