Statistical Problems in Quality Control, Stochastic Systems and Genetic Analysis

Lai和Siegmund 9704324研究人员开发了一种变化点检测的顺序方法，该方法涉及的算法对在线实现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。从序列测试理论和随机场边界穿越问题的最新进展中衍生出了解决这一问题的强大技术。一个密切相关的研究方向是固定样本变化点问题及其在信号检测和基因定位中的应用。本文还研究了随机过程和随机场的边界跨越概率的相关基本问题，并最终解决了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。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。通过采用并行递归算法，并将序列变化点检测中的一些新思想与经验贝叶斯方法相结合，解决了这些困难，得到了复杂度可控的渐近有效的估计和控制方案。本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。另一项客观发展统计方法，适用于分析与人类、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相关信息，最终可能导致更好的疾病诊断测试和治疗方法。应用涉及制造业和生物技术的战略领域。

Lai and Siegmund 9704324 The investigators develop a sequential method of change-point detection involving algorithms that are not too demanding in computational and memory requirements for on-line implementation and yet are nearly optimal from a statistical viewpoint. Powerful techniques to tackle this problem are derived from recent advances in sequential testing theory and boundary crossing problems in random fields. A closely related direction of research is fixed sample change-point problems and their applications to signal detection and gene mapping. Related fundamental problems in boundary crossing probabilities of random processes and random fields are also investigated and lead to definitive solutions of some long-standing questions 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, these difficulties are resolved to obtain asymptotically efficient estimation and control schemes of manageable complexity. One important objective of this 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 objective development of 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 ultimately lead to better diagnostic tests and tr eatments of the disease. Applications involve the strategic areas of manufacturing and biotechnology.