Statistical Methodology and Applications to Genetics, Engineering and Economics

在基因图谱、脑图谱、生物信息学和天文学中搜索参数集以在噪声背景中定位一个或多个信号是一种常见的方法。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。这项研究发展了一种统一的分析方法来评估这些跨越边界的概率，并发展了重要抽样和序贯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参数随时间变化的时间序列模型和随机动力系统中的估计和预测问题。虽然在实际中参数的突然变化通常很少发生，但未知的发生时间已经导致文献中贝叶斯估计器和预报器的复杂性令人望而却步。通过使用并行递归算法，将变点检测中的一些新思想与经验贝叶斯方法相结合，提出了一种渐近有效的估计和预测方案，该方案具有可控的复杂性。这项研究的一个目的是在一般状态空间上发展一种有效的隐马尔可夫模型参数估计、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经济学时间序列和随机优化问题。这项研究的重要目标是发展统计方法，用于基因图谱、信号处理、工程系统的自适应控制以及金融市场的决策和定价问题。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，其中作图可以是迈向更好的疾病诊断或治疗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.