Sparse Approximations of Fractional Matérn Fields. (20th September 2017)

• Record Type: Journal Article
• Authors: Roininen, Lassi; Lasanen, Sari; Orispää, Mikko; Särkkä, Simo
• Is Part Of: Scandinavian journal of statistics. Volume 45:Number 1(2018:Mar.)
• Page Start: 194
• Page End: 216
• Publication Date: 2017-09-20
• Subjects: Gaussian Markov random fields -- stochastic partial differential equations -- fractional order SPDE -- inverse problems -- spatial interpolation; Statistics -- Periodicals; 310
• DOI: 10.1111/sjos.12297
• Languages: English
• ISSNs: 0303-6898

Abstract

Abstract: We consider fast lattice approximation methods for a solution of a certain stochastic non‐local pseudodifferential operator equation. This equation defines a Matérn class random field. We approximate the pseudodifferential operator with truncated Taylor expansion, spectral domain error functional minimization and rounding approximations. This allows us to construct Gaussian Markov random field approximations. We construct lattice approximations with finite‐difference methods. We show that the solutions can be constructed with overdetermined systems of stochastic matrix equations with sparse matrices, and we solve the system of equations with a sparse Cholesky decomposition. We consider convergence of the truncated Taylor approximation by studying band‐limited Matérn fields. We consider the convergence of the discrete approximations to the continuous limits. Finally, we study numerically the accuracy of different approximation methods with an interpolation problem.