Spatial Mixture Copula Model For Multiple Correlated Responses With An Environmental Application

Abstract In environmental monitoring, multiple measurements are often collected at many locations and these measurements depend on each other in complex ways, such as nonlinear dependence. In this research, a novel copula-based geostatistical modelling approach was developed to model multivariate continuous spatial random fields using mixture copulas that captures both spatial and joint dependence of multiple responses over two-dimensional locations. In a bivariate context, the mixture copulas were used to capture the joint spatial dependence of a bivariate random field and the spatial copula of the bivariate random field was constructed as the convex combination of mixture copulas. The proposed model was applied to real forest data and simulated nonlinear data. The performance of the novel method was compared with existing spatial methods, which included a univariate spatial pair-copula model, a multivariate spatial pair-copula model that utilises nonlinear principal component analysis (NLPCA), and conventional kriging. The results show that the proposed model outperforms the existing methods in the interpolation of individual responses and reproduction of their bivariate dependence.