2013/11/28 by George Mohler
Mathematics · #stat.AP
paper · pdf · doi:10.1214/13-aoas647
published as Annals of Applied Statistics 2013, Vol. 7, No. 3, 1525-1539 · Published in at http://dx.doi.org/10.1214/13-AOAS647 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)
arxiv created 2013/11/28 · arxiv updated 2013/12/02
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.