Some covariance models based on normal scale mixtures

TL;DR

This paper introduces a new class of covariance models for spatio-temporal processes based on normal scale mixtures, generalizing existing models and including new multivariate extensions.

Contribution

It presents a novel class of covariance functions that unify and extend prior models, with new models and a multivariate extension.

Findings

Unified framework for covariance models

Generalization of Gneiting and Stein models

Introduction of multivariate covariance models

Abstract

Modelling spatio-temporal processes has become an important issue in current research. Since Gaussian processes are essentially determined by their second order structure, broad classes of covariance functions are of interest. Here, a new class is described that merges and generalizes various models presented in the literature, in particular models in Gneiting (J. Amer. Statist. Assoc. 97 (2002) 590--600) and Stein (Nonstationary spatial covariance functions (2005) Univ. Chicago). Furthermore, new models and a multivariate extension are introduced.