Statistical Problems in Quality Control, Stochastic Systems and Genetic Analysis

质量控制、随机系统和遗传分析中的统计问题

• 批准号: 9704324
• 负责人: Tze Lai
• 金额: $ 25.5万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704324&HistoricalAwards=false
• 关键词: Statistical; Problems; Quality; Control; Stochastic

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.

Lai和Siegmund 9704324 研究人员开发了一种顺序的方法，涉及算法的变化点检测，不太苛刻的计算和内存要求的在线实施，但从统计的角度来看，几乎是最佳的。 强有力的技术来解决这个问题，来自最近的进展，序贯测试理论和边界穿越问题的随机领域。 一个密切相关的研究方向是固定样本变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穿越概率的相关基本问题，并最终解决了一些长期存在的问题，这些问题涉及变点模型中广义似然比统计量的分布。 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，并结合一些新的思想，在序贯变点检测与经验贝叶斯方法，这些困难得到解决，渐近有效的估计和控制方案的管理复杂性。 这项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。 另一个目标是发展统计方法，适用于分析与人类、动物和植物的疾病易感性和其他性状有关的遗传连锁数据， 从这些数据中获得相关信息，最终可能导致更好的诊断测试和疾病治疗。 应用涉及制造业和生物技术的战略领域。