A bridge representation of Gaussian Whittle-Matérn fields on compact metric graphs

2026-09-16

AI Summary

本文通过开发一种新的桥表示方法解决高斯Whittle-Matérn场在紧致度量图上的有效评估、预测和模拟问题，提高数值稳定性和计算效率。

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.

Problem

• Gaussian Whittle-Matérn fields
• compact metric graphs
• Markov properties
• numerical stability
• computational efficiency

Innovation

• Gaussian Whittle-Matérn fields
• bridge representation
• compact metric graphs
• Markov properties
• numerical stability