Statistical Methodology and Applications to Genetics, Engineering and Economics

在噪声背景中搜索一个或多个信号位置的参数集出现在基因定位、脑定位、生物信息学和天文学中。解决这些问题的一个重要部分涉及随机场超过高阈值的概率。提出了一种统一的分析方法来评估这些边界跨越概率，并使用重要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时间序列模型和随机动力系统的估计和预测问题，其参数可能随时间变化。虽然在实践中，参数突变通常很少发生，但它们发生的未知时间导致了文献中贝叶斯估计器和预测器的复杂性。利用并行递归算法，结合经验贝叶斯方法在变点检测中的一些新思想，提出了复杂度可控的渐近高效估计和预测方案。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。提出的研究目标是在一般状态空间的隐马尔可夫模型中建立有效的参数估计、滤波和平滑的综合理论。另一个相关的研究方向是金融经济学中的计量时间序列和随机优化问题。该研究的重要目标是开发基因定位、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的统计方法。这项研究的更广泛的影响包括：(i)在工程、金融和遗传学方面的直接应用，在这些领域，绘制地图可以成为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.