Non-Gaussian Mat\'ern fields with an application to precipitation modeling

The recently proposed non-Gaussian Mat\'{e}rn random field models, generated through Stochastic Partial differential equations (SPDEs), are extended by considering the class of Generalized Hyperbolic processes as noise forcings. The models are also extended to the standard geostatistical setting where irregularly spaced observations are modeled using measurement errors and covariates. A maximum likelihood estimation technique based on the Monte Carlo Expectation Maximization (MCEM) algorithm is presented, and it is shown how the model can be used to do predictions at unobserved locations. Finally, an application to precipitation data over the United States for two month in 1997 is presented, and the performance of the non-Gaussian models is compared with standard Gaussian and transformed Gaussian models through cross-validation.