A new mixture copula model for spatially correlated multiple variables with an environmental application

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

Multivariate anisotropic spatial modelling and sampling design using copulas

This thesis presents novel copula-based spatial models to improve the accuracy of predictions for spatial variables with multivariate and anisotropic relationships. These models are utilised to develop more effective sampling design frameworks, which can benefit industries modelling and analysing data measured over space. The methods presented in this research have broad applicability, such as to the fields of geology, meteorology, geochemistry, and forestry, and can lead to more informed management decisions while reducing field sampling costs