Inference for dynamical systems

动力系统的推理

• 批准号: 0805533
• 负责人: Edward Ionides
• 金额: $ 20万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-06-01 至 2012-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0805533&HistoricalAwards=false
• 关键词: Inference; dynamical; systems; Inference; dynamical; systems

The starting point of the proposed research is a new algorithm that has recently been shown to make maximum likelihood estimation feasible for previously intractable partially-observed nonlinear stochastic dynamical systems. The algorithm is based on a sequence of filtering operations which converges to a maximum likelihood parameter estimate, and is therefore termed iterated filtering. The availability of iterated filtering methodology opens up many possibilities for developing new classes of stochastic dynamic models for use as data analysis tools. One component of the proposed research program is development of a new class of Markov chain models appropriate for biological systems, consisting of interacting Poisson processes whose rates are subject to white noise. Another goal is to broaden the class of dynamical systems for which likelihood based inference is practical, via increased theoretical understanding of iterated filtering. Specifically, a new theoretical framework for iterated filtering will be developed, based on identifying a relationship with previously studied stochastic approximation techniques. Techniques of averaging over iterations and searching over a sequence of random directions, which have good theoretical and practical properties for other stochastic approximation methods, are expected to be applicable to iterated filtering. The third component of the proposed research is to demonstrate the role of the new methodology in facilitating a novel and scientifically relevant data analysis of malaria transmission. Infectious diseases pose challenging and important questions which have long been a testing ground for inference methodology for dynamical systems. Carrying out data analysis via new classes of continuous time dynamic models will require handling novel situations for diagnosing goodness of fit, and appropriate techniques will be developed and demonstrated.Nonlinear stochastic dynamical models are widely used to study systems occurring throughout the sciences and engineering. Such models are natural to formulate and can be analyzed mathematically and numerically. Despite decades of work, carrying out statistical inference for nonlinear dynamical models remains a challenging and important problem. Recently, progress has been made possible by new methodology taking advantage of increasing computational resources. Continued progress requires building theoretical understanding of successfully demonstrated methodology, developing new methodologies, and showing how these advances can be used to further scientific knowledge about dynamical systems of interest. Recent motivations for understanding infectious disease dynamics include the threats posed by emerging diseases (HIV/AIDS, SARS, pandemic influenza), re-emerging diseases (malaria, tuberculosis) and bioterrorism. Inference for dynamical systems arises in many diverse fields, including economics, neuroscience, chemical engineering, signal processing, and molecular biochemistry. The field of Statistics forms a natural bridge to make methodological advances available to a wider research community.

拟议的研究的起点是一种新算法，最近已证明该算法使得对先前棘手的部分观察到的非线性非线性随机动力学系统的最大似然估计可行。 该算法基于一系列过滤操作，该序列将收敛到最大似然参数估计，因此称为迭代过滤。 迭代过滤方法的可用性为开发新类别的随机动态模型以用作数据分析工具开辟了许多可能性。 拟议的研究计划的一个组成部分是开发适合生物系统的新型马尔可夫链模型，该模型包括相互作用的泊松工艺，其比率易于白噪声。另一个目标是通过增加对迭代过滤的理论理解，扩大基于可能性的推理的动力学系统类别。 具体而言，基于与先前研究的随机近似技术的关系，将开发用于迭代过滤的新理论框架。预计在一系列随机方向上进行平均迭代和搜索的技术，这些方向具有良好的理论和实际属性，用于其他随机近似方法，预计将适用于迭代过滤。 拟议研究的第三个组成部分是证明新方法在促进疟疾传播的新型且科学相关的数据分析中的作用。传染病提出了具有挑战性的重要问题，这些问题长期以来一直是动态系统推理方法的测试基础。 通过新类别的连续时间动态模型进行数据分析将需要处理新的情况以诊断拟合良好，并将开发和演示适当的技术。NonlinelareAr随机动力学模型被广泛用于研究整个科学和工程中发生的系统。 这样的模型是自然的，可以在数学上和数字上进行分析。尽管工作了数十年，但对非线性动力学模型进行统计推断仍然是一个具有挑战性且重要的问题。 最近，通过利用增加计算资源的新方法，已经取得了进步。 持续的进步需要建立对成功证明方法论，开发新方法的理论理解，并展示如何将这些进步用于进一步有关感兴趣动态系统的科学知识。了解传染病动态的最新动机包括新兴疾病（HIV/AIDS，SARS，大流行性流感）构成的威胁，重新出现疾病（疟疾，结核病）和生物恐怖主义。动态系统的推断是在许多不同领域中出现的，包括经济学，神经科学，化学工程，信号处理和分子生物化学。 统计领域构成了自然桥梁，以使更广泛的研究社区获得方法论进步。