Geographic Profiling from Kinetic Models of Criminal Behavior

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, etc.) are naturally incorporated into the probability density estimate, as well as directional bias and distance to crime preferences in offender target selection. The resulting equations are steady state advection-diffusion-reaction PDEs. We test our methodology against crime data provided by the Los Angeles Police Department, and our results highlight the benefits of incorporating these elements of criminal behavior and geographic inhomogeneities into profiling estimates.