Hierarchical Bayesian Model for Gaussian, Poisson and Ordinal Random Fields

As most georeferenced data sets are multivariate and concern variables of different kinds, spatial mapping methods must be able to deal with such data. The main difficulties are the prediction of non Gaussian variables and the modelling of the dependence between processes. The aim of this paper is to propose a new approach that permits simultaneous modelling of Gaussian, count and ordinal spatial processes. We consider a hierarchical model implemented within a Bayesian framework. The method used for Gaussian and count variables is based on the generalized linear mixed models. Ordinal variable is taken into account through a generalization of the ordinal probit model. We use a moving average approach to model the spatial dependence between the processes. The proposed model is applied to pedological data collected in French Guiana.