高斯 Whittle-Matérn 场构成了紧致度量图上一类灵活的高斯过程，其空间依赖性通过分数阶随机偏微分方程由网络的几何结构和连通性决定。本文针对具有马尔可夫性质的半整数光滑度参数情形，发展了这些场的一种新的桥表示。该表示将场分解为有限维的图分量以及各条边上独立的 Whittle-Matérn 桥过程。由此产生的分解方法可实现高效的似然评估、克里金预测和模拟。研究表明，与以往方法相比，该方法提高了数值稳定性并显著减少了计算时间。在芝加哥街道网络图上的模拟研究展示了采样方法的计算效率，而对马德里交通强度数据的应用则证明了其在基于似然的推断和预测中的实际优势。相关方法已在 R 包 MetricGraph 中实现。

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.