The Rational SPDE Approach for Gaussian Random Fields With General Smoothness
Journal article, 2020

A popular approach for modeling and inference in spatial statistics is to represent Gaussian random fields as solutions to stochastic partial differential equations (SPDEs) of the form , where is Gaussian white noise, L is a second-order differential operator, and is a parameter that determines the smoothness of u. However, this approach has been limited to the case , which excludes several important models and makes it necessary to keep beta fixed during inference. We propose a new method, the rational SPDE approach, which in spatial dimension is applicable for any , and thus remedies the mentioned limitation. The presented scheme combines a finite element discretization with a rational approximation of the function to approximate u. For the resulting approximation, an explicit rate of convergence to u in mean-square sense is derived. Furthermore, we show that our method has the same computational benefits as in the restricted case . Several numerical experiments and a statistical application are used to illustrate the accuracy of the method, and to show that it facilitates likelihood-based inference for all model parameters including beta. for this article are available online.

Stochastic partial differential equations

Nonstationary Gaussian fields

Spatial statistics

Fractional operators

Matern covariances

Author

David Bolin

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Kristin Kirchner

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Journal of Computational and Graphical Statistics

1061-8600 (ISSN) 1537-2715 (eISSN)

Vol. 29 2 274-285

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Control Engineering

DOI

10.1080/10618600.2019.1665537

More information

Latest update

12/15/2020