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A comparative study of Gaussian geostatistical models and Gaussian Markov random field models
Journal article   Open access   Peer reviewed

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

Hae-Ryoung Song, Montserrat Fuentes and Sujit Ghosh
Journal of multivariate analysis, Vol.99(8), pp.1681-1697
09/2008
DOI: 10.1016/j.jmva.2008.01.012
PMCID: PMC2662683
PMID: 19337581
url
https://doi.org/10.1016/j.jmva.2008.01.012View
Published (Version of record) Open Access

Abstract

Gaussian geostatistical models (GGMs) and Gaussian Markov random fields (GMRFs) are two distinct approaches commonly used in spatial models for modeling point-referenced and areal data, respectively. In this paper, the relations between GGMs and GMRFs are explored based on approximations of GMRFs by GGMs, and approximations of GGMs by GMRFs. Two new metrics of approximation are proposed : (i) the Kullback–Leibler discrepancy of spectral densities and (ii) the chi-squared distance between spectral densities. The distances between the spectral density functions of GGMs and GMRFs measured by these metrics are minimized to obtain the approximations of GGMs and GMRFs. The proposed methodologies are validated through several empirical studies. We compare the performance of our approach to other methods based on covariance functions, in terms of the average mean squared prediction error and also the computational time. A spatial analysis of a dataset on PM2.5 collected in California is presented to illustrate the proposed method.

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