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

在对空间过程建模时，通常会做出二阶平稳性假设。然而，对于在广阔域上观察到的空间数据，协方差函数经常随空间变化，导致异质的空间依赖结构，因此需要非平稳建模。空间变形是非平稳过程建模的主要方法之一，假设非平稳过程在变形空间中有静止的对应物。变形函数的估计提出了严峻的挑战。在这里，我们介绍了一种新的非平稳地质统计建模方法，当观察到空间过程的单一实现时，使用空间变形。我们的方法基于对齐区域变异函数，其中与每个子区域的距离的翘曲变异性解释了空间的非平稳性。我们建议使用多维缩放来将扭曲距离映射到空间位置。我们使用多个模拟研究来评估我们的新方法的性能。此外，我们说明了我们的降水数据方法，以估计异质空间依赖性并执行空间预测。