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Efficient likelihood computations for some multivariate Gaussian Markov random fields

Author

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  • Ippoliti, L.
  • Martin, R.J.
  • Romagnoli, L.

Abstract

Data collected from spatial locations are often multivariate. Gaussian conditional autoregressive (CAR) models, also known as Gaussian Markov random fields, are frequently used to analyze such continuous data, or as models for the parameters of discrete distributions. Two difficulties in Gaussian maximum likelihood estimation are ensuring that the parameter estimates are allowable values, and computing the likelihood efficiently. It is shown here that, for some commonly-used multivariate CAR models, checking for allowable parameter values can be facilitated, and the likelihood can be computed very quickly.

Suggested Citation

  • Ippoliti, L. & Martin, R.J. & Romagnoli, L., 2018. "Efficient likelihood computations for some multivariate Gaussian Markov random fields," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 185-200.
    • Handle: RePEc:eee:jmvana:v:168:y:2018:i:c:p:185-200
    DOI: 10.1016/j.jmva.2018.07.007
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    References listed on IDEAS

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    1. Sain, Stephan R. & Cressie, Noel, 2007. "A spatial model for multivariate lattice data," Journal of Econometrics, Elsevier, vol. 140(1), pages 226-259, September.
    2. Mardia, K. V., 1988. "Multi-dimensional multivariate Gaussian Markov random fields with application to image processing," Journal of Multivariate Analysis, Elsevier, vol. 24(2), pages 265-284, February.
    3. Miguel A. Martinez-Beneito, 2013. "A general modelling framework for multivariate disease mapping," Biometrika, Biometrika Trust, vol. 100(3), pages 539-553.
    4. Xiaoping Jin & Bradley P. Carlin & Sudipto Banerjee, 2005. "Generalized Hierarchical Multivariate CAR Models for Areal Data," Biometrics, The International Biometric Society, vol. 61(4), pages 950-961, December.
    5. Xiaoping Jin & Sudipto Banerjee & Bradley P. Carlin, 2007. "Order‐free co‐regionalized areal data models with application to multiple‐disease mapping," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 817-838, November.
    6. Kim H. & Sun D. & Tsutakawa R.K., 2001. "A Bivariate Bayes Method for Improving the Estimates of Mortality Rates With a Twofold Conditional Autoregressive Model," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1506-1521, December.
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    Cited by:

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    2. 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.

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