Sampling the posterior: An approach to non-Gaussian data assimilation
Sampling the posterior: An approach to non-Gaussian data assimilation
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DOI：
10.1016/j.physd.2006.06.009
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发表时间：
2007-06-01
影响因子：
4
通讯作者：
Voss, J.
中科院分区：
文献类型：
--
作者：
Apte, A.;Hairer, M.;Voss, J.
本文的观点是，数据同化从根本上说是一个统计问题，这个问题应该在贝叶斯框架。在没有模型误差的情况下，数据同化问题的正确解决方案是找到贝叶斯设置所隐含的后验分布。处理数据同化的方法应根据其探测这种分布的能力来判断。在本文中，我们提出了一系列的技术探测后验分布的基础上，Largevin方程，我们比较这些新技术与现有的methods.When潜在的动力学是确定性的，后验分布是在空间上的初始条件导致在这个空间上的采样问题。当潜在的动态是随机的后验分布是在连续时间路径的空间。写下a。密度和条件的观测，它是可能的，以定义一系列的马尔可夫链蒙特卡罗（MCMC）方法的样本从所需的后验分布，从而解决数据同化问题。MCMC方法的基本组成部分，我们集中在本文中是Langevin方程是遍历的，其不变的措施，给出了所需的分布，在路径空间采样的情况下，这些是随机偏微分方程（SPDEs）。两个例子来显示如何数据同化可以制定一个贝叶斯时尚。第一个是天气预报，第二个是海洋速度场的拉格朗日数据同化。此外，这里概述的贝叶斯方法和常用的卡尔曼滤波器为基础的技术，在实践中普遍存在的关系，进行了讨论。通过两个简单的教学实例，具体说明了贝叶斯抽样在资料同化中的应用。最后，一系列开放的数学和计算问题，所产生的贝叶斯方法，概述。(c)2006 Elsevier B.V保留所有权利。
The viewpoint taken in this paper is that data assimilation is fundamentally a statistical problem and that this problem should be cast in a Bayesian framework. In the absence of model error, the correct solution to the data assimilation problem is to find the posterior distribution implied by this Bayesian setting. Methods for dealing with data assimilation should then be judged by their ability to probe this distribution. In this paper we propose a range of techniques for probing the posterior distribution, based around the Largevin equation; and we compare these new techniques with existing methods.When the underlying dynamics is deterministic, the posterior distribution is on the space of initial conditions leading to a sampling problem over this space. When the underlying dynamics is stochastic the posterior distribution is on the space of continuous time paths. By writing down a. density, and conditioning on observations, it is possible to define a range of Markov Chain Monte Carlo (MCMC) methods which sample from the desired posterior distribution, and thereby solve the data assimilation problem. The basic building-blocks for the MCMC methods that we concentrate on in this paper are Langevin equations which are ergodic and whose invariant measures give the desired distribution; in the case of path space sampling these are stochastic partial differential equations (SPDEs).Two examples are given to show how data assimilation can be formulated in a Bayesian fashion. The first is weather prediction, and the second is Lagrangian data assimilation for oceanic velocity fields. Furthermore the relationship between the Bayesian approach outlined here and the commonly used Kalman filter based techniques, prevalent in practice, is discussed. Two simple pedagogical examples are studied to illustrate the application of Bayesian sampling to data assimilation concretely. Finally a range of open mathematical and computational issues, arising from the Bayesian approach, are outlined. (c) 2006 Elsevier B.V All rights reserved.