A McKean optimal transportation perspective on Feynman-Kac formulae with application to data assimilation
A McKean optimal transportation perspective on Feynman-Kac formulae with application to data assimilation
复制标题
Feynman-Kac 公式的 McKean 最优运输视角及其在数据同化中的应用
DOI：
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复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
S. Reich
中科院分区：
文献类型：
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作者：
Yuan Cheng;S. Reich
数据同化是将数学模型与观测数据相结合的任务。从数学的角度来看，数据同化导致贝叶斯推理问题，可以用费曼-卡茨公式表示。本文重点讨论了许多数据同化问题的顺序性质及其在蒙特卡罗方法中的数值实现。我们演示了顺序数据同化如何被解释为时间相关的马尔可夫过程，这通常被称为费曼-卡茨公式的麦基恩方法。结果表明，McKean方法与随机变量和最优运输的耦合有着非常自然的联系。这个链接允许人们提出新的顺序蒙特卡罗方法/粒子滤波器。结合局部化，这些新算法有可能打破维度的诅咒，这阻碍了粒子滤波器在空间扩展系统中的应用。
Data assimilation is the task of combining mathematical models with observational data. From a mathematical perspective data assimilation leads to Bayesian inference problems which can be formulated in terms of Feynman-Kac formulae. In this paper we focus on the sequential nature of many data assimilation problems and their numerical implementation in form of Monte Carlo methods. We demonstrate how sequential data assimilation can be interpreted as time-dependent Markov processes, which is often referred to as the McKean approach to Feynman-Kac formulae. It is shown that the McKean approach has very natural links to coupling of random variables and optimal transportation. This link allows one to propose novel sequential Monte Carlo methods/particle filters. In combination with localization these novel algorithms have the potential of beating the curse of dimensionality, which has prevented particle filters from being applied to spatially extended systems.
DOI：
10.1364/josaa.20.001434
发表时间：
2003-07-01
影响因子：
1.9
作者：
Lee, TS;Mumford, D
通讯作者：
Mumford, D
影响因子：
1.2
作者：
A. Beskos;D. Crisan;A. Jasra;N. Whiteley
通讯作者：
A. Beskos;D. Crisan;A. Jasra;N. Whiteley
影响因子：
4
作者：
Livings, David M.;Dance, Sarah L.;Nichols, Nancy K.
通讯作者：
Nichols, Nancy K.