Measuring and Modeling Repeat and Near-Repeat Burglary Effects

Abstract

We develop a mathematical framework aimed at analyzing repeat and nearrepeat effects in crime data. Parsing burglary data from Long Beach, CA according to different counting methods, we determine the probability distribution functions for the time interval s between repeat offenses. We then compare these observed distributions to theoretically derived distributions in which the repeat effects are due solely to persistent risk heterogeneity. We find that risk heterogeneity alone cannot explain the observed distributions, while a form of event dependence (boosts) can. Using this information, we model repeat victimization as a series of random events, the likelihood of which changes each time an offense occurs. We are able to estimate typical time scales for repeat burglary events in Long Beach by fitting our data to this model. Computer simulations of this model using these observed parameters agree with the empirical data.

Self-exciting point process models of civilian deaths in Iraq

“…Drawing on concepts developed in the study of crime patterns (Short, D'Orsogna, Brantingham, & Tita, 2009), we propose that violence in Iraq arises from a combination of exogenous and endogenous effects. Spatial heterogeneity in background rates is conditioned by fixed environmental characteristics, a fact well-documented in criminology (Andresen, Brantingham, & Kinney, 2010).…”

“…Related work has also been done in Short et al (2009) where the authors show that clusters of residential burglaries can not be explained by risk heterogeneity alone. If we assume that correlations are present between nearby events and that these correlations are positive, then we arrive at what is called a self-exciting point process.…”

A mathematical model of serious and minor criminal activity

“…It is also possible to adopt a different approach altogether in estimating parameter values, such as Bayesian methods, which is work in progress. Finally, it should be mentioned that the framework set in this paper can be expanded to model crime distribution in space for serious and minor crime, along the lines of [18,20,21]. A model that successfully captures the points mentioned here and expands them to account for spatial variation as well is also work in progress.…”

“…Specifically, the formation of areas of increased criminal activity (hotspots) and their evolution in time and space has drawn the attention of crime scientists [9,10]. A novel mathematical modelling approach in attacking this problem is presented in a series of papers by Short et al [18,20,21], where the authors derive a continuous model that captures the behaviour of burglars and which leads to the formation of hotspots.…”

Crime concentration theory

“…For example, neighbouring and nearby households are more likely to be victimized after a break-in (Townsley et al 2003, Johnson et al 2007a, while Ratcliffe and Rengert (2008) found repeat shootings in Philadelphia more likely within a city block and two weeks. Thus repeats and near repeats together offer insight into why crime concentrates spatially and underpin the algorithms of predictive policing (Groff and LaVigne 2001;Chainey et al 2008;Short et al 2009;Johnson 2010;Pease and Tseloni 2014). Levy and Tartaro (2010) refer to repeat victimization locations as inclusive of repeats and near repeats, hot dots and hot spots, writing:…”