Statistical Problems in Quality Control, Stochastic Systems and Genetic Analysis

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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.