Detection, Estimation and Optimization Problems in Stochastic Systems, and Applications to Genetics, Engineering and Economics

题目：随机系统的检测、估计和优化问题及其在遗传学、工程学和经济学中的应用摘要：研究人员将研究工业质量控制、复杂工程系统的自动故障检测和基因定位中出现的大量类似变化点的问题。这些问题的一个共同特征涉及随机场超过高阈值的概率。将发展一种统一的分析方法来评估有关的跨界概率。重要抽样技术和顺序蒙特卡罗方法也将发展，以补充解析近似。对于联机应用程序，将开发相对简单的并行递归算法，这些算法在计算和内存要求方面不太苛刻，但从统计角度来看几乎是最佳的。另一个研究方向是金融经济学中的金融时间序列和随机控制问题。将开发新的统计模型、计算算法、数据分析和预测方法，以解决投资和金融市场中的各种顺序决策、投资组合选择和定价问题。该项目将解决以下问题：(i)工业质量控制，特别是复杂工程系统的控制；（ii）基因定位，即识别包含影响人类、模型实验生物或农业重要作物感兴趣的特征的基因（或多个基因）的基因组区域；（iii）金融经济学，特别是金融数据的时间序列分析。这些问题将利用概率论和统计理论的最新发展，以及涉及计算机模拟的大量实验来研究。将开发计算算法以促进应用。研究人员还将在统计遗传学和金融数学方面开设新的本科和研究生课程，并为这些课程编写教科书。

Proposal: DMS-0305749PI: Tze L. LaiTitle: Detection, Estimation and Optimization Problems in Stochastic Systems, and Applications to Genetics, Engineering and EconomicsABSTRACT: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.