How to model the covariance structure in a spatial framework: variogram or correlation function?

TL;DR

This paper examines the modeling of covariance structures in spatial analysis, comparing the use of variograms versus correlation functions within the Kriging framework, emphasizing the parameterization choices.

Contribution

It provides a detailed discussion on using the variogram as a parameterization in Gaussian spatial models, highlighting its implications for Kriging.

Findings

Variogram and correlation matrix are equivalent in characterizing spatial dependence.

Using the variogram as a parameterization offers specific modeling advantages.

The paper clarifies the relationship between variogram and correlation in Gaussian models.

Abstract

The basic Kriging's model assumes a Gaussian distribution with stationary mean and stationary variance. In such a setting, the joint distribution of the spatial process is characterized by the common variance and the correlation matrix or, equivalently, by the common variance and the variogram matrix. We discuss in in detail the option to actually use the variogram as a parameterization.