Capturing Multivariate Spatial Dependence: Model, Estimate and then Predict

TL;DR

This paper discusses modeling multivariate spatial dependence to improve prediction of interacting physical processes, emphasizing the importance of valid covariance matrices for accurate multivariate field estimation.

Contribution

It introduces a framework for capturing and estimating multivariate spatial dependence, focusing on ensuring nonnegative definiteness of covariance matrices for better prediction.

Findings

Proposes a method for modeling multivariate spatial dependence

Ensures covariance matrices are nonnegative definite

Enhances prediction accuracy of multivariate fields

Abstract

Physical processes rarely occur in isolation, rather they influence and interact with one another. Thus, there is great benefit in modeling potential dependence between both spatial locations and different processes. It is the interaction between these two dependencies that is the focus of Genton and Kleiber's paper under discussion. We see the problem of ensuring that any multivariate spatial covariance matrix is nonnegative definite as important, but we also see it as a means to an end. That "end" is solving the scientific problem of predicting a multivariate field. [arXiv:1507.08017].