Nonlinear Spatial Prediction with Non-Gaussian Data: A Maximum Entropy Viewpoint

Abstract

We propose to look here at the problem of nonlinear spatial prediction from a maximum entropy viewpoint, where the marginal probability distribution function (pdf) is assumed to belong to the parametric family of exponential polynomials of order p, i.e. the family of maximum entropy solutions under constraints for the p first moments. The general methodology for modeling this marginal pdf is given first, allowing afterwards an estimation of multivariate maximum entropy pdf’s that account at the same time for the marginal pdf and a specified covariance function.

As it is notorious that obtaining maximum entropy solutions is computationally heavy, an implementation of the method is proposed using Monte-Carlo integration, with preference sampling as main variance reduction technique. The advantages and drawbacks of using maximum entropy distributions over standard marginal transformation are explained and discussed in the light of a real case study.