Geographic Profiling from Kinetic Models of Criminal Behavior

@article{Mohler2012GeographicPF,
  title={Geographic Profiling from Kinetic Models of Criminal Behavior},
  author={George O. Mohler and Martin B. Short},
  journal={SIAM J. Appl. Math.},
  year={2012},
  volume={72},
  pages={163-180}
}
We consider the problem of estimating the probability density of the “anchor point” (residence, place of work, etc.) of a criminal offender given a set of observed spatial locations of crimes committed by the offender. Starting from kinetic models of criminal motion and target selection, we derive the probability density of anchor points using the Fokker–Planck equation and Bayes' theorem. Here, geographic inhomogeneities such as housing densities and geographic barriers (bodies of water, parks… 

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References

SHOWING 1-10 OF 41 REFERENCES

A STATISTICAL MODEL OF CRIMINAL BEHAVIOR

This work focuses on a two-dimensional lattice model for residential burglary, where each site is characterized by a dynamic attractiveness variable, and where each criminal is represented as a random walker.

Self-Exciting Point Process Modeling of Crime

The implementation of self-exciting point process models in the context of urban crime is illustrated using residential burglary data provided by the Los Angeles Police Department to gain insight into the form of the space–time triggering function and temporal trends in the background rate of burglary.

The mathematics of geographic profiling

A new mathematical framework for the geographic profiling problem based on Bayesian statistical methods that makes explicit connections between assumptions on offender behaviour and the components of the mathematical model is presented.

Offender as Forager? A Direct Test of the Boost Account of Victimization

Recent research has demonstrated that burglary clusters in space and time, resulting in temporal changes in crime hotspot patterns. Offender foraging behavior would yield the observed pattern. The

Implementing a Bayesian approach to criminal geographic profiling

New software based on Bayesian methods that attempts to solve the geographic profiling problem of a serial criminal from the known locations of the offense sites are released.

Measuring and Modeling Repeat and Near-Repeat Burglary Effects

A mathematical framework aimed at analyzing repeat and near-repeat effects in crime data is developed, which model repeat victimization as a series of random events, the likelihood of which changes each time an offense occurs.

The environmental range of serial rapists

Offender Mobility and Crime Pattern Formation from First Principles

Foraging theory is the domain of ecology that seeks to model how organisms deploy alternative behavioral strategies to bring themselves into contact with the resources that they need for survival.

Predicting Serial Killers' Home Base Using a Decision Support System

The effectiveness of a geographical decision support tool (Dragnet) for locating the base of serial offenders was compared across 570 models consisting of a range of negative exponential functions, buffer zone components, and normalization parameters to support the potential for operational tools using such procedures as well as contribute to the understanding of criminal's geographicalbehavior.

Routine activity and rational choice

Two new criminological approaches are defined and applied to categories of crime in Routine Activity and Rational Choice, now available in paperback. Routine activity analyzes the criminal event, and