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Spatial statistics is traditionally based on stationary models on$\mathbb{R^d}$ like Mat\'ern fields. The adaptation of traditional spatialstatistical methods, originally designed for stationary models in Euclideanspaces, to effectively model phenomena on linear networks such as streamsystems and urban road networks is challenging. The current study aims toanalyze the incidence of traffic accidents on road networks using threedifferent methodologies and compare the model performance for each methodology.Initially, we analyzed the application of spatial triangulation precisely onroad networks instead of traditional continuous regions. However, this approachposed challenges in areas with complex boundaries, leading to the emergence ofartificial spatial dependencies. To address this, we applied an alternativecomputational method to construct nonstationary barrier models. Finally, weexplored a recently proposed class of Gaussian processes on compact metricgraphs, the Whittle-Mat\'ern fields, defined by a fractional SPDE on the metricgraph. The latter fields are a natural extension of Gaussian fields withMat\'ern covariance functions on Euclidean domains to non-Euclidean metricgraph settings. A ten-year period (2010-2019) of daily traffic-accident recordsfrom Barcelona, Spain have been used to evaluate the three models referredabove. While comparing model performance we observed that the Whittle-Mat\'ernfields defined directly on the network outperformed the network triangulationand barrier models. Due to their flexibility, the Whittle-Mat\'ern fields canbe applied to a wide range of environmental problems on linear networks such asspatio-temporal modeling of water contamination in stream networks or modelingair quality or accidents on urban road networks.

Enhanced spatial modeling on linear networks using Gaussian Whittle-Mat\'ern fields