The investigators will study a large number of change-point like problems that arise in industrial quality control, automated fault detection of complex engineering systems and gene mapping. A common feature of these problems involves the probability that a random field exceeds a high threshold. A unified analytic approach will be developed to evaluate the relevant boundary crossing probabilities. Importance sampling techniques and sequential Monte Carlo methods will also be developed to supplement the analytic approximations. For on-line applications, relatively simple parallel, recursive algorithms, which are not too demanding in computational and memory requirements and yet are nearly optimal from a statistical viewpoint, will be developed. Another direction of research is financial time series and stochastic control problems in financial economics. New statistical models, computational algorithms, and data analysis and forecasting methods will be developed to address a variety of sequential decision, portfolio selection, and pricing problems in investments and financial markets.
The project will address problems of (i) industrial quality control, especially control of complex engineering systems, (ii) gene mapping, i.e., the identification of genomic regions containing a gene (or genes) affecting a trait of interest in humans, model experimental organisms, or agriculturally important crops, and (iii) financial economics, especially time series analysis of financial data. The problems will be studied by using recent developments in probability and statistical theory, and by extensive experiments involving computer simulations. Computational algorithms will be developed to facilitate applications. The investigators will also develop new undergraduate and graduate courses in statistical genetics and in financial mathematics and write textbooks for these courses.
