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Exploring data assimilation and forecasting issues for an urban crime model

Published online by Cambridge University Press:  02 December 2015

DAVID J. B. LLOYD ,
NARATIP SANTITISSADEEKORN  and
MARTIN B. SHORT
DAVID J. B. LLOYD
Affiliation:
Department of Mathematics, University of Surrey, Guildford, GU2 7XH, UK email: D.J.Lloyd@surrey.ac.uk; n.santitissadeekorn@surrey.ac.uk
NARATIP SANTITISSADEEKORN
Affiliation:
Department of Mathematics, University of Surrey, Guildford, GU2 7XH, UK email: D.J.Lloyd@surrey.ac.uk; n.santitissadeekorn@surrey.ac.uk
MARTIN B. SHORT
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA, USA email: mbshort@math.gatech.edu
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Abstract

In this paper, we explore some of the various issues that may occur in attempting to fit a dynamical systems (either agent- or continuum-based) model of urban crime to data on just the attack times and locations. We show how one may carry out a regression analysis for the model described by Short et al. (2008, Math. Mod. Meth. Appl. Sci.) by using simulated attack data from the agent-based model. It is discussed how one can incorporate the attack data into the partial differential equations for the expected attractiveness to burgle and the criminal density to predict crime rates between attacks. Using this predicted crime rate, we derive a likelihood function that one can maximise in order to fit parameters and/or initial conditions for the model. We focus on carrying out data assimilation for two different parameter regions, namely in the case where stationary and non-stationary crime hotspots form. It is found that the likelihood function is ‘flat’ for large ranges of parameters, and that this has major implications for crime forecasting. Hence, we look at how one might carry out a goodness-of-fit and forecasting analysis for crime rates given the range of parameter fits. We show how one can use the Kolmogorov–Smirnov statistic to assess the goodness-of-fit. The dynamical systems analysis of the partial differential equations proves invaluable to understanding how the crime rate forecasts depend on the parameters and their sensitivity. Finally, we outline several interesting directions for future research in this area where we believe that the combination of dynamical systems modelling, analysis, and data assimilation can prove effective in developing policing strategies for urban crime.

Keywords

Crime hotspotsData assimilationMaximum likelihoodPoint processParameter estimation
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 3: Mathematical Modelling of Crime and Security , June 2016 , pp. 451 - 478
Copyright
Copyright © Cambridge University Press 2015 

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