Gaussian Processes are powerful tools for modelling spatial data. In this context, a significant amount of modelling focus is placed on specifying the covariance function, which is required to be symmetric and positive definite. Covariance functions have classically been defined and used in Euclidean space. However, as data collected from the globe becomes more prevalent, accounting for Earth's geometry becomes increasingly important. Using Euclidean distance can be suboptimal for these data. We survey the literature for recent developments related to construction of nonstationary covariance functions on spheres, which historically has been a challenging area. We present contributions in this effort by providing three general forms for families of parametric nonstationary covariance functions.

中文翻译：

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球体上的参数非平稳协方差函数

高斯过程是用于建模空间数据的强大工具。在这种情况下，大量的建模重点放在指定协方差函数上，该函数需要是对称的和正定的。协方差函数经典地在欧几里得空间中定义和使用。然而，随着从全球收集的数据变得越来越普遍，说明地球的几何形状变得越来越重要。对于这些数据，使用欧几里得距离可能不是最优的。我们调查了有关在球体上构建非平稳协方差函数的最新进展的文献，这在历史上一直是一个具有挑战性的领域。我们通过为参数非平稳协方差函数族提供三种一般形式来展示这项工作的贡献。