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Approximate Bayesian inference in spatial GLMM with skew normal latent variables

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  • Hosseini, Fatemeh
  • Eidsvik, Jo
  • Mohammadzadeh, Mohsen
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    Abstract

    Spatial generalized linear mixed models are common in applied statistics. Most users are satisfied using a Gaussian distribution for the spatial latent variables in this model, but it is unclear whether the Gaussian assumption holds. Wrong Gaussian assumptions cause bias in the parameter estimates and affect the accuracy of spatial predictions. Thus, there is a need for more flexible priors for the latent variables, and to perform efficient inference and spatial prediction in the resulting models. In this paper we use a skew normal prior distribution for the spatial latent variables. We propose new approximate Bayesian methods for the inference and spatial prediction in this model. A key ingredient in our approximations is using the closed skew normal distribution to approximate the full conditional for the latent variables. Our approximate inference and spatial prediction methods are fast and deterministic, using no sampling based strategies. The results indicate that the skew normal prior model can give better predictions than the normal model, while avoiding overfitting.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 55 (2011)
    Issue (Month): 4 (April)
    Pages: 1791-1806

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    Handle: RePEc:eee:csdana:v:55:y:2011:i:4:p:1791-1806

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Approximate Bayesian inference Closed skew normal distribution Geostatistics Latent variables MCMC Skew normal distribution Spatial generalized linear mixed model;

    References

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    1. Quinn McNemar, 1947. "Note on the sampling error of the difference between correlated proportions or percentages," Psychometrika, Springer, vol. 12(2), pages 153-157, June.
    2. Kim, Ji-Hyun, 2009. "Estimating classification error rate: Repeated cross-validation, repeated hold-out and bootstrap," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 53(11), pages 3735-3745, September.
    3. Komárek, Arnost & Lesaffre, Emmanuel, 2008. "Generalized linear mixed model with a penalized Gaussian mixture as a random effects distribution," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 52(7), pages 3441-3458, March.
    4. Varin, Cristiano & Host, Gudmund & Skare, Oivind, 2005. "Pairwise likelihood inference in spatial generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 49(4), pages 1173-1191, June.
    5. Jo Eidsvik & Sara Martino & H�Vard Rue, 2009. "Approximate Bayesian Inference in Spatial Generalized Linear Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 1-22.
    6. Ainsworth, L.M. & Dean, C.B., 2006. "Approximate inference for disease mapping," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 50(10), pages 2552-2570, June.
    7. H�vard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392.
    8. Gelfand, Alan E. & Kottas, Athanasios & MacEachern, Steven N., 2005. "Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 100, pages 1021-1035, September.
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    Cited by:
    1. 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, Elsevier, vol. 55(4), pages 1748-1759, April.
    2. Martins, Thiago G. & Simpson, Daniel & Lindgren, Finn & Rue, HÃ¥vard, 2013. "Bayesian computing with INLA: New features," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 67(C), pages 68-83.

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