Abstract
We provide a method for fast and exact simulation of Gaussian random fields on the sphere having isotropic covariance functions. The method proposed is then extended to Gaussian random fields defined over the sphere cross time and having covariance functions that depend on geodesic distance in space and on temporal separation. The crux of the method is in the use of block circulant matrices obtained working on regular grids defined over longitude and latitude.
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Acknowledgements
The first author was supported by The Danish Council for Independent Research—Natural Sciences, Grant DFF 7014-00074 “Statistics for point processes in space and beyond,” and by the “Centre for Stochastic Geometry and Advanced Bioimaging,” funded by Grant 8721 from the Villum Foundation. Third author was supported by FONDECYT Number 1170290.
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Cuevas, F., Allard, D. & Porcu, E. Fast and exact simulation of Gaussian random fields defined on the sphere cross time. Stat Comput 30, 187–194 (2020). https://doi.org/10.1007/s11222-019-09873-1
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DOI: https://doi.org/10.1007/s11222-019-09873-1