The Annals of Applied Statistics

Modeling and estimation of multi-source clustering in crime and security data

George Mohler

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Appl. Stat. Volume 7, Number 3 (2013), 1525-1539.

Dates
First available in Project Euclid: 3 October 2013

Permanent link to this document
http://projecteuclid.org/euclid.aoas/1380804805

Digital Object Identifier
doi:10.1214/13-AOAS647

Mathematical Reviews number (MathSciNet)
MR3127957

Zentralblatt MATH identifier
06237186

Keywords
Markov Chain Monte Carlo Hawkes process Cox process crime terrorism

Citation

Mohler, George. Modeling and estimation of multi-source clustering in crime and security data. Ann. Appl. Stat. 7 (2013), no. 3, 1525--1539. doi:10.1214/13-AOAS647. http://projecteuclid.org/euclid.aoas/1380804805.


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