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

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...