A non-parametric bivariate entropy estimator for spatial processes

Abstract

In this paper, entropy is presented as an alternative measure to characterize the bivariate distribution of a stationary spatial process. This non-parametric estimator attempts to quantify the concept of spatial ordering, and it provides a measure of how Gaussian the experimental bivariate distribution is. The concept of entropy is explained and the classical definition presented, along with some important results. In particular, the reader is reminded that, for a known mean and covariance, the bivariate Gaussian distribution maximizes entropy. A “relative entropy” estimator is introduced in order to measure departure of an experimental bivariate distribution from the bivariate Gaussian. Two case studies are presented as examples.