论文标题
Riemannian流形的大型数据集的地统计学：无基质方法
Geostatistics for large datasets on Riemannian manifolds: a matrix-free approach
论文作者
论文摘要
在许多环境和气候研究中，大型或非常大的空间（和时空）数据集已成为普遍的位置。这些数据通常收集在非欧几里得空间（例如地球）中，它们通常呈现非静态各向异性。本文提出了一种通用方法，以对紧凑的Riemannian歧管建模高斯随机场（GRF），该歧管弥合了非稳态GRF上现有作品与歧管上的随机字段之间的差距。该方法可以应用于任何光滑的紧凑型歧管，尤其是任何紧凑的表面。通过定义一个解释相关性优先方向的Riemannian度量，我们的方法产生了对域的“局部”变形而产生的“局部各向异性”的解释。我们为参数的估计提供了可扩展的算法，并通过Kriging和模拟能够应对非常大的网格来进行最佳预测。提供了固定和非平稳插图。
Large or very large spatial (and spatio-temporal) datasets have become common place in many environmental and climate studies. These data are often collected in non-Euclidean spaces (such as the planet Earth) and they often present non-stationary anisotropies. This paper proposes a generic approach to model Gaussian Random Fields (GRFs) on compact Riemannian manifolds that bridges the gap between existing works on non-stationary GRFs and random fields on manifolds. This approach can be applied to any smooth compact manifolds, and in particular to any compact surface. By defining a Riemannian metric that accounts for the preferential directions of correlation, our approach yields an interpretation of the ''local anisotropies'' as resulting from ''local'' deformations of the domain. We provide scalable algorithms for the estimation of the parameters and for optimal prediction by kriging and simulation able to tackle very large grids. Stationary and non-stationary illustrations are provided.
