Statistical Methodology and Applications to Economics, Engineering and Genetics

这项研究的一个重要目标是开发基因图谱的方法，即识别包含一个或多个影响人类或实验生物体感兴趣的性状的基因的基因组区域。在噪声背景中搜索一个或多个信号的位置的参数集出现在基因映射中，其中信号指示基因的存在。类似的问题也出现在脑图、天文学和生物信息学上。他们解决方案的一个重要部分涉及随机场超过高阈值的概率。将开发一种统一的解析方法和顺序蒙特卡罗方法来评估这些跨越边界的概率。该研究的其他方法论创新包括新的动态经验贝叶斯模型和方法，序贯监视程序，以及针对可能发生结构突变的输入输出系统的自适应控制方案。正在开发中的动态经验贝叶斯方法应用于保险费率制定、经济学中的动态面板数据、生物医学研究中的纵向数据和风险管理。在最近的金融危机和漏油灾难之后，顺序监测和适应性风险控制具有及时的相关性。序贯蒙特卡罗方法在非线性滤波、通信网络中的罕见事件模拟和风险管理等方面有着重要的应用。基因图谱为研究人类疾病以及农牧业提供了重要工具。拟议研究的更广泛影响包括(I)在遗传学、工程学、金融、保险、风险管理和监测方面的直接影响，以及(Ii)通过开发新的高级课程并让研究生参与研究的所有阶段来培训学术界、工业界和政府的下一代科学家。

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.