Mathematical Sciences: Detection and Estimation Problems inQuality Control, Dynamical Systems and Genetic Analysis

所提出的研究的一个主要方向是在连续的变点检测方案。强有力的技术来解决这个问题，目前可从最近的进展，序贯测试理论和边界穿越问题的随机领域。预计相对简单的算法，这是不是太苛刻的计算和存储器的要求，在线实施，但从统计的角度来看，几乎是最佳的，将开发各种各样的实际应用。不仅将开发的方法解决了广泛公认的传统控制图和当今的工业流程的基础假设之间的差异，但它也将结合检测方面和工业质量控制的质量测量方面。另一个密切相关的研究方向是固定样本变点问题及其在计量经济学、信号重构和遗传连锁分析中的应用。随机过程和随机场的边界穿越概率的相关基本问题将被研究，并有望导致一些长期存在的问题的最终解决方案，有关广义似然比统计量的分布在变点模型。第三个相关的研究领域是估计和控制的时间序列模型和随机动态系统的参数可能会随时间而变化。虽然在实践中突然的参数变化通常很少发生，其发生的未知时间已导致在文献中的贝叶斯估计器和控制器的令人望而却步的复杂性。通过使用并行递归算法，并结合一些新的想法，在连续的变化点检测与经验贝叶斯方法，预计渐近有效的估计和控制计划，具有可管理的复杂性，并可以实现在线将被开发。 提出的研究的一个重要目标是发展一个强大的统计方法，用于现代工业过程的质量控制和复杂制造系统的自动故障检测。另一个重要的目标是制定统计方法，以分析与人类、动物和植物的疾病易感性和其他特征有关的遗传连锁数据，并从这些数据中提取相关信息，从而更好地诊断和治疗疾病。

A major direction of the proposed research is in sequential change-point detection schemes. Powerful techniques to tackle this problem are currently available from recent advances in sequential testing theory and boundary crossing problems in random fields. It is expected that relatively simple algorithms which are not too demanding in computational and memory requirements for on-line implementation and yet are nearly optimal from a statistical viewpoint will be developed for a wide variety of practical applications. Not only will the methodology to be developed address the widely recognized discrepancies between the assumptions underlying conventional control charts and today's industrial processes, but it will also integrate both the detection aspect and the quality measurement aspect of industrial quality control. Another closely related direction of research is in fixed sample change-point problems and its applications to econometrics, signal reconstruction and genetic linkage analysis. Related fundamental problems in boundary crossing probabilities of random processes and random fields will be investigated, and are expected to lead to definitive solutions of some long-standing problems concerning the distribution of generalized likelihood ratio statistics in change-point models. A third related area of research is estimation and control of time series models and stochastic dynamical systems whose parameters may change with time. Although in practice abrupt parameter changes typically occur very infrequently, the unknown times of their occurrence have led to prohibitive complexity of the Bayes estimators and controllers in the literature. By using parallel recursive algorithms and combining some new ideas in sequential change-point detection with empirical Bayes methodology, it is anticipated that asymptotically efficient estimation and control schemes which have manageable complexity and which can be implemented on-line will be developed. An important objeat ive of the proposed research is the development of a powerful statistical methodology for quality control of modern industrial processes and for automated fault detection in complex manufacturing systems. Another important goal is to develop statistical methods appropriate for analysis of genetic linkage data related to disease susceptibility and other traits in humans, animals and plants and for extraction of relevant information from these data that may lead to better diagnostic tests and treatments of the disease.