A bridge representation of Gaussian Whittle-Matérn fields on compact metric graphs
Abstract
Gaussian Whittle-Matérn fields form a flexible class of Gaussian processes on compact metric graphs, where spatial dependence is governed by the geometry and connectivity of the network through a fractional-order stochastic partial differential equation. This paper develops a new bridge representation of these fields in the case of half-integer smoothness parameters, when the fields have Markov properties. This representation decomposes the field into a finite-dimensional graph component and independent Whittle-Matérn bridge processes on the individual edges. The resulting decomposition leads to efficient likelihood evaluation, kriging prediction, and simulation methods. We show that this improves numerical stability and can greatly reduce computation time compared to previous methods. A simulation study on a Chicago street-network graph illustrates the computational efficiency of the sampling method and an application to Madrid traffic intensity data demonstrates the practical gains for likelihood-based inference and prediction. The methods are implemented in the R package MetricGraph.
Related
- Whittle--Matérn metrics and isotropic Gaussian processes on compact metric graphs
- Smoothness estimation for Whittle–Matérn processes on closed Riemannian manifolds
- Discrete Exterior Calculus-based Whittle-Matérn Fields on Meshes
- Bigraphical Matérn-Whittle (BMW) Processes for Fast Inference of Big Multivariate Spatial Data on General Domains
- An irreducible decomposition of the Weil representation restricted to open compact subgroups
BibTeX
@misc{bolin2026bridge,
title = {{A bridge representation of Gaussian Whittle-Matérn fields on compact metric graphs}},
author = {David Bolin and Alexandre B. Simas and Jonas Wallin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18375},
eprint = {2609.18375},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18375},
}
RIS
TY - UNPB
TI - A bridge representation of Gaussian Whittle-Matérn fields on compact metric graphs
AU - David Bolin
AU - Alexandre B. Simas
AU - Jonas Wallin
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18375
UR - https://arxiv.org/abs/2609.18375
AB - Gaussian Whittle-Matérn fields form a flexible class of Gaussian processes on compact metric graphs, where spatial dependence is governed by the geometry and connectivity of the network through a fractional-order stochastic partial differential equation. This paper develops a new bridge representation of these fields in the case of half-integer smoothness parameters, when the fields have Markov properties. This representation decomposes the field into a finite-dimensional graph component and independent Whittle-Matérn bridge processes on the individual edges. The resulting decomposition leads to efficient likelihood evaluation, kriging prediction, and simulation methods. We show that this improves numerical stability and can greatly reduce computation time compared to previous methods. A simulation study on a Chicago street-network graph illustrates the computational efficiency of the sampling method and an application to Madrid traffic intensity data demonstrates the practical gains for likelihood-based inference and prediction. The methods are implemented in the R package MetricGraph.
ER -