Abstract

In modeling spatial processes, a second-order stationarity assumption is often made. However, for spatial data observed on a vast domain, the covariance function often varies over space, leading to a heterogeneous spatial dependence structure, therefore requiring nonstationary modeling. Spatial deformation is one of the main methods for modeling nonstationary processes, assuming the nonstationary process has a stationary counterpart in the deformed space. The estimation of the deformation function poses severe challenges. Here, we introduce a novel approach for nonstationary geostatistical modeling, using space deformation, when a single realization of the spatial process is observed. Our method is based on aligning regional variograms, where warping variability of the distance from each subregion explains the spatial nonstationarity. We propose to use multi-dimensional scaling to map the warped distances to spatial locations. We assess the performance of our new method using multiple simulation studies. Additionally, we illustrate our methodology on precipitation data to estimate the heterogeneous spatial dependence and to perform spatial predictions.

摘要

在对空间过程进行建模时，通常会进行二阶平稳假设。但是，对于在广阔域上观察到的空间数据，协方差函数通常会随空间变化，从而导致异构的空间依赖性结构，因此需要进行非平稳建模。假设非平稳过程在变形空间中具有固定的对应部分，则空间变形是建模非平稳过程的主要方法之一。变形函数的估计提出了严峻的挑战。在此，当观察到空间过程的单个实现时，我们将介绍一种使用空间变形进行非平稳地统计建模的新方法。我们的方法基于对齐区域变异函数，其中到每个子区域的距离的翘曲变异性说明了空间非平稳性。我们建议使用多维缩放将扭曲的距离映射到空间位置。我们使用多个模拟研究来评估新方法的性能。此外，我们举例说明了降水数据的方法，以估算非均质的空间依赖性并进行空间预测。