A latent variable approach to modelling multivariate geostatistical skew-normal data

In this paper we propose a spatial latent factor model to deal with multivariate geostatistical skew-normal data. In this model we assume that the unobserved latent structure, responsible for the correlation among different variables as well as for the spatial autocorrelation among different sites is Gaussian, and that the observed variables are skew-normal. For this model we provide some of its properties like its spatial autocorrelation structure and its finite dimensional marginal distributions. Estimation of the unknown parameters of the model is carried out by employing a Monte Carlo Expectation Maximization algorithm, whereas prediction at unobserved sites is performed by using closed form formulas and Markov chain Monte Carlo algorithms. Simulation studies have been performed to evaluate the soundness of the proposed procedures