A Multi-Resolution Approximation for Massive Spatial Datasets
A Multi-Resolution Approximation for Massive Spatial Datasets
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DOI：
10.1080/01621459.2015.1123632
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发表时间：
2017-01-01
影响因子：
3.7
通讯作者：
Katzfuss, Matthias
中科院分区：
文献类型：
--
作者：
Katzfuss, Matthias
卫星和飞机上的自动传感仪器使人们能够收集大面积空间区域的大量高分辨率空间场观测数据。如果这些数据集能够得到有效利用，它们可以为各种问题提供新的见解。然而，传统的空间统计技术，如克里金法，在计算上不适用于大数据集。我们提出了一个多分辨率近似（M-RA）的高斯过程中观察到的空间不规则位置。M-RA过程被指定为在多个空间分辨率水平上的基函数的线性组合，其可以捕获从非常精细到非常大尺度的空间结构。基函数被自动选择以近似给定的协方差函数，该协方差函数可以是非平稳的。所有涉及M-RA的计算，包括参数推断和预测，对于大规模数据集都是高度可扩展的。重要的是，推理算法也可以并行化，以充分利用大型分布式内存计算环境。在使用模拟数据和大型卫星数据集的比较中，M-RA优于相关的最先进的方法。本文的补充材料可在网上查阅。
Automated sensing instruments on satellites and aircraft have enabled the collection of massive amounts of high-resolution observations of spatial fields over large spatial regions. If these datasets can be efficiently exploited, they can provide new insights on a wide variety of issues. However, traditional spatial-statistical techniques such as kriging are not computationally feasible for big datasets. We propose a multi-resolution approximation (M-RA) of Gaussian processes observed at irregular locations in space. The M-RA process is specified as a linear combination of basis functions at multiple levels of spatial resolution, which can capture spatial structure from very fine to very large scales. The basis functions are automatically chosen to approximate a given covariance function, which can be nonstationary. All computations involving the M-RA, including parameter inference and prediction, are highly scalable for massive datasets. Crucially, the inference algorithms can also be parallelized to take full advantage of large distributed-memory computing environments. In comparisons using simulated data and a large satellite dataset, the M-RA outperforms a related state-of-the-art method. Supplementary materials for this article are available online.