Sequential Monte Carlo Methods for Computationally Intensive Problems

序贯蒙特卡罗方法为解决复杂的统计推断问题提供了一种通用而有力的工具。本建议的目的是在三个重要领域发展序贯蒙特卡罗技术：多向表的条件推理，群体遗传学中的似然推理和非线性随机系统的自适应控制。在这些应用程序中的一个共同主题是计算的复杂性。 调查员开发有效的建议distributionsand reservation技术，以改善目前的方法，在这三个应用程序。 从这些应用中产生的新理论阐明了与序列蒙特卡罗方法的实现有关的几个基本问题，特别是将高维问题分解为小的组成部分，以便每个组成部分易于处理，并且可以利用问题的序列性质，和选择的建议分布，使其易于抽样和足够接近真正的潜在分布。调查员开发创新的序贯Monte卡洛技术在三个重要领域。 第一个领域是多向列联表的条件推理。这些表格通常来自社会科学和医学科学，包括大型调查数据和具有几个风险因素的分组病例对照数据。第二个领域是群体遗传学中基于可能性的推断，这是由推断新型隐球菌（一种人类严重呼吸道疾病的病原体）的主要致病血清型的关键生物学特征的兴趣所激发的。第三个领域是非线性随机系统的在线辨识与自适应控制。研究者改进了这三种应用中使用的当前方法，并开发了一种系统的理论，为应用顺序蒙特卡洛方法提供了一般策略。 从这些应用中产生的新理论在统计学、科学和其他领域的广泛领域都很有趣。 本研究对博士生参与教育具有重要意义。学生直接在拟议的研究和成果纳入本科和研究生课程。

Sequential Monte Carlo methods provide a versatile and powerful tool forsolving complex statistical inference problems. The objective of thisproposal is to develop sequential Monte Carlo techniques in threeimportant areas: conditional inference on multiway tables, likelihoodinference in population genetics, and adaptive control of nonlinearstochastic systems. A common theme in these applications is computationalcomplexity. The investigator develops efficient proposal distributionsand resampling techniques to improve current methods in these threeapplications. New theories arising from these applications shed light onseveral fundamental issues related to the implementation of sequentialMonte Carlo methods, in particular, the decomposition of a highdimensional problem into small components so that each component is easyto handle and the sequential nature of the problem can be utilized, andthe choice of the proposal distribution so that it is easy to sample andclose enough to the true underlying distribution.The investigator develops innovative sequential Monte Carlo techniques inthree important areas. The first area is conditional inference onmultiway contingency tables. Such tables arise very often from social andmedical sciences, including large survey data and grouped case-controldata with several risk factors. The second area is likelihood-basedinference in population genetics, which is motivated by the interest ininferring key biological characteristics of the major pathogenic serotypesof Cryptococcus neoformans, an agent of serious respiratory disease inhumans. The third area is on-line identification and adaptive control ofnonlinear stochastic systems. The investigator improves the current methodsused in these three applications and develops a systematic theory thatprovides insight into general strategies for applying sequential MonteCarlo methods. New theories arising from these applications are ofinterest across a broad range of areas in statistics, science and beyond. The proposed research has significant impact on education throughinvolvement of Ph.D. students directly in the proposed research andincorporation of results into undergraduate and graduate courses.