Rapid developments in satellite remote-sensing technology have enabled the collection of geospatial data on a global scale, hence increasing the need for covariance functions that can capture spatial dependence on spherical domains. We propose a general method of constructing nonstationary, locally anisotropic covariance functions on the sphere based on covariance functions in R^3. We also provide theorems that specify the conditions under which the resulting correlation function is isotropic or axially symmetric. For large datasets on the sphere commonly seen in modern applications, the Vecchia approximation is used to achieve higher scalability on statistical inference. The importance of flexible covariance structures is demonstrated numerically using simulated data and a precipitation dataset.
翻译:卫星遥感技术的迅速发展使得能够在全球范围内收集地理空间数据,从而增加了对可捕捉对球域空间依赖性的共变量功能的需要,我们提出了一个基于R ⁇ 3中的共变量功能在球体上构建非静止、局部厌异共变量功能的一般方法。我们还提供了一些理论,以具体说明由此产生的相关功能在何种条件下是异向或反向对称。对于在现代应用中常见的球体上的大型数据集,使用Vecchia近比值来提高统计推论的可伸缩性。使用模拟数据和降水数据集从数字上表明了灵活共变量结构的重要性。