Security Journal

, Volume 25, Issue 3, pp 244–264 | Cite as

Self-exciting point process models of civilian deaths in Iraq

  • Erik Lewis
  • George Mohler
  • P Jeffrey Brantingham
  • Andrea L Bertozzi
Original Article


Our goal in this article is to characterize temporal patterns of violent civilian deaths in Iraq. These patterns are expected to evolve on time-scales ranging from years to minutes as a result of changes in the security environment on equally varied time-scales. To assess the importance of multiple time-scales in evolving security threats, we develop a self-exciting point process model similar to that used in earthquake analysis. Here the rate of violent events is partitioned into a background rate and a foreground self-exciting component. Background rates are assumed to change on relatively long time-scales. Foreground self-excitation, in which events trigger an increase in the rate of violence, is assumed to be short-lived. We explore the model using data from Iraq Body Count on civilian deaths between 2003 and 2007. Our results indicate that self-excitation makes up as much as 37–50 per cent of all violent events and that self-excitation lasts at most between two and six weeks, depending upon the district in question. Appropriate security responses may benefit from taking these different time-scales of violence into consideration.


modeling violence point process rational choice theory routine activity theory density estimation 


  1. Akaike, H. (1973) Information theory and an extension of the maximum likelihood principle. In: B.N. Petrov and F. Caski (eds.) Proceedings of the Second International Symposium on Information Theory. Budapest, Hungary: Akademiai Kiado.Google Scholar
  2. Akaike, H. (1974) A new look at statistical model identification. IEEE Transactions on Automatic Control AC19 (6): 716–723.CrossRefGoogle Scholar
  3. Akers, R. (2008) Social Learning and Social Structure: A General Theory of Crime and Deviance. Boston, MA: Northeastern University Press.Google Scholar
  4. Andresen, M.A., Brantingham, P.J. and Kinney, J.B. (2009) Classics in Environmental Criminology. Boca Raton, FL: CRC Press.Google Scholar
  5. Berman, E. (2009) Radical, Religious, and Violent: The New Economics of Terrorism. Cambridge, MA: The MIT Press.Google Scholar
  6. Bjelopera, J.P. and Randol, M.A. (2010) American Jihadist terrorism: Combating a complex threat. Congressional Research Service.Google Scholar
  7. Bozdogan, H. (1987) Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions. Psychometrika 52 (3): 345–370.CrossRefGoogle Scholar
  8. Brantingham, P. and Brantingham, P. (1995) Criminality of place. European Journal on Criminal Policy and Research 3 (3): 5–26.CrossRefGoogle Scholar
  9. Brantingham, P., Brantingham, P. and Taylor, W. (2005) Situational crime prevention as a key component in embedded crime prevention. Canadian Journal of Criminology and Criminal Justice/La Revue canadienne de criminologie et de justice pénale 47 (2): 271–292.CrossRefGoogle Scholar
  10. Brantingham, P.J. and Brantingham, P.L. (1984) Patterns in Crime. New York: Macmillan.Google Scholar
  11. Canela-Cacho, J.A., Blumstein, A. and Cohen, J. (1997) Relationship between the offending frequency (λ) of imprisoned and free offenders. Criminology 35 (1): 133–176.CrossRefGoogle Scholar
  12. Chabat, J. (2002) Mexico's war on drugs: No margin for maneuver. The Annals of the American Academy of Political and Social Science 582 (1): 134–148.CrossRefGoogle Scholar
  13. Clarke, R.V. and Newman, G.R. (2006) Outsmarting the Terrorists. Westport, CT: Praeger Security International.Google Scholar
  14. Cohen, L.E. and Felson, M. (1979) Social-change and crime rate trends: A routine activity approach. American Sociological Review 44 (4): 588–608.CrossRefGoogle Scholar
