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

该项目侧重于发展新的理论和方法的顺序多重比较。它的目的是开发成本最小化的方法和支持理论进行多个统计推论顺序。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。本研究将最近获得的多重比较的升压和降压程序扩展到顺序设计。它搜索最优的停止规则，使实验的预期成本最小化，同时控制假阳性和假阴性率。新方法结合了灵活性和成本优化顺序程序与现代统计方法的能力，多重比较，以控制家庭的错误率和功率。所提出的同时置信区间序列将重复置信区间的思想推广到多个参数的情况下，达到了期望的总体置信水平。新的多重假设检验方法用于推导对任何一个或几个参数的变化敏感的顺序变化点检测算法。该项目的可交付成果包括以最低预期成本设计多个比较实验的可靠统计方法。其中一个主要应用是连续的临床试验，这些试验是为了回答多个问题而进行的，例如，关于测试治疗的有效性和安全性。这种医学研究的成本优化最终导致保健费用的降低。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病前的模式以及生物恐怖袭击。在控制误报率的前提下，提出的变化点检测方案旨在最小化预期的检测延迟，确保对意外变化的快速反应。它们的应用揭示了许多全球性问题。经济（福利、气候、环境）变化了吗？它以什么方式和方向变化？这种变化是什么时候开始的？变化是否继续，或者过程是否稳定？提出的顺序统计工具解决了这些和其他涉及多个统计比较的重要问题。

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.