Analysing Positive-Valued Spatial Data: the Transformed Gaussian Model

Abstract

The Gaussian assumption is often inappropriate for analysing geostatistical data. In such cases transformations can be used in an attempt to get nearly-Gaussian behaviour. In this paper we study the transformed Gaussian model, which includes an additional parameter corresponding to the Box-Cox family of transformations. In particular we consider maximum likelihood estimation and minimum mean square error prediction for this model. As an example we apply the model to rainfall data. We discuss the limitations of the transformed Gaussian model, and suggest that it should be used primarily as a first line of attack in dealing with non-Gaussianity and non-linearity, before proceeding to more complex models.