Fast kriging of large data sets with Gaussian Markov random fields

Spatial data sets are analysed in many scientific disciplines. Kriging, i.e. minimum mean squared error linear prediction, is probably the most widely used method of spatial prediction. Computation time and memory requirement can be an obstacle for kriging for data sets with many observations. Calculations are accelerated and memory requirements decreased by using a Gaussian Markov random field on a lattice as an approximation of a Gaussian field. The algorithms are well suited also for nonlattice data when exploiting a bilinear interpolation at nonlattice locations.