Mathematical Sciences: Research in Sequential Analysis

数学科学：序贯分析研究

• 批准号: 8802486
• 负责人: Gary Lorden
• 金额: $ 8.2万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1991-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802486&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Sequential; Analysis

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.

首席研究员将继续他在两个主题上的工作。第一种称为多阶段测试，可以看作是标准固定样本量方法和最优顺序方法之间的实际折衷。顺序的一次一个的测试程序有显著的实际问题。研究者以前的工作表明，渐近最优性可以通过三个阶段的程序，其中样本的大小可能取决于前一阶段实现。多阶段程序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。第二个问题是在底层分布发生变化后尽可能快地检测变化。新方法将采用贝叶斯过程来利用变化点位置的先验信息。在一系列的测试中，标准内曼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，在这种方法中，预期样本量的加权平均值在所需的误差概率下被最小化。