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Approximate Bayesian Inference in Spatial Generalized Linear Mixed Models

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  • JO EIDSVIK
  • SARA MARTINO
  • H�VARD RUE
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    Abstract

    In this paper we propose fast approximate methods for computing posterior marginals in spatial generalized linear mixed models. We consider the common geostatistical case with a high dimensional latent spatial variable and observations at known registration sites. The methods of inference are deterministic, using no simulation-based inference. The first proposed approximation is fast to compute and is 'practically sufficient', meaning that results do not show any bias or dispersion effects that might affect decision making. Our second approximation, an improvement of the first version, is 'practically exact', meaning that one would have to run MCMC simulations for very much longer than is typically done to detect any indication of error in the approximate results. For small-count data the approximations are slightly worse, but still very accurate. Our methods are limited to likelihood functions that give unimodal full conditionals for the latent variable. The methods help to expand the future scope of non-Gaussian geostatistical models as illustrated by applications of model choice, outlier detection and sampling design. The approximations take seconds or minutes of CPU time, in sharp contrast to overnight MCMC runs for solving such problems. Copyright (c) 2008 Board of the Foundation of the Scandinavian Journal of Statistics.

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    Bibliographic Info

    Article provided by Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association in its journal Scandinavian Journal of Statistics.

    Volume (Year): 36 (2009)
    Issue (Month): 1 ()
    Pages: 1-22

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    Handle: RePEc:bla:scjsta:v:36:y:2009:i:1:p:1-22

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    Cited by:
    1. Eidsvik, Jo & Finley, Andrew O. & Banerjee, Sudipto & Rue, Håvard, 2012. "Approximate Bayesian inference for large spatial datasets using predictive process models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1362-1380.
    2. Martins, Thiago G. & Simpson, Daniel & Lindgren, Finn & Rue, Håvard, 2013. "Bayesian computing with INLA: New features," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 68-83.
    3. Higgs, Megan Dailey & Hoeting, Jennifer A., 2010. "A clipped latent variable model for spatially correlated ordered categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1999-2011, August.
    4. De Oliveira, Victor, 2013. "Hierarchical Poisson models for spatial count data," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 393-408.
    5. Baghishani, Hossein & Mohammadzadeh, Mohsen, 2011. "A data cloning algorithm for computing maximum likelihood estimates in spatial generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1748-1759, April.
    6. Hosseini, Fatemeh & Eidsvik, Jo & Mohammadzadeh, Mohsen, 2011. "Approximate Bayesian inference in spatial GLMM with skew normal latent variables," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1791-1806, April.

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