Cross-Covariance Functions for Multivariate Geostatistics
Cross-Covariance Functions for Multivariate Geostatistics
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DOI：
10.1214/14-sts487
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发表时间：
2015-05-01
影响因子：
5.7
通讯作者：
Kleiber, William
中科院分区：
文献类型：
--
作者：
Genton, Marc G.;Kleiber, William
在地球物理、生态、环境和气候科学中，多变量连续索引数据集已经变得无处不在，这给科学家和统计学家带来了巨大的分析挑战。多年来，科学家们开发了旨在捕捉单个过程的空间行为的模型；直到最近几十年，对多个过程联合建模才变得司空见惯。关键的困难在于指定互协方差函数，即负责不同变量之间关系的函数。事实上，这些互协方差函数必须选择为与边际协方差函数一致，以使二阶结构总是产生非负定协方差矩阵。我们回顾了建立互协方差模型的主要方法，包括协区域化的线性模型、卷积方法、多元MATRITN方法以及这些方法的非平稳和时空扩展等。此外，我们还包括专门的结构，包括那些为不对称、紧凑支撑和球域而设计的结构，并回顾了物理约束模型。我们举例说明了温度和气压的双变量区域气候模式输出示例以及双变量最低和最高气温观测数据集上的选定模型；我们通过似然值以及交叉验证联合克里格法研究来比较模型。文章最后讨论了一些尚未解决的问题。
Continuously indexed datasets with multiple variables have become ubiquitous in the geophysical, ecological, environmental and climate sciences, and pose substantial analysis challenges to scientists and statisticians. For many years, scientists developed models that aimed at capturing the spatial behavior for an individual process; only within the last few decades has it become commonplace to model multiple processes jointly. The key difficulty is in specifying the cross-covariance function, that is, the function responsible for the relationship between distinct variables. Indeed, these cross-covariance functions must be chosen to be consistent with marginal covariance functions in such a way that the second-order structure always yields a nonnegative definite covariance matrix. We review the main approaches to building cross-covariance models, including the linear model of coregionalization, convolution methods, the multivariate Matern and nonstationary and space time extensions of these among others. We additionally cover specialized constructions, including those designed for asymmetry, compact support and spherical domains, with a review of physics-constrained models. We illustrate select models on a bivariate regional climate model output example for temperature and pressure, along with a bivariate minimum and maximum temperature observational dataset; we compare models by likelihood value as well as via cross-validation co-kriging studies. The article closes with a discussion of unsolved problems.