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A non-homogeneous skew-Gaussian Bayesian spatial model

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  • Hossein Boojari
  • Majid Khaledi
  • Firoozeh Rivaz

Abstract

In spatial statistics, models are often constructed based on some common, but possible restrictive assumptions for the underlying spatial process, including Gaussianity as well as stationarity and isotropy. However, these assumptions are frequently violated in applied problems. In order to simultaneously handle skewness and non-homogeneity (i.e., non-stationarity and anisotropy), we develop the fixed rank kriging model through the use of skew-normal distribution for its non-spatial latent variables. Our approach to spatial modeling is easy to implement and also provides a great flexibility in adjusting to skewed and large datasets with heterogeneous correlation structures. We adopt a Bayesian framework for our analysis, and describe a simple MCMC algorithm for sampling from the posterior distribution of the model parameters and performing spatial prediction. Through a simulation study, we demonstrate that the proposed model could detect departures from normality and, for illustration, we analyze a synthetic dataset of CO $$_2$$ 2 measurements. Finally, to deal with multivariate spatial data showing some degree of skewness, a multivariate extension of the model is also provided. Copyright Springer-Verlag Berlin Heidelberg 2016

Suggested Citation

  • Hossein Boojari & Majid Khaledi & Firoozeh Rivaz, 2016. "A non-homogeneous skew-Gaussian Bayesian spatial model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(1), pages 55-73, March.
    • Handle: RePEc:spr:stmapp:v:25:y:2016:i:1:p:55-73
    DOI: 10.1007/s10260-015-0331-x
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    References listed on IDEAS

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    1. Sudipto Banerjee & Alan E. Gelfand & Andrew O. Finley & Huiyan Sang, 2008. "Gaussian predictive process models for large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 825-848, September.
    2. Fuentes, Montserrat, 2007. "Approximate Likelihood for Large Irregularly Spaced Spatial Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 321-331, March.
    3. 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.
    4. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    5. Noel Cressie & Gardar Johannesson, 2008. "Fixed rank kriging for very large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 209-226, February.
    6. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    7. R.B. Arellano-Valle & H. Bolfarine & V.H. Lachos, 2007. "Bayesian Inference for Skew-normal Linear Mixed Models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(6), pages 663-682.
    8. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    9. Zareifard, Hamid & Jafari Khaledi, Majid, 2013. "Non-Gaussian modeling of spatial data using scale mixing of a unified skew Gaussian process," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 16-28.
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