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Spatiotemporal Multi-Resolution Approximations for Analyzing Global Environmental Data
arXiv - CS - Distributed, Parallel, and Cluster Computing Pub Date : 2020-06-30 , DOI: arxiv-2006.16606
Marius Appel and Edzer Pebesma

Technological developments and open data policies have made large, global environmental datasets accessible to everyone. For analysing such datasets, including spatiotemporal correlations using traditional models based on Gaussian processes does not scale with data volume and requires strong assumptions about stationarity, separability, and distance measures of covariance functions that are often unrealistic for global data. Only very few modeling approaches suitably model spatiotemporal correlations while addressing both computational scalability as well as flexible covariance models. In this paper, we provide an extension to the multi-resolution approximation (MRA) approach for spatiotemporal modeling of global datasets. MRA has been shown to be computationally scalable in distributed computing environments and allows for integrating arbitrary user-defined covariance functions. Our extension adds a spatiotemporal partitioning, and fitting of complex covariance models including nonstationarity with kernel convolutions and spherical distances. We evaluate the effect of the MRA parameters on estimation and spatiotemporal prediction using simulated data, where computation times reduced around two orders of magnitude with an increase of the root-mean-square prediction error of around five percent. This allows for trading off computation times against prediction errors, and we derive a practical strategy for selecting the MRA parameters. We demonstrate how the approach can be practically used for analyzing daily sea surface temperature and precipitation data on global scale and compare models with different complexities in the covariance function.

中文翻译:

用于分析全球环境数据的时空多分辨率近似值

技术发展和开放数据政策使每个人都可以访问大型全球环境数据集。对于分析此类数据集,包括使用基于高斯过程的传统模型的时空相关性不随数据量而扩展,并且需要对协方差函数的平稳性、可分离性和距离度量进行强有力的假设,这对于全局数据通常是不切实际的。只有极少数建模方法可以在解决计算可扩展性和灵活的协方差模型的同时适当地对时空相关性进行建模。在本文中,我们为全球数据集的时空建模提供了多分辨率逼近 (MRA) 方法的扩展。MRA 已被证明在分布式计算环境中具有计算可扩展性,并允许集成任意用户定义的协方差函数。我们的扩展添加了时空分区,以及复杂协方差模型的拟合,包括具有内核卷积和球面距离的非平稳性。我们使用模拟数据评估 MRA 参数对估计和时空预测的影响,其中计算时间减少了大约两个数量级,均方根预测误差增加了大约 5%。这允许在计算时间与预测误差之间进行权衡,并且我们推导出了选择 MRA 参数的实用策略。
更新日期:2020-07-01
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