  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.
