Robust Sequential Analysis

序贯分析涉及的是当样本数量不是先验给定的，而是随着时间的推移而增加时的统计推断。设计目标是最小化满足推断量的可靠性和/或准确性约束所需的平均样本数。序贯过程已被证明可以显着减少平均样本数相比，等效的固定样本大小的程序，并发现在医疗诊断，环境监测，质量控制，危险检测，图像处理和频谱sensing.The的想法支撑鲁棒统计是牺牲一些标称条件下的效率，以便不太敏感偏离理想情况下的不同领域的应用。因此，稳健的程序被设计为在假设模型的邻域中表现良好，通常允许小的但任意的偏差。从这个意义上说，稳健方法形成了参数和非参数方法之间的中间地带。本项目的想法是将序贯统计和稳健统计的好处联合收割机结合起来：序贯执行稳健程序补偿了名义效率的损失。稳健地执行顺序过程可以降低模型不匹配的敏感性。首先，我们要发展一个简洁的理论框架，稳健的序贯分析，统一检测和估计。我们猜想，我们在以前的工作中开发的顺序二元假设检验的极大极小解的特点相同的数学工具，可以应用于多个假设，以及联合检测和估计。更确切地说，我们期望极大极小最优停止和决策策略由Fredholm积分方程的解确定，而相应的最不利分布由状态依赖的f-相异度族确定。第二个目标是发展实用算法。同样，我们的目标是一个统一的方法，可以应用于所有定义良好的推理问题。我们还希望避免对底层应用和分布的严格假设，而是专注于问题的常见数学结构。因此，两个中心任务，实现强大的顺序程序是解决Fredholm积分方程和最小化f-差异的凸集合的distributions. Bending信号处理组的专业知识的两个主要领域，该项目将基于现有的工作和经验的坚实基础。信号处理小组在稳健估计方面的工作得到国际认可，近年来在稳健和顺序检测方面做出了显著贡献。因此，我们认为自己处于成功完成拟议项目的独特有利地位。

Sequential Analysis is concerned with statistical inference when the number of samples is not given a priori, but is increasing over time. The design goal is to minimize the average number of samples required to fulfill constraints on the reliability and/or accuracy of the inferred quantities. Sequential procedures have been shown to significantly reduce the average number of samples compared to equivalent fixed-sample-size procedures and find application in fields as diverse as medical diagnosis, environment monitoring, quality control, hazard detection, image processing, and spectrum sensing.The idea underpinning robust statistics is to sacrifice some efficiency under nominal conditions in order to be less sensitive to deviations from the ideal case. Hence, robust procedures are designed to perform well in a neighborhood of the assumed model, typically allowing for small, but arbitrary deviations. In this sense, robust methods form the middle ground between parametric and nonparametric approaches.The idea of this project is to combine the benefits of sequential and robust statistics: Sequentially performing a robust procedure compensates the loss in nominal efficiency. Robustly performing a sequential procedure reduces its sensitivity to model mismatch.The two main goals of the project are as follows. First, we want to develop a concise theoretical framework for robust sequential analysis that unifies detection and estimation. We conjecture that the same mathematical tools that we developed in previous work to characterize the minimax solution of sequential binary hypothesis tests can be applied to multiple hypotheses as well as joint detection and estimation. More precisely, we expect the minimax optimal stopping and decision policy to be determined by the solution of a Fredholm integral equation and the corresponding least favorable distributions to be determined by a state dependent family of f-dissimilarities.The second goal is the development of practical algorithms. Again, we aim for a unified approach that can be applied to all well-defined inference problems. We further want to avoid strict assumptions about the underlying applications and distributions, but instead focus on the common mathematical structure of the problems. Consequently, the two central tasks for implementing robust sequential procedures are to solve Fredholm integral equations and to minimize f-dissimilarities over convex sets of distributions.Bringing together two main areas of expertise of the Signal Processing Group, the project will be based on a solid foundation of existing work and experience. The Signal Processing Group is internationally recognized for its work on robust estimation and has made notable contributions to robust and sequential detection in recent years. Therefore, we see ourselves in a uniquely favorable position for a successful completion of the proposed project.