A Hierarchical Bayesian Model for Spatial Prediction of Multivariate Non-Gaussian Random Fields

Authors

  • Pierrette Chagneau,

    Corresponding author
    1. CIRAD, UR Dynamique des forêts naturelles, 34 398 Montpellier, France
    2. I3M, UMR CNRS 5149, Université de Montpellier 2, 34 095 Montpellier, France
      email: pierrette.chagneau@cirad.fr
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  • Frédéric Mortier,

    Corresponding author
    1. CIRAD, UR Diversité génétique et amélioration des espèces forestières, 34 398 Montpellier, France
      email: frederic.mortier@cirad.fr
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  • Nicolas Picard,

    Corresponding author
    1. CIRAD, UR Dynamique des forêts naturelles, Libreville, Gabon
      email: nicolas.picard@cirad.fr
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  • Jean-Noël Bacro

    Corresponding author
    1. I3M, UMR CNRS 5149, Université de Montpellier 2, 34 095 Montpellier, France
      email: bacro@math.univ-montp2.fr
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email:pierrette.chagneau@cirad.fr

email:frederic.mortier@cirad.fr

email:nicolas.picard@cirad.fr

email:bacro@math.univ-montp2.fr

Abstract

Summary As most georeferenced data sets are multivariate and concern variables of different types, spatial mapping methods must be able to deal with such data. The main difficulties are the prediction of non-Gaussian variables and the modeling of the dependence between processes. The aim of this article is to present a new hierarchical Bayesian approach that permits simultaneous modeling of dependent Gaussian, count, and ordinal spatial fields. This approach is based on spatial generalized linear mixed models. We use a moving average approach to model the spatial dependence between the processes. The method is first validated through a simulation study. We show that the multivariate model has better predictive abilities than the univariate one. Then the multivariate spatial hierarchical model is applied to a real data set collected in French Guiana to predict topsoil patterns.

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