Spatial Matérn fields driven by non-Gaussian noise

The article studies non-Gaussian extensions of a recently discovered link between certain Gaussian random fields, expressed as solutions to stochastic partial differential equations (SPDEs), and Gaussian Markov random fields. The focus is on non-Gaussian random fields with Mat\'ern covariance functions, and in particular we show how the SPDE formulation of a Laplace moving average model can be used to obtain an efficient simulation method as well as an accurate parameter estimation technique for the model. This should be seen as a demonstration of how these techniques can be used, and generalizations to more general SPDEs are readily available.