School of Mathematical Sciences, Faculty of Science, Queensland University of Technology (QUT), Brisbane, Australia.
QUT Centre for Data Science, Brisbane, Australia.
Sci Rep. 2022 Aug 16;12(1):13867. doi: 10.1038/s41598-022-18007-z.
In environmental monitoring, multiple spatial variables are often sampled at a geographical location that can depend on each other in complex ways, such as non-linear and non-Gaussian spatial dependence. We propose a new mixture copula model that can capture those complex relationships of spatially correlated multiple variables and predict univariate variables while considering the multivariate spatial relationship. The proposed method is demonstrated using an environmental application and compared with three existing methods. Firstly, improvement in the prediction of individual variables by utilising multivariate spatial copula compares to the existing univariate pair copula method. Secondly, performance in prediction by utilising mixture copula in the multivariate spatial copula framework compares with an existing multivariate spatial copula model that uses a non-linear principal component analysis. Lastly, improvement in the prediction of individual variables by utilising the non-linear non-Gaussian multivariate spatial copula model compares to the linear Gaussian multivariate cokriging model. The results show that the proposed spatial mixture copula model outperforms the existing methods in the cross-validation of actual and predicted values at the sampled locations.
在环境监测中，通常在地理位置上对多个空间变量进行采样，这些变量之间的关系可能非常复杂，例如非线性和非正态空间相关性。我们提出了一种新的混合 Copula 模型，可以捕捉到这些具有空间相关性的多变量之间的复杂关系，并在考虑多变量空间关系的情况下预测单变量。该方法通过环境应用进行了演示，并与三种现有方法进行了比较。首先，利用多元空间 Copula 对个体变量进行预测的改进优于现有的单变量对 Copula 方法。其次，在多元空间 Copula 框架中利用混合 Copula 进行预测的性能优于使用非线性主成分分析的现有多元空间 Copula 模型。最后，利用非线性非正态多元空间 Copula 模型对个体变量的预测优于线性正态多元协克里金模型。结果表明，在所采样位置的实际值和预测值的交叉验证中，所提出的空间混合 Copula 模型优于现有方法。
