巴塞罗那和波哥大城市道路网络碰撞计数的边缘谱模式贝叶斯选择

中文摘要 AI 辅助

城市道路网络上的碰撞计数表现出空间依赖性，这种依赖性由道路连通性驱动，而非仅由欧几里得邻近性决定。我们提出了一种贝叶斯负二项模型，通过直接在道路段上定义的谱分量的简约组合来表示空间变化。该模型将归一化随机边缘邻域高斯（RENeGe）算子与连续尖峰-板先验相结合，其中混合指标被边缘化。依赖于特征值的板方差将谱正则化与网络支持的平滑性联系起来，而后验板成员概率量化了对各个分量的支持以及有效谱复杂性的不确定性。段长被用作暴露偏移量，因此拟合的比率描述每单位道路长度的碰撞频率，而非交通调整后的风险。在一项包含1,200个数据集和4,800次贝叶斯拟合的模拟研究中，所提出的模型在稀疏RENeGe真实情况下实现了最低的平均空间场恢复误差和最高的平均测试对数预测密度。在替代生成机制下，其预测性能仍接近密集谱模型，并超过非空间模型。对巴塞罗那和波哥大市中心的应用程序显示了不同的后验谱模式。探索性留一段交叉比较发现，所提出的模型与低秩边缘CAR模型具有相似的预测准确性，两者均优于非空间负二项模型，而谱BYM2模型实现了最高的探索性预测得分。这些结果支持谱复杂性的概率总结，而相对于相应的CAR模型没有可检测的预测惩罚。

英文摘要

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.

发表机构

• Universidad Nacional de Colombia（哥伦比亚国立大学）

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