While the presence of clustering in crime and security event data is well
established, the mechanism(s) by which clustering arises is not fully
understood. Both contagion models and history independent correlation models
are applied, but not simultaneously. In an attempt to disentangle contagion
from other types of correlation, we consider a Hawkes process with background
rate driven by a log Gaussian Cox process. Our inference methodology is an
efficient Metropolis adjusted Langevin algorithm for filtering of the intensity
and estimation of the model parameters. We apply the methodology to property
and violent crime data from Chicago, terrorist attack data from Northern
Ireland and Israel, and civilian casualty data from Iraq. For each data set we
quantify the uncertainty in the levels of contagion vs. history independent
correlation.

本文探讨了犯罪事件和安全事件数据的聚类机制，通过使用 Hawkes 过程和背景速率为高斯 Cox 进程的滤波算法，对芝加哥的财产犯罪数据、北爱尔兰和以色列的恐怖袭击数据以及伊拉克的平民伤亡数据进行了分析，量化了传染程度与独立历史相关性水平之间的不确定性。