A comparative study of Gaussian geostatistical and Gaussian Markov random field models 1

Abstract

Gaussian geostatistical models (GGMs) and Gaussian Markov random fields (GM-RFs) are two distinct approaches commonly used in modeling point referenced and areal data, respectively. In this work the relations between GMRFs and GGMs are explored based on approximations of GMRFs by GGMs, and vice versa. The pro-posed framework for the comparison of GGMS and GMRFs is based on minimizing the distance between the corresponding spectral density functions. In particular, the Kullback-Leibler discrepancy of spectral densities and the chi-squared distance be-tween spectral densities are used as the metrics for the approximation. The proposed methodology is illustrated using simulation studies. We also apply the methods to a air pollution dataset in California to study the relation between GMRFs and GGMs