Bayesian Selection of Edge Spectral Modes for Crash Counts on Urban Road Networks with Applications in Barcelona and Bogotá
Abstract
Crash counts on urban road networks exhibit spatial dependence driven by road connectivity rather than Euclidean proximity alone. We propose a Bayesian negative binomial model that represents spatial variation through a parsimonious combination of spectral components defined directly on road segments. The model combines the normalized random edge neighborhood Gaussian (RENeGe) operator with a continuous spike-and-slab prior, with mixture indicators marginalized out. Eigenvalue-dependent slab variances link spectral regularization to network-supported smoothness, while posterior slab-membership probabilities quantify support for individual components and uncertainty in effective spectral complexity. Segment length is used as an exposure offset, so fitted rates describe crash frequency per unit road length rather than traffic-adjusted risk. In a simulation study with 1,200 datasets and 4,800 Bayesian fits, the proposed model achieved the lowest mean spatial-field recovery error and highest mean test log predictive density under sparse RENeGe truth. Under alternative generating mechanisms, its predictive performance remained close to dense spectral models and exceeded that of a nonspatial model. Applications to Barcelona and central Bogota showed distinct posterior spectral patterns. Exploratory leave-one-segment-out comparisons found similar predictive accuracy for the proposed model and a low-rank edge CAR model, both outperforming a nonspatial negative binomial model, while a spectral BYM2 model achieved the highest exploratory predictive score. These results support probabilistic summaries of spectral complexity without a detectable predictive penalty relative to the corresponding CAR model.
Related
- SelectPFN: Amortized Bayesian Variable Selection for Sparse Nonlinear Regression with Prior-Data Fitted Networks
- A novel Arctan-based model: Bayesian analysis, progressive censoring, and practical applications
- Testing Group Differences in Network Models using Bayesian Model Selection: A Tutorial
- Bayesian Variable Selection for High-Dimensional Predictors with Missing Psychometric Outcomes
- A Bayesian Bi-Directional Splitting Framework for Variable Selection in Large Datasets
BibTeX
@misc{cruzreyes2026bayesian,
title = {{Bayesian Selection of Edge Spectral Modes for Crash Counts on Urban Road Networks with Applications in Barcelona and Bogotá}},
author = {Danna L. Cruz-Reyes and Juan Sosa and Carlos A. Martínez},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36268},
eprint = {2609.36268},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36268},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bayesian Selection of Edge Spectral Modes for Crash Counts on Urban Road Networks with Applications in Barcelona and Bogotá
AU - Danna L. Cruz-Reyes
AU - Juan Sosa
AU - Carlos A. Martínez
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36268
UR - https://arxiv.org/abs/2609.36268
AB - Crash counts on urban road networks exhibit spatial dependence driven by road connectivity rather than Euclidean proximity alone. We propose a Bayesian negative binomial model that represents spatial variation through a parsimonious combination of spectral components defined directly on road segments. The model combines the normalized random edge neighborhood Gaussian (RENeGe) operator with a continuous spike-and-slab prior, with mixture indicators marginalized out. Eigenvalue-dependent slab variances link spectral regularization to network-supported smoothness, while posterior slab-membership probabilities quantify support for individual components and uncertainty in effective spectral complexity. Segment length is used as an exposure offset, so fitted rates describe crash frequency per unit road length rather than traffic-adjusted risk. In a simulation study with 1,200 datasets and 4,800 Bayesian fits, the proposed model achieved the lowest mean spatial-field recovery error and highest mean test log predictive density under sparse RENeGe truth. Under alternative generating mechanisms, its predictive performance remained close to dense spectral models and exceeded that of a nonspatial model. Applications to Barcelona and central Bogota showed distinct posterior spectral patterns. Exploratory leave-one-segment-out comparisons found similar predictive accuracy for the proposed model and a low-rank edge CAR model, both outperforming a nonspatial negative binomial model, while a spectral BYM2 model achieved the highest exploratory predictive score. These results support probabilistic summaries of spectral complexity without a detectable predictive penalty relative to the corresponding CAR model.
ER -