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

提出的一个主要研究方向是序列变化点检测方案。从序列测试理论和随机场边界穿越问题的最新进展中，目前可以获得解决这一问题的强大技术。预计将为各种实际应用开发相对简单的算法，这些算法对联机执行的计算和内存要求不太高，但从统计角度来看几乎是最佳的。要开发的方法不仅要解决传统控制图和当今工业过程的假设之间广泛公认的差异，而且还将集成工业质量控制的检测方面和质量测量方面。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、信号重建和遗传连锁分析中的应用。本文将研究随机过程和随机场的边界跨越概率的相关基本问题，并期望对一些长期存在的关于变点模型中广义似然比统计分布的问题给出明确的解决方案。第三个相关研究领域是时间序列模型和随机动力系统的估计和控制，其参数可能随时间变化。虽然在实践中，参数突变通常很少发生，但它们发生的未知时间导致了文献中贝叶斯估计器和控制器的复杂性。利用并行递归算法，并将序列变点检测中的一些新思想与经验贝叶斯方法相结合，可望开发出复杂度可控且可在线实现的渐近高效估计和控制方案。提出的研究的一个重要目标是开发一种强大的统计方法，用于现代工业过程的质量控制和复杂制造系统中的自动故障检测。另一项重要目标是制定适合于分析与人类、动物和植物的疾病易感性和其他特征有关的遗传联系数据的统计方法，并从这些数据中提取相关信息，从而改进疾病的诊断测试和治疗方法。

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.