In order to make spatial statistics computationally feasible, we need to forget about the covariance function

Daniel Simpson, Finn Lindgren, Håvard Rue

Research output: Contribution to journalArticleResearchpeer-review

69 Citations (Scopus)


Gaussian random fields (GRFs) are the most common way of modeling structured spatial random effects in spatial statistics. Unfortunately, their high computational cost renders the direct use of GRFs impractical for large problems and approximations are commonly used. In this paper, we compare two approximations to GRFs with Matérn covariance functions: the kernel convolution approximation and the Gaussian Markov random field representation of an associated stochastic partial differential equation. We show that the second approach is a natural way to tackle the problem and is better than methods based on approximating the kernel convolution. Furthermore, we show that kernel methods, as described in the literature, do not work when the random field is not smooth.

Original languageEnglish
Pages (from-to)65-74
Number of pages10
Issue number1
Publication statusPublished - Feb 2012
Externally publishedYes


  • Covariance functions
  • GMRF
  • Kernel methods
  • SPDE

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