AI 中文总结
该研究针对空间模糊化的街道犯罪数据，提出基于度量图的对数高斯 Cox 过程框架，经模拟和伦敦市多类犯罪数据验证，其拟合与参数恢复效果优于平面模型，为网络约束的隐私保护空间事件分析提供了原则性方法。
AI 中文摘要
我们开发了一种对数高斯 Cox 过程框架，用于对道路网络上观测到的、事件位置被空间模糊化的街道级犯罪数据进行建模。受英国警方街道级犯罪数据的启发，这些数据中公布的坐标是匿名代理位置而非精确事件位置，我们通过在街道网络上用聚合支撑表示每个观测值来解决由此产生的支撑不匹配问题。潜在的对数强度被建模为在度量图上通过 SPDE 表示定义的 Whittle–Matérn 高斯场，这使得犯罪强度可沿街道连续变化，同时符合道路网络的几何结构。我们将所提出的度量图聚合模型与两种替代模型进行比较：一种是将公布位置视为精确点的平面点模型，另一种是考虑空间聚合但忽略网络支撑的平面聚合模型。在一项在街道网络上生成数据的模拟研究中，度量图模型比平面替代模型提供了更准确的参数恢复和更好的整体拟合。在伦敦市的应用中，度量图模型在多种犯罪类型中也实现了最佳拟合，包括人身盗窃、抢劫、毒品犯罪和自行车盗窃。结果进一步表明，环境便利设施与犯罪风险之间的关系因犯罪类型而异，其中超市显示出最一致的正相关关系。所提出的框架为分析具有隐私保护和不精确位置的网络约束空间事件数据提供了一种原则性方法。
英文摘要
We develop a log-Gaussian Cox process framework for modelling street-level crime data observed on a road network when the released event locations are spatially obfuscated. Motivated by UK Police street-level crime data, where published coordinates are anonymised proxy locations rather than exact event locations, we address the resulting support mismatch by representing each observation through an aggregated support on the street network. The latent log-intensity is modelled as a Whittle--Matérn Gaussian field defined on a metric graph through an SPDE representation, allowing the crime intensity to vary continuously along streets while respecting the geometry of the road network. We compare the proposed metric-graph aggregated model with two alternatives: a planar point model that treats the released locations as exact points, and a planar aggregated model that accounts for spatial aggregation but ignores the network support. In a simulation study where data are generated on a street network, the metric-graph model provides more accurate parameter recovery and better overall fit than the planar alternative. In the City of London application, the metric-graph model also achieves the best fit across several crime types, including theft from the person, robbery, drugs, and bicycle theft. The results further suggest that the relationship between environmental amenities and crime risk varies by crime type, with supermarkets showing the most consistent positive associations. The proposed framework provides a principled approach for analysing network-constrained spatial event data with privacy-protected and imprecise locations.
