2013/04/25 by Geir‐Arne Fuglstad, Fuglstad, Geir-Arne, Finn Lindgren +5 · 4 citations
Economics, Econometrics and Finance · Environmental Science · #Economic and Environmental Valuation #FOS: Computer and information sciences #Methodology (stat.ME) #Soil Geostatistics and Mapping #Spatial and Panel Data Analysis
paper · pdf · doi:10.48550/arxiv.1304.6949
openalex publication_date 2013/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Gaussian random fields (GRFs) constitute an important part of spatial\nmodelling, but can be computationally infeasible for general covariance\nstructures. An efficient approach is to specify GRFs via stochastic partial\ndifferential equations (SPDEs) and derive Gaussian Markov random field (GMRF)\napproximations of the solutions. We consider the construction of a class of\nnon-stationary GRFs with varying local anisotropy, where the local anisotropy\nis introduced by allowing the coefficients in the SPDE to vary with position.\nThis is done by using a form of diffusion equation driven by Gaussian white\nnoise with a spatially varying diffusion matrix. This allows for the\nintroduction of parameters that control the GRF by parametrizing the diffusion\nmatrix. These parameters and the GRF may be considered to be part of a\nhierarchical model and the parameters estimated in a Bayesian framework. The\nresults show that the use of an SPDE with non-constant coefficients is a\npromising way of creating non-stationary spatial GMRFs that allow for physical\ninterpretability of the parameters, although there are several remaining\nchallenges that would need to be solved before these models can be put to\ngeneral practical use.\n