Probabilistic spatial prediction of categorical data using elliptical copulas

This study uses elliptical copulas and transition probabilities for uncertainty modeling of categorical spatial data. It begins by discussing the expressions of the cumulative distribution function and probability density function of two major elliptical copulas: Gaussian copula and t copula. The basic form of spatial copula discriminant function is then derived based on Bayes’ theorem, which consists of three parts: the prior probability, the conditional marginal densities, and the conditional copula density. Finally, three kinds of parameter estimation methods are discussed, including maximum likelihood estimation, inference functions for margins and canonical maximum likelihood (CML). To avoid making assumptions on the form of marginal distributions, the CML approach is adopted in the real-world case study. Results show that the occurrence probability maps generated by these two elliptical copulas are similar to each other. However, the prediction map interpolated by Gaussian copula has a relatively higher classification accuracy than t copula.