  15. Cornish, D.B. and Clarke, R.V. (eds.) (1986) The Reasoning Criminal: Rational Choice Perspectives on Criminal Offending. New York: Springer-Verlag.CrossRefGoogle Scholar
  16. Cornish, D.B. and Clarke, R.V. (1987) Understanding crime displacement: An application of rational choice theory. Criminology 25 (4): 933–947.CrossRefGoogle Scholar
  17. Daley, D. and Vere-Jones, D. (2003) An Introduction to the Theory of Point Processes. New York: Springer Verlag.Google Scholar
  18. Daley, D. and Vere-Jones, D. (2008) An Introduction to the Theory of Point Processes, 2nd edn. New York: Springer Verlag.CrossRefGoogle Scholar
  19. Dugan, L. (1999) The effect of criminal victimization on a household's moving decision. Criminology 37 (4): 903–930.CrossRefGoogle Scholar
  20. Egesdal, M., Fathauer, C., Louie, K. and Neuman, J. (2010) Statistical and stochastic modeling of gang rivalries in Los Angeles. SIAM Undergraduate Research Online 3: 72–94.CrossRefGoogle Scholar
  21. Farrell, G., Tilley, N., Tseloni, A. and Mailley, J. (2010) Explaining and sustaining the crime drop: Clarifying the role of opportunity-related theories. Crime Prevention & Community Safety 12 (1): 24–41.CrossRefGoogle Scholar
  22. Felson, M. and Clarke, R.V. (1998) Opportunity Makes the Thief: Practical Theory for Crime Prevention. London: Home Office Policing and Reducing Crime Unit.Google Scholar
  23. Felson, R.B. and Steadman, H.J. (1983) Situational factors in disputes leading to criminal violence. Criminology 21 (1): 59–74.CrossRefGoogle Scholar
  24. Fisher, R. (1922) On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London. Series A 222 (602): 309–368.CrossRefGoogle Scholar
  25. Hawkes, A.G. (1971) Spectra of some self-exciting and mutually exciting point processes. Biometrika 58 (1): 83.CrossRefGoogle Scholar
  26. Hawkes, A.G. and Oakes, D. (1974) Cluster process representation of a self-exciting process. Journal of Applied Probability 11 (3): 493–503.CrossRefGoogle Scholar
  27. Hicks, M.H.-R., Dardagan, H., Guerrero Serdán, G., Bagnall, P.M., Sloboda, J.A. and Spagat, M. (2011) Violent deaths of Iraqi civilians, 2003–2008: Analysis by perpetrator, weapon, time, and location. PLoS Medicine 8 (2): e1000415.CrossRefGoogle Scholar
  28. Hipp, J.R. (2010) A dynamic view of neighborhoods: The reciprocal relationship between crime and neighborhood structural characteristics. Social Problems 57 (2): 205–230.CrossRefGoogle Scholar
  29. Holden, R.T. (1987) Time series analysis of a contagious process. Journal of the American Statistical Association 82 (400): 1019–1026.CrossRefGoogle Scholar
  30. Hough, M., Mayhew, P. and Britain, G. (1983) The British Crime Survey: First Report. London: Her Majesty's Stationery Office.Google Scholar
  31. Iraq Body Count. (2008) Data with spatial information additions supplied by IBC in February 2008.
  32. Izady, M. (2011) Baghdad, Iraq, ethnic composition, 2003–2009,
  33. Jacobs, B.A. and Wright, R. (2006) Street Justice: Retaliation in the Criminal Underworld. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
  34. Johnson, S. (2008) Repeat burglary victimisation: A tale of two theories. Journal of Experimental Criminology 4 (3): 215–240.CrossRefGoogle Scholar
  35. Johnson, S.D. et al (2007) Space-time patterns of risk: A cross national assessment of residential burglary victimization. Journal of Quantitative Criminology 23: 201–219.CrossRefGoogle Scholar
  36. Keizer, K., Lindenberg, S. and Steg, L. (2008) The spreading of disorder. Science 322 (5908): 1681–1685.CrossRefGoogle Scholar
  37. Kilcullen, D. (2009) The Accidental Guerrilla: Fighting Small Wars in the Midst of a Big One. Oxford, UK: Oxford University Press.Google Scholar
