论文标题
通过变形对非平稳和非对称多元空间协方差进行建模
Modeling Nonstationary and Asymmetric Multivariate Spatial Covariances via Deformations
论文作者
论文摘要
在建模环境和社会人口统计学过程时，通常使用多元空间统计模型。多元空间协方差的最常用模型同时具有跨构剂的平稳性和对称性，但是在实践中，这些假设很少是可以定位的。在本文中，我们介绍了一种新的且高度灵活的非组织和不对称的多元空间协方差模型，该模型是通过在扭曲的域中建模更简单，更熟悉的固定式和对称的多变量协方差来构建的。受单变量案例的最新发展的启发，我们建议将翘曲功能建模为在深度学习框架中许多简单的注射式翘曲功能的组成。重要的是，通过施工来保证协方差模型的有效性。我们建立了允许跨互相对称性和不对称性的经感的类型，并使用基于可能性的方法来进行计算上的推理。这类新模型的实用性通过两个数据图表显示：一项关于非组织数据的模拟研究和两个不同深度下海洋温度的应用。
Multivariate spatial-statistical models are often used when modeling environmental and socio-demographic processes. The most commonly used models for multivariate spatial covariances assume both stationarity and symmetry for the cross-covariances, but these assumptions are rarely tenable in practice. In this article we introduce a new and highly flexible class of nonstationary and asymmetric multivariate spatial covariance models that are constructed by modeling the simpler and more familiar stationary and symmetric multivariate covariances on a warped domain. Inspired by recent developments in the univariate case, we propose modeling the warping function as a composition of a number of simple injective warping functions in a deep-learning framework. Importantly, covariance-model validity is guaranteed by construction. We establish the types of warpings that allow for cross-covariance symmetry and asymmetry, and we use likelihood-based methods for inference that are computationally efficient. The utility of this new class of models is shown through two data illustrations: a simulation study on nonstationary data and an application on ocean temperatures at two different depths.
