Log-Gaussian Cox process on general metric graphs
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ID: 319113
2026
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Abstract
Summary The modelling of spatial point processes has advanced considerably, yet extending these models to non-Euclidean domains, such as road networks, remains a challenging problem. We propose a novel framework for log-Gaussian Cox processes on general compact metric graphs by leveraging the Gaussian Whittle–Matérn fields, which are solutions to fractional-order stochastic differential equations on metric graphs. To achieve computationally efficient likelihood-based inference, we introduce a numerical approximation of the likelihood that eliminates the need to approximate the Gaussian process. This method, coupled with the exact evaluation of finite-dimensional distributions for Whittle–Matérn fields with integer smoothness, ensures scalability and theoretical rigour, with derived convergence rates for posterior distributions. The framework is implemented in the open-source MetricGraph R package, which integrates seamlessly with R-INLA to support fully Bayesian inference. We demonstrate the applicability and scalability of this approach through an analysis of road accident data from Al-Ahsa, Saudi Arabia, consisting of over 160,000 road segments. By identifying high-risk road segments using exceedance probabilities and excursion sets, our framework provides localized insights into accident hotspots and offers a powerful tool for modelling spatial point processes directly on complex networks.
| Reference Key |
openalex_W7166503398
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|---|---|
| Authors | David Bolin, Damilya Saduakhas, Alexandre B. Simas |
| Journal | jurnal biometrika dan kependudukan |
| Year | 2026 |
| DOI |
10.1093/biomet/asag043
|
| URL | |
| Keywords | Keywords not found |
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