Empirical Bayes Methods for the Transformed Gaussian Random Field Model with Additive Measurement Errors
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,  propose the Bayesian transformed Gaussian model where they use the Box-Cox family of power transformation  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,  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  and  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 . See also  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.
This is a manuscript of a chapter from Vivekananda Roy, Evangelos Evangelou, and Zhengyuan Zhu (2015), Empirical Bayes methods for Transformed Gaussian Random Fields Model with Additive Measurement Errors. In D. K. Dey, U. Singh and A. Loganathan (eds.), Current Trends in Bayesian Methodology with Applications, Chapman & Hall/CRC Press. Posted with permission.