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Fast estimation of spatially dependent temporal vegetation trends using Gaussian Markov random fields

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  • Bolin, David
  • Lindström, Johan
  • Eklundh, Lars
  • Lindgren, Finn

Abstract

There is a need for efficient methods for estimating trends in spatio-temporal Earth Observation data. A suitable model for such data is a space-varying regression model, where the regression coefficients for the spatial locations are dependent. A second order intrinsic Gaussian Markov Random Field prior is used to specify the spatial covariance structure. Model parameters are estimated using the Expectation Maximisation (EM) algorithm, which allows for feasible computation times for relatively large data sets. Results are illustrated with simulated data sets and real vegetation data from the Sahel area in northern Africa. The results indicate a substantial gain in accuracy compared with methods based on independent ordinary least squares regressions for the individual pixels in the data set. Use of the EM algorithm also gives a substantial performance gain over Markov Chain Monte Carlo-based estimation approaches.

Suggested Citation

  • Bolin, David & Lindström, Johan & Eklundh, Lars & Lindgren, Finn, 2009. "Fast estimation of spatially dependent temporal vegetation trends using Gaussian Markov random fields," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2885-2896, June.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:8:p:2885-2896
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    References listed on IDEAS

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    2. Gamerman, Dani & Moreira, Ajax R. B. & Rue, Havard, 2003. "Space-varying regression models: specifications and simulation," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 513-533, March.
    3. R. B. Myneni & C. D. Keeling & C. J. Tucker & G. Asrar & R. R. Nemani, 1997. "Increased plant growth in the northern high latitudes from 1981 to 1991," Nature, Nature, vol. 386(6626), pages 698-702, April.
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    Cited by:

    1. LeSage, James & Banerjee, Sudipto & Fischer, Manfred M. & Congdon, Peter, 2009. "Spatial statistics: Methods, models & computation," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2781-2785, June.
    2. Osafu Augustine Egbon & Omodolapo Somo-Aina & Ezra Gayawan, 2021. "Spatial Weighted Analysis of Malnutrition Among Children in Nigeria: A Bayesian Approach," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(3), pages 495-523, December.
    3. Bolin, David & Wallin, Jonas & Lindgren, Finn, 2019. "Latent Gaussian random field mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 80-93.
    4. Zammit-Mangion, Andrew & Rougier, Jonathan, 2018. "A sparse linear algebra algorithm for fast computation of prediction variances with Gaussian Markov random fields," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 116-130.

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