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18 February 2025
 
  » arxiv » 2301.01372

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Spatially Varying Anisotropy for Gaussian Random Fields in Three-Dimensional Space
Martin Outzen Berild ; Geir-Arne Fuglstad ;
Date 3 Jan 2023
AbstractIsotropic covariance structures can be unreasonable for phenomena in three-dimensional spaces. We construct a class of non-stationary anisotropic Gaussian random fields (GRFs) in three dimensions through stochastic partial differential equations allowing for Gaussian Markov random field approximations. The class is proven in a simulation study where we explore the amount of data required to estimate these models. Then, we apply it to an ocean mass outside Trondheim, Norway, based on simulations from a numerical ocean model. And our model outperforms a stationary anisotropic GRF on predictions using in-situ measurements collected with an autonomous underwater vehicle.
Source arXiv, 2301.01372
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