The SPDE approach for Gaussian and non-Gaussian fields: 10 years and still running
Embargo End Date:
KAUST DepartmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
Preprint Posting Date2021-11-01
Embargo End Date2024-01-09
Permanent link to this recordhttp://hdl.handle.net/10754/673096
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AbstractGaussian processes and random fields have a long history, covering multiple approaches to representing spatial and spatio-temporal dependence structures, such as covariance functions, spectral representations, reproducing kernel Hilbert spaces, and graph based models. This article describes how the stochastic partial differential equation approach to generalising Matérn covariance models via Hilbert space projections connects with several of these approaches, with each connection being useful in different situations. In addition to an overview of the main ideas, some important extensions, theory, applications, and other recent developments are discussed. The methods include both Markovian and non-Markovian models, non-Gaussian random fields, non-stationary fields and space-time fields on arbitrary manifolds, and practical computational considerations.
CitationLindgren, F., Bolin, D., & Rue, H. (2022). The SPDE approach for Gaussian and non-Gaussian fields: 10 years and still running. Spatial Statistics, 100599. doi:10.1016/j.spasta.2022.100599
SponsorsAs part of the EUSTACE project, Finn Lindgren received funding from the European Union’s “Horizon 2020 Programme for Research and Innovation”, under Grant Agreement no 640171.