Sequential testing of multiple hypotheses, simultaneous confidence estimation, and multichannel change-point detection

多个假设的顺序测试、同时置信度估计和多通道变化点检测

• 批准号: 1007775
• 负责人: Michael Baron
• 金额: $ 20万
• 依托单位: University of Texas at Dallas
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-06-01 至 2014-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1007775&HistoricalAwards=false
• 关键词: Sequential; testing; multiple; hypotheses; simultaneous

The project focuses on the development of new theory and methodology of sequential multiple comparisons. It aims to develop cost-minimizing methods and supporting theory for conducting multiple statistical inferences sequentially. This includes testing multiple hypotheses, constructing sequences of simultaneous confidence sets, detecting changes in multiple channels, and making other sequential statistical decisions involving multiple parameters or multiple measurements. This study extends the recently obtained step-up and step-down procedures for multiple comparisons to sequential designs. It searches for optimal stopping rules that minimize the expected cost of the experiment while controlling for the false positive and false negative rates. The new methodology combines flexibility and cost-optimization of sequential procedures with the ability of modern statistical methods for multiple comparisons to control the familywise error rate and power. Proposed sequences of simultaneous confidence sets generalize the idea of repeated confidence intervals to the case of multiple parameters and achieve the desired overall confidence level. The new multiple hypothesis testing methodology is used for the derivation of sequential change-point detection algorithms sensitive to a change in any one or several parameters.Deliverables of the project include a sound statistical methodology for designing multiple comparison experiments at the minimum expected cost. One of the main applications is in sequential clinical trials that are conducted to answer multiple questions, for example, about the efficacy and safety of the tested treatment. Cost-optimization of such medical studies ultimately results in the reduced cost of health care. The new change-point detection procedures allow simultaneous tracking of changes in multiple parameters, which is used for the timely discovery of epidemic and pre-epidemic patterns and bioterrorist attacks. Controlling for the rate of false alarms, proposed change-point detection schemes are aimed to minimize the expected detection delay ensuring prompt reaction to unexpected changes. Their application sheds light to a number of global questions. Is the economy (welfare, climate, environment) changing? In what way and what direction is it changing? When did the change begin? Does the change continue, or has the process stabilized? Proposed sequential statistical tools address these and other important questions that involve multiple statistical comparisons.

该项目侧重于序贯多重比较的新理论和方法的发展。它的目的是开发成本最小化方法和支持理论来顺序进行多个统计推断。这包括测试多个假设、构建同时置信集的序列、检测多个通道中的变化以及做出涉及多个参数或多个测量的其他顺序统计决策。这项研究将最近获得的用于多重比较的升压和降压程序扩展到顺序设计。它寻找最佳停止规则，最大限度地减少实验的预期成本，同时控制假阳性和假阴性率。新方法将顺序程序的灵活性和成本优化与现代统计方法的多重比较能力相结合，以控制系列错误率和功效。所提出的同时置信集序列将重复置信区间的思想推广到多个参数的情况，并实现所需的总体置信水平。新的多重假设检验方法用于推导对任何一个或多个参数的变化敏感的连续变化点检测算法。该项目的交付成果包括一种完善的统计方法，用于以最低的预期成本设计多重比较实验。主要应用之一是序贯临床试验，旨在回答多个问题，例如有关所测试治疗的有效性和安全性的问题。此类医学研究的成本优化最终会降低医疗保健成本。新的变化点检测程序允许同时跟踪多个参数的变化，用于及时发现流行病和流行前模式以及生物恐怖袭击。为了控制误报率，提出的变化点检测方案旨在最大限度地减少预期检测延迟，确保对意外变化做出及时反应。他们的应用揭示了许多全球性问题。经济（福利、气候、环境）是否正在发生变化？正在以何种方式、向什么方向发生变化？改变是从什么时候开始的？变化是否仍在继续，或者过程是否已经稳定？所提出的序贯统计工具解决了涉及多重统计比较的这些和其他重要问题。