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Spatial Matérn Fields Driven by Non‐Gaussian Noise
Author(s) -
Bolin David
Publication year - 2014
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12046
Subject(s) - mathematics , random field , gaussian random field , gaussian , gaussian noise , covariance , laplace transform , covariance function , focus (optics) , stochastic partial differential equation , statistical physics , gaussian process , partial differential equation , mathematical analysis , algorithm , statistics , physics , optics , quantum mechanics
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 Matérn 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.