Extensions of the Parametric Inference of Spatial Covariances by Maximum Likelihood

Abstract

The limitations of the maximum likelihood method for estimating spatial covariance parameters are: the assumption that the experimental data follow a multi-dimensional Gaussian distribution, biased estimates, impracticality for large data sets and the common assumption of a polynomial drift. The advantages are easy evaluation of parameter uncertainty, no information loss in binning and the ability to include additional information using a Bayesian framework. We provide extensions to overcome the disadvantages whilst maintaining the advantages. We provide an algorithm for obtaining covariance estimates for non-Gaussian data using Gaussian maximum likelihood. We provide a means of generating unbiased estimates of spatial covariance parameters without increasing the estimation variance. We overcome the impracticality for larger data sets by an approximation to the complete maximum likelihood. Finally, we extend the polynomial drift to other forms.