An important objective of the proposed research is to develop methods for gene mapping, i.e., the identification of genomic regions containing a gene (or genes) affecting a trait of interest in either humans or in experimental organisms. Searching a parameter set for the location of one or more signals in a noisy background arise in gene mapping where the signals indicate the presence of a gene. Similar problems arise in brain mapping, astronomy, and bioinformatics. An important part of their solution involves the probability that a random field exceeds a high threshold. A unified analytic approach and sequential Monte Carlo methods will be developed to evaluate these boundary crossing probabilities. Other methodological innovations of the proposed research are new dynamic empirical Bayes models and methods, sequential surveillance procedures, and adaptive control schemes for input-output systems that may undergo occasional abrupt structural changes.
The dynamic empirical Bayes approach under development has applications to insurance rate-making, dynamic panel data in economics, longitudinal data in biomedical studies, and risk management. Sequential surveillance and adaptive risk control are of timely relevance in the aftermath of the recent financial crisis and oil spill disaster. Sequential Monte Carlo methods have important applications to nonlinear filtering and to rare event simulation in communication networks and risk management. Gene mapping provides an important tool in the study of human diseases, and in agriculture and animal husbandry. The broader implications of the proposed research include (i) direct implications in genetics, engineering, finance, insurance, risk management and surveillance, and (ii) training of the next generation of scientists in academia, industry, and government by developing new advanced courses and involving graduate students in all phases of the research.