Spatial Interpolation Using Copula-Based Geostatistical Models

It is common practice in geostatistics to use the variogram to describe the spatial dependence structure of the underlying random field. However, the variogram is sensitive to outlying observations and strongly influenced by the marginal distribution of the random field. As an alternative to spatial modeling using the variogram we consider describing the spatial correlation by means of copula functions. We present three methods for performing spatial interpolation using copulas. By exploiting the relationship between bivariate copulas and indicator covariances, the first method performs indicator kriging and disjunctive kriging. As a second method we propose a simple kriging of the rank-transformed data. The third method is a plug-in Bayes predictor, where the predictive distribution is calculated using the conditional copula given the observed data and the model parameters. We show that the latter approach generalizes the frequently applied trans-Gaussian kriging. Finally, we report on the results obtained for the so-called Joker data set from the spatial interpolation comparison SIC2004.