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

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  • Song, Hae-Ryoung
  • Fuentes, Montserrat
  • Ghosh, Sujit

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.

Suggested Citation

  • Song, Hae-Ryoung & Fuentes, Montserrat & Ghosh, Sujit, 2008. "A comparative study of Gaussian geostatistical models and Gaussian Markov random field models," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1681-1697, September.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:8:p:1681-1697
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    1. Daniel A. Griffith & Ferenc Csillag, 1993. "Exploring Relationships Between Semi‐Variogram And Spatial Autoregressive Models," Papers in Regional Science, Wiley Blackwell, vol. 72(3), pages 283-295, July.
    2. Julian Besag & Jeremy York & Annie Mollié, 1991. "Bayesian image restoration, with two applications in spatial statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 1-20, March.
    3. Montserrat Fuentes & Hae-Ryoung Song & Sujit K. Ghosh & David M. Holland & Jerry M. Davis, 2006. "Spatial Association between Speciated Fine Particles and Mortality," Biometrics, The International Biometric Society, vol. 62(3), pages 855-863, September.
    4. Hååvard Rue & Hååkon Tjelmeland, 2002. "Fitting Gaussian Markov Random Fields to Gaussian Fields," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 31-49, March.
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    Cited by:

    1. Verzelen, Nicolas, 2010. "Data-driven neighborhood selection of a Gaussian field," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1355-1371, May.
    2. Herbei, Radu & Berry Lyons, W. & Laybourn-Parry, Johanna & Gardner, Christopher & Priscu, John C. & McKnight, Diane M., 2010. "Physiochemical properties influencing biomass abundance and primary production in Lake Hoare, Antarctica," Ecological Modelling, Elsevier, vol. 221(8), pages 1184-1193.
    3. White, Gentry & Ghosh, Sujit K., 2009. "A stochastic neighborhood conditional autoregressive model for spatial data," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3033-3046, June.
    4. Angela Ferretti & L. Ippoliti & P. Valentini & R. J. Bhansali, 2023. "Long memory conditional random fields on regular lattices," Environmetrics, John Wiley & Sons, Ltd., vol. 34(5), August.
    5. I. Gede Nyoman Mindra Jaya & Henk Folmer, 2022. "Spatiotemporal high-resolution prediction and mapping: methodology and application to dengue disease," Journal of Geographical Systems, Springer, vol. 24(4), pages 527-581, October.
    6. Bolin, David & Lindgren, Finn, 2013. "A comparison between Markov approximations and other methods for large spatial data sets," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 7-21.

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    91B76 86A32 62H11 91D72 60J20;

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