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

TL;DR

This paper extends non-Gaussian Matérn random field models using Generalized Hyperbolic processes, applies them to precipitation data, and compares their predictive performance with Gaussian models.

Contribution

It introduces non-Gaussian Matérn models with hyperbolic noise, extends them to irregular data, and develops a Monte Carlo EM estimation method for spatial prediction.

Findings

Non-Gaussian models outperform Gaussian models in precipitation prediction.

The MCEM algorithm effectively estimates model parameters.

Non-Gaussian models provide better fit and uncertainty quantification.

Abstract

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.