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Statistical Modeling for Spatio-Temporal Data From Stochastic Convection-Diffusion Processes
Journal of the American Statistical Association ( IF 3.7 ) Pub Date : 2021-02-03 , DOI: 10.1080/01621459.2020.1863223
Xiao Liu 1 , Kyongmin Yeo 2 , Siyuan Lu 2
Affiliation  

Abstract

This article proposes a physical-statistical modeling approach for spatio-temporal data arising from a class of stochastic convection-diffusion processes. Such processes are widely found in scientific and engineering applications where fundamental physics imposes critical constraints on how data can be modeled and how models should be interpreted. The idea of spectrum decomposition is employed to approximate a physical spatio-temporal process by the linear combination of spatial basis functions and a multivariate random process of spectral coefficients. Unlike existing approaches assuming spatially and temporally invariant convection-diffusion, this article considers a more general scenario with spatially varying convection-diffusion and nonzero-mean source-sink. As a result, the temporal dynamics of spectral coefficients is coupled with each other, which can be interpreted as the nonlinear energy redistribution across multiple scales from the perspective of physics. Because of the spatially varying convection-diffusion, the space-time covariance is nonstationary in space. The theoretical results are integrated into a hierarchical dynamical spatio-temporal model. The connection is established between the proposed model and the existing models based on integro-difference equations. Computational efficiency and scalability are also investigated to make the proposed approach practical. The advantages of the proposed methodology are demonstrated by numerical examples, a case study, and comprehensive comparison studies. Computer code is available on GitHub. Supplementary materials for this article are available online.



中文翻译:

来自随机对流扩散过程的时空数据的统计建模

摘要

本文针对一类随机对流-扩散过程产生的时空数据提出了一种物理统计建模方法。这样的过程在科学和工程应用中广泛存在,其中基础物理学对如何建模数据以及如何解释模型施加了严格的限制。采用频谱分解的思想,通过空间基函数的线性组合和频谱系数的多元随机过程来逼近物理时空过程。与假设空间和时间不变的对流扩散的现有方法不同,本文考虑了具有空间变化的对流扩散和非零均值源汇的更一般的场景。因此,光谱系数的时间动态是相互耦合的,从物理学的角度可以解释为跨多个尺度的非线性能量重新分布。由于空间变化的对流扩散,时空协方差在空间中是非平稳的。理论结果被整合到一个层次化的动态时空模型中。所提出的模型与基于积分差分方程的现有模型之间建立了联系。还研究了计算效率和可扩展性,以使所提出的方法实用。通过数值示例、案例研究和综合比较研究证明了所提出方法的优点。计算机代码可在 GitHub 上获得。本文的补充材料可在线获取。从物理学的角度来看,这可以解释为跨多个尺度的非线性能量重新分布。由于空间变化的对流扩散,时空协方差在空间中是非平稳的。理论结果被整合到一个层次化的动态时空模型中。所提出的模型与基于积分差分方程的现有模型之间建立了联系。还研究了计算效率和可扩展性,以使所提出的方法实用。通过数值示例、案例研究和综合比较研究证明了所提出方法的优点。计算机代码可在 GitHub 上获得。本文的补充材料可在线获取。从物理学的角度来看,这可以解释为跨多个尺度的非线性能量重新分布。由于空间变化的对流扩散,时空协方差在空间中是非平稳的。理论结果被整合到一个层次化的动态时空模型中。所提出的模型与基于积分差分方程的现有模型之间建立了联系。还研究了计算效率和可扩展性,以使所提出的方法实用。通过数值示例、案例研究和综合比较研究证明了所提出方法的优点。计算机代码可在 GitHub 上获得。本文的补充材料可在线获取。

更新日期:2021-02-03
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