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August 2020 Isotropic covariance functions on graphs and their edges
Ethan Anderes, Jesper Møller, Jakob G. Rasmussen
Ann. Statist. 48(4): 2478-2503 (August 2020). DOI: 10.1214/19-AOS1896

Abstract

We develop parametric classes of covariance functions on linear networks and their extension to graphs with Euclidean edges, that is, graphs with edges viewed as line segments or more general sets with a coordinate system allowing us to consider points on the graph which are vertices or points on an edge. Our covariance functions are defined on the vertices and edge points of these graphs and are isotropic in the sense that they depend only on the geodesic distance or on a new metric called the resistance metric (which extends the classical resistance metric developed in electrical network theory on the vertices of a graph to the continuum of edge points). We discuss the advantages of using the resistance metric in comparison with the geodesic metric as well as the restrictions these metrics impose on the investigated covariance functions. In particular, many of the commonly used isotropic covariance functions in the spatial statistics literature (the power exponential, Matérn, generalized Cauchy and Dagum classes) are shown to be valid with respect to the resistance metric for any graph with Euclidean edges, whilst they are only valid with respect to the geodesic metric in more special cases.

Citation

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Ethan Anderes. Jesper Møller. Jakob G. Rasmussen. "Isotropic covariance functions on graphs and their edges." Ann. Statist. 48 (4) 2478 - 2503, August 2020. https://doi.org/10.1214/19-AOS1896

Information

Received: 1 June 2018; Revised: 1 May 2019; Published: August 2020
First available in Project Euclid: 14 August 2020

MathSciNet: MR4134803
Digital Object Identifier: 10.1214/19-AOS1896

Subjects:
Primary: 62M99
Secondary: 60K99, 62M30

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 4 • August 2020
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