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.
