Detection, Estimation and Optimization Problems in Stochastic Systems, Genetics and Economics

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Abstract: Statistical Problems in Quality control, Stochastic Systems and Genetic AnalysisThis project will address a number of related statistical problems having applications in (i) industrial quality control and complex engineering systems, (ii) in molecular biology and genetics, and (iii) in financial economics. (i) One objective of the proposed research is to develop a unified methodology of sequential change-point detection in industrial quality control and of automated fault detection in complex engineering systems. Relatively simple algorithms that 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 variety of practical applications. This methodology will not only address the recognized discrepancies between the assumptions underlying conventional control charts and today's industrial processes, but it will also provide methodological advances for on-line detection and diagnosis of faults and potential failures of automated engineering systems. In this connection, estimation and forecasting problems in time series models and stochastic dynamical systems having parameters that may change with time will also be investigated. Although in practice abrupt parameter changes usually occur infrequently, the unknown times of their occurrence have led to detection algorithms of prohibitive complexity. By using parallel recursive algorithms and combining new ideas in change-point detection with empirical Bayes methodology, it is anticipated that asymptotically efficient estimation and prediction schemes of manageable complexity will be developed. (ii) Another direction of research involves fixed sample change-point problems and their applications to biomolecular sequence analysis and other problems of signal detection. A comprehensive statistical methodology will be developed for genome scanning to map anonymous genes using data based on crosses of pure strains in experimental genetics or based on regions of identity by descent of related individuals in human genetics. Related mathematical problems in boundary crossing probabilities of random fields will be investigated. (iii) A third direction of research is financial time series and stochastic control problems of financial economics. New statistical models, computational algorithms, and methods for data analysis and forecasting will be developed to address a variety of sequential decision, portfolio selection, and pricing problems in investments and financial markets.The interdisciplinary research in financial economics and molecular biology not only leads to the development of new stochastic models and statistical methods, but it also provides valuable research opportunities for graduate and undergraduate students in these rapidly developing fields.