Interpolation of spatial and spatio-temporal Gaussian fields using Gaussian Markov random fields

This paper considers interpolation on a lattice of covariance-based Gaussian Random Field models (Geostatistics models) using Gaussian Markov Random Fields (GMRFs) (conditional autoregression models). Two methods for estimating the GMRF parameters are considered. One generalises maximum likelihood for complete data, and the other ensures a better correspondence between fitted and theoretical correlations for higher lags. The methods can be used both for spatial and spatio-temporal data. Some different cross-validation methods for model choice are compared. The predictive ability of the GMRF is demonstrated by a simulation study, and an example using a real image is considered.