Iterated filtering: New theory, algorithms and applications

迭代过滤：新理论、算法和应用

• 批准号: 1308919
• 负责人: Edward Ionides
• 金额: $ 10万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1308919&HistoricalAwards=false
• 关键词: Iterated; filtering; New; theory; algorithms

Partially observed Markov process models provide a general framework for formulating and answering questions about dynamic systems. Evaluation of the likelihood for these models can be formulated as a filtering problem. Iterated filtering algorithms carry out repeated sequential Monte Carlo filtering operations to maximize the likelihood. Current theory for iterated filtering justifies the parameter update at each iteration via a stochastic approximation to the first derivative of the log likelihood. Our new approach to iterated filtering theory and methodology draws on similarities with data cloning (i.e., methods where Markov chain Monte Carlo algorithms are applied to multiple copies of the data to provide likelihood-based inference). The relationship with iterated filtering is that each filtering iteration is analogous to creating a new clone of the data. This new theoretical perspective leads to novel novel algorithms. In the context of the previous stochastic approximation theory of iterated filtering, the new algorithms behave as though the intractable second derivative of the likelihood were known. Indeed, the proposed algorithm generates an estimate of the Fisher information as a bi-product. Preliminary results, on a simple ecological model and on a challenging inference problem arising from fitting a malaria transmission model to time series data, show that a new iterated filtering algorithm out-performs previous methods. As well as advancing methodological capabilities for time series analysis via mechanistic models, the investigators will develop applications to two other related classes of statistical problems: longitudinal data analysis via mechanistic models, and inference for complex dynamic data structures. As concrete examples, the investigators will study the use of iterated filtering techniques for (i) relating pathogen genetic sequence data to HIV transmission models; (ii) using longitudinal data to inform stochastic dynamic models of sexual behaviors related to HIV transmission; (iii) inference via summary statistics and pseudo likelihood criteria, with an application to partially observed dynamic network models.Many scientific challenges involve the study of nonlinear stochastic dynamic systems about which only noisy or incomplete measurements are available. Except when the system is small, state-of-the-art statistical methods are required to make efficient use of available data and to provide modeling flexibility that promotes model criticism. The novel iterated filtering algorithms developed by the investigators will be used to study disease transmission systems with the goal of informing policy for the detection, control and potential eradication of infectious diseases. The PI is already engaged in the interface between statistical methodology development, epidemiology and public policy. The proposed research will directly benefit understanding of malaria and HIV transmission, but will also provide methodological tools and case studies relevant to other disease systems. More broadly, the methodology developed will be applicable to inference problems for dynamic systems arising throughout the biological, physical, social, health and engineering sciences. Open source software for all the methodology developed will be included in the R package {pomp} (http://cran.r-project.org/web/packages/pomp) for which the PI is a co-developer. Advances in iterated filtering methodology will be disseminated as part of the PIs ongoing agenda to spread the use of formal statistic methods for partially observed dynamic systems.

部分观测马尔可夫过程模型提供了一个一般框架，制定和回答有关动态系统的问题。这些模型的可能性评估可以用公式表示为过滤问题。迭代滤波算法执行重复的顺序蒙特卡罗滤波操作以最大化可能性。迭代滤波的当前理论证明在每次迭代时通过对对数似然的一阶导数的随机近似来更新参数是合理的。我们迭代过滤理论和方法的新方法借鉴了与数据克隆的相似之处（即，将马尔可夫链蒙特卡罗算法应用于数据的多个副本以提供基于可能性的推断的方法）。与迭代过滤的关系是，每次过滤迭代类似于创建数据的新克隆。这种新的理论视角导致了新颖的算法。在以前的随机近似理论的迭代滤波的背景下，新的算法表现得好像棘手的二阶导数的可能性是已知的。事实上，所提出的算法生成的Fisher信息作为一个双产品的估计。初步结果表明，一个简单的生态模型和一个具有挑战性的推理问题所产生的拟合疟疾传播模型的时间序列数据，一个新的迭代过滤算法优于以前的方法。除了通过机械模型提高时间序列分析的方法能力外，研究人员还将开发其他两类相关统计问题的应用程序：通过机械模型进行纵向数据分析，以及复杂动态数据结构的推理。作为具体的例子，研究人员将研究迭代过滤技术的使用：（i）将病原体基因序列数据与艾滋病毒传播模型联系起来;（ii）使用纵向数据为与艾滋病毒传播有关的性行为的随机动态模型提供信息;（iii）通过汇总统计和伪似然准则的推断，应用于部分可观测的动态网络模型。许多科学挑战涉及对只有噪声或不完整测量可用的非线性随机动态系统的研究。除非系统很小，否则需要最先进的统计方法来有效利用可用数据，并提供建模灵活性，以促进模型批评。研究人员开发的新型迭代过滤算法将用于研究疾病传播系统，目的是为传染病的检测、控制和潜在根除提供信息。PI已经参与了统计方法开发、流行病学和公共政策之间的接口。拟议的研究将直接有助于了解疟疾和艾滋病毒的传播，但也将提供与其他疾病系统相关的方法工具和案例研究。更广泛地说，开发的方法将适用于整个生物，物理，社会，健康和工程科学中出现的动态系统的推理问题。所开发的所有方法的开放源码软件将被纳入R软件包{pomp}（http：//cran.r-project.org/web/packages/pomp），PI是该软件包的共同开发者。迭代过滤方法的进展将作为PI正在进行的议程的一部分进行传播，以推广使用部分观测动态系统的正式统计方法。