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Bayesian spatial prediction of skew and censored data via a hybrid algorithm

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  • Firoozeh Rivaz
  • Majid Jafari Khaledi

Abstract

A correct detection of areas with excess of pollution relies first on accurate predictions of pollutant concentrations, a task that is usually complicated by skewed histograms and the presence of censored data. The unified skew-Gaussian (SUG) random field proposed by Zareifard and Jafari Khaledi [19] offers a more flexible class of sampling spatial models to account for skewness. In this paper, we adopt a Bayesian framework to perform prediction for the SUG model in the presence of censored data. Owing to the presence of many latent variables with strongly dependent components in the model, we encounter convergence issues when using Monte Carlo Markov Chain algorithms. To overcome this obstacle, we use a computationally efficient inverse Bayes formulas sampling procedure to obtain approximately independent samples from the posterior distribution of latent variables. Then they are applied to update parameters in a Gibbs sampler scheme. This hybrid algorithm provides effective samples, resulting in some computational advantages and precise predictions. The proposed approach is illustrated with a simulation study and applied to a spatial data set which contains right censored data.

Suggested Citation

  • Firoozeh Rivaz & Majid Jafari Khaledi, 2015. "Bayesian spatial prediction of skew and censored data via a hybrid algorithm," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(9), pages 1993-2009, September.
  • Handle: RePEc:taf:japsta:v:42:y:2015:i:9:p:1993-2009
    DOI: 10.1080/02664763.2015.1014895
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    4. Wang, Wan-Lun & Fan, Tsai-Hung, 2012. "Bayesian analysis of multivariate t linear mixed models using a combination of IBF and Gibbs samplers," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 300-310.
    5. 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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