Mathematical Sciences: Research in Sequential Analysis

首席调查员将继续就两个专题开展工作。第一种称为多阶段检验的方法可以看作是标准固定样本量方法和最优序贯方法之间的实际折衷。一次一次的顺序测试程序有很大的实际问题。研究者以前的工作已经表明，渐近最优性可以通过三阶段过程来实现，其中样本的大小可能取决于前一阶段。多阶段过程以复杂的方式改变问题的错误概率。洛登博士将研究误差概率和连续样本量的选择。第二个问题是在基础分布发生变化后尽快检测到它。新方法将使用贝叶斯过程来利用关于变化点位置的先验信息。在序列检验中，标准的Neyman型方法和贝叶斯方法都被证明是有价值的。洛登博士研究了一种部分贝叶斯方法，在该方法中，预期样本量的加权平均值在所需误差概率的约束下最小化。

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.