Empirical Bayes Methods for the Transformed Gaussian Random Field Model with Additive Measurement Errors

Abstract

<p>If geostatistical observations are continuous but can not be modeled by the Gaussian distribution, a more appropriate model for these data may be the transformed Gaussian model. In transformed Gaussian models it is assumed that the random field of interest is a nonlinear transformation of a Gaussian random field (GRF). For example, [9] propose the Bayesian transformed Gaussian model where they use the Box-Cox family of power transformation [3] on the observations and show that prediction for unobserved random fields can be done through posterior predictive distribution where uncertainty about the transformation parameter is taken into account. More recently, [5] consider maximum likelihood estimation of the parameters and a “plug-in” method of prediction for transformed Gaussian model with Box-Cox family of transformations. Both [9] and [5] consider spatial prediction of rainfall to illustrate their model and method of analysis. A review of the Bayesian transformed Gaussian random fields model is given in [8]. See also [6] who discusses several issues regarding the formulation and interpretation of transformed Gaussian random field models, including the approximate nature of the model for positive data based on Box-Cox family of transformations, and the interpretation of the model parameters.</p>