Statistical Methodology and Applications to Genetics, Engineering and Economics

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图谱、脑图谱、生物信息学和天文学中。这些问题的解决方案的一个重要部分涉及随机场超过高阈值的概率。拟议的研究开发了一个统一的分析方法来评估这些边界交叉概率，重要性抽样和顺序蒙特卡罗方法来补充解析近似。一个密切相关的研究领域是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会随时间变化。虽然在实践中，突然的参数变化通常很少发生，其发生的未知时间导致了在文献中的贝叶斯估计和预测的复杂性。通过使用并行递归算法，结合变点检测的一些新思想和经验贝叶斯方法，本文的研究发展了渐近有效的估计和预测方案，其复杂性易于管理。马尔可夫系统参数变化的贝叶斯模型是隐马尔可夫模型的特殊情况。所提出的研究的一个目标是发展一个全面的理论，有效的参数估计，过滤和平滑的隐马尔可夫模型一般状态空间。另一个相关的研究方向是金融经济学中的计量经济学时间序列和随机优化问题。拟议研究的重要目标是为基因定位、信号处理、工程系统的自适应控制以及金融市场中的决策和定价问题开发统计方法。研究的更广泛的影响包括：（i）在工程，金融和遗传学中的直接应用，其中映射可以是更好地诊断或治疗疾病或改善植物或动物种群的第一步，以及（ii）通过让研究生参与研究的所有阶段来培训下一代科学家。

Searching a parameter set for the location of one or more signals in a noisy background arises in gene mapping, brain mapping, bioinformatics and astronomy. An important part of the solution of these problems involves the probability that a random field exceeds a high threshold. The proposed research develops a unified analytic approach to evaluate these boundary crossing probabilities, and importance sampling and sequential Monte Carlo methods to supplement the analytic approximations. A closely related area of research is estimation and forecasting problems in time series models and stochastic dynamical systems whose parameters may change with time. Although in practice abrupt parameter changes typically occur very infrequently, the unknown times of their occurrence have led to prohibitive complexity of the Bayes estimators and predictors in the literature. By using parallel recursive algorithms and combining some new ideas in change-point detection with empirical Bayes methodology, the proposed research develops asymptotically efficient estimation and prediction schemes with manageable complexity.Bayesian models of parameter changes in Markovian systems are special cases of hidden Markov models. A goal of the proposed research is to develop a comprehensive theory of efficient parameter estimation, filtering and smoothing in hidden Markov models on general state spaces. Another related direction of research is econometric time series and stochastic optimization problems in financial economics.Important objectives of the proposed research are to develop statistical methods for gene mapping, signal processing, adaptive control of engineering systems, and decision and pricing problems in financial markets. The broader implications of the research include (i) direct applications in engineering, finance, and genetics where mapping can be the first step towards better diagnostics or treatment of a disease or towards improving plant or animal stock, and (ii) training the next generation of scientists by involving graduate students in all phases of the research.