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

该项目致力于发展序贯多重比较的新理论和新方法。它的目的是开发成本最小化方法和支持理论，以便按顺序进行多个统计推断。这包括测试多个假设、构建同时置信度集序列、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多重比较的递增和递减程序扩展到序贯设计。它寻找最优的停止规则，使实验的预期成本最小化，同时控制假阳性和假阴性比率。新的方法结合了顺序程序的灵活性和成本最优化，以及现代统计方法进行多重比较的能力，以控制家庭错误率和功率。所提出的同时置信度集序列将重复置信度区间的思想推广到多参数的情况，并达到期望的总体置信度水平。新的多重假设检验方法被用于推导对任何一个或多个参数的变化敏感的序贯变点检测算法。该项目的成果包括以最小的预期成本设计多个比较实验的可靠的统计方法。主要应用之一是进行顺序临床试验，以回答多个问题，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医疗保健成本的降低。新的变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疫情前模式以及生物恐怖袭击。通过对虚警率的控制，提出的变点检测方案旨在最小化预期检测延迟，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)正在发生变化吗？它正在以什么方式和方向发生变化？这种变化是从什么时候开始的？这种变化还在继续，还是过程已经稳定下来了？拟议的顺序统计工具涉及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.