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arXiv · 2501.18558

Log-Gaussian Cox Processes on General Metric Graphs

David Bolin·Damilya Saduakhas·Alexandre B. Simas
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Abstract

The modeling 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-Mat\'ern 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-Mat\'ern 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 150,000 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 modeling spatial point processes directly on complex networks.

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David Bolin, Damilya Saduakhas, Alexandre B. Simas. 2025-01-30. Log-Gaussian Cox Processes on General Metric Graphs. https://arxiv.org/abs/2501.18558

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