  38. Klein, M.W. and Maxson, C.L. (2006) Street Gang Patterns and Policies. New York: Oxford University Press.CrossRefGoogle Scholar
  39. Livingston, M. (2008) Alcohol outlet density and assault: A spatial analysis. Addiction 103 (4): 619–628.CrossRefGoogle Scholar
  40. Luckenbill, D.F. (1977) Criminal homicide as a situated transaction. Social Problems 25 (2): 176–186.CrossRefGoogle Scholar
  41. Malm, A.E., Kinney, B.J. and Pollard, N. (2008) Social network and distance correlates of criminal associates involved in illicit drug production. Security Journal 21 (1): 77–94.CrossRefGoogle Scholar
  42. McCauley, C. and Moskalenko, S. (2008) Mechanisms of political radicalization: Pathways toward terrorism. Terrorism and Political Violence 20 (3): 415–433.CrossRefGoogle Scholar
  43. Miethe, T.D. and Sousa, W.H. (2010) Carjacking and its consequences: A situational analysis of risk factors for differential outcomes. Security Journal 23 (4): 241–258.CrossRefGoogle Scholar
  44. Mohler, G.O., Short, M.B., Brantingham, P.J., Schoenberg, F.P. and Tita, G.E. (2011) Self-exciting point process modeling of crime. Journal of the American Statistical Association 106 (493): 100–108.CrossRefGoogle Scholar
  45. Morenoff, J., Sampson, R. and Raudenbush, S. (2001) Neighborhood inequality, collective efficacy, and the spatial dynamics of urban violence. Criminology 39 (3): 517–558.CrossRefGoogle Scholar
  46. Myung, I.J. (2003) Tutorial on maximum likelihood estimation. Journal of Mathematical Psychology 47 (1): 90–100.CrossRefGoogle Scholar
  47. Ogata, Y. (1988) Statistical models for earthquake occurrences and residual analysis for point-processes. Journal of the American Statistical Association 83 (401): 9–27.CrossRefGoogle Scholar
  48. Ogata, Y. (1998) Space-time point-process models for earthquake occurrences. Annals of the Institute of Statistical Mathematics 50 (2): 379–402.CrossRefGoogle Scholar
  49. Osgood, D.W., Wilson, J.K., O'malley, P.M., Bachman, J.G. and Johnston, L.D. (1996) Routine activities and individual deviant behavior. American Sociological Review 61 (4): 635–655.CrossRefGoogle Scholar
  50. Ozaki, T. (1979) Maximum likelihood estimation of Hawkes' self-exciting point processes. Annals of the Institute of Statistical Mathematics 31: 145–155.CrossRefGoogle Scholar
  51. Rubin, I. (1972) Regular point processes and their detection. IEEE Transactions on Information Theory 18 (5): 547.CrossRefGoogle Scholar
  52. Sampson, R.J. (2011) The community. In: J.Q. Wilson and J. Petersilia (eds.) Crime and Public Policy, 2nd edn. New York: Oxford University Press.Google Scholar
  53. Sampson, R.J., Morenoff, J.D. and Gannon-Rowley, T. (2002) Assessing ‘Neighborhood Effects’: Social processes and new directions in research. Annual Review of Sociology 28: 443–478.CrossRefGoogle Scholar
  54. Sampson, R.J. and Wooldredge, J.D. (1987) Linking the micro- and macro-level dimensions of lifestyle-routine activity and opportunity models of predatory victimization. Journal of Quantitative Criminology 3 (4): 371–393.CrossRefGoogle Scholar
  55. Sanchez-Jankowski, M.S. (1991) Islands in the Street: Gangs and American Urban Society. Berkeley, CA: University of California Press.Google Scholar
  56. Schoenberg, F.P. (2003) Multidimensional residual analysis of point process models for earthquake occurrences. Journal of the American Statistical Association 98 (464): 789–795.CrossRefGoogle Scholar
  57. Schoenberg, F.P., Brillinger, D.R. and Guttorp, P. (2006) Point processes, spatial–temporal. In: A. El Shaarawi and W. Piegorsch (eds.) Encyclopedia of Environmetrics. New York: Wiley.Google Scholar
  58. Short, M.B., D'Orsogna, M.R., Brantingham, P.J. and Tita, G. (2009) Measuring and modeling repeat and