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

本文提出的一个主要研究方向是序贯变点检测方案。目前，从序列测试理论和随机场中的边界跨越问题的最新进展中可以获得解决这一问题的强大技术。预计将为广泛的实际应用开发相对简单的算法，这些算法对在线实施的计算和存储要求不是太高，但从统计学的角度来看几乎是最优的。将要开发的方法不仅将解决作为传统控制图基础的假设与当今工业过程之间公认的差异，而且还将整合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。研究随机过程和随机场跨越边界概率的相关基本问题，并有望最终解决一些长期存在的关于变点模型中广义似然比统计量分布的问题。第三个相关的研究领域是参数随时间变化的时间序列模型和随机动力系统的估计和控制。虽然在实际中参数的突变通常很少发生，但未知的发生时间已经导致文献中贝叶斯估计器和控制器的复杂性。通过使用并行递归算法，并将序贯变点检测中的一些新思想与经验贝叶斯方法相结合，有望开发出具有可控复杂性的、可在线实现的渐近有效的估计和控制方案。这项研究的一个重要目标是发展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。另一个重要目标是开发适当的统计方法，用于分析与人类、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，并从这些数据中提取可能导致更好的疾病诊断测试和治疗的相关信息。

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.