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A stochastic neighborhood conditional autoregressive model for spatial data

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  • White, Gentry
  • Ghosh, Sujit K.

Abstract

A spatial process observed over a lattice or a set of irregular regions is usually modeled using a conditionally autoregressive (CAR) model. The neighborhoods within a CAR model are generally formed deterministically using the inter-distances or boundaries between the regions. An extension of CAR model is proposed in this article where the selection of the neighborhood depends on unknown parameter(s). This extension is called a Stochastic Neighborhood CAR (SNCAR) model. The resulting model shows flexibility in accurately estimating covariance structures for data generated from a variety of spatial covariance models. Specific examples are illustrated using data generated from some common spatial covariance functions as well as real data concerning radioactive contamination of the soil in Switzerland after the Chernobyl accident.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:8:p:3033-3046
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    References listed on IDEAS

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    1. 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.
    2. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    3. 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.
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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. Guanyu Hu & Yishu Xue & Zhihua Ma, 2020. "Bayesian Clustered Coefficients Regression with Auxiliary Covariates Assistant Random Effects," Papers 2004.12022, arXiv.org, revised Aug 2021.
    3. Rodrigues, E.C. & Assunção, R., 2012. "Bayesian spatial models with a mixture neighborhood structure," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 88-102.

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