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

摘要：质量控制、随机系统和遗传分析中的统计问题本项目将解决一些相关的统计问题，这些问题在(i)工业质量控制和复杂工程系统、（ii）分子生物学和遗传学以及（iii）金融经济学中有应用。(i)拟议研究的一个目标是发展一种统一的方法，用于工业质量控制中的顺序变化点检测和复杂工程系统中的自动故障检测。将为各种实际应用开发相对简单的算法，这些算法对在线实现的计算和内存要求不太高，但从统计角度来看几乎是最佳的。这种方法不仅可以解决传统控制图和当今工业过程的假设之间公认的差异，而且还可以为自动化工程系统的故障和潜在故障的在线检测和诊断提供方法上的进步。在这方面，估计和预测问题的时间序列模型和随机动力系统的参数可能随着时间的变化也将进行研究。虽然在实践中，参数突变通常不经常发生，但它们发生的未知时间导致检测算法的复杂性过高。通过使用并行递归算法，并将变化点检测的新思想与经验贝叶斯方法相结合，预计将开发出可管理复杂性的渐近有效估计和预测方案。（ii）另一个研究方向涉及固定样本变点问题及其在生物分子序列分析和其他信号检测问题中的应用。将开发一种全面的统计方法，用于基因组扫描，利用基于实验遗传学中纯菌株杂交的数据或基于人类遗传学中相关个体血统的身份区域来绘制匿名基因。研究随机场边界穿越概率的相关数学问题。（三）第三个研究方向是金融经济学的金融时间序列和随机控制问题。将开发新的统计模型、计算算法和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。金融经济学和分子生物学的交叉研究不仅带来了新的随机模型和统计方法的发展，而且为研究生和本科生在这些快速发展的领域提供了宝贵的研究机会。

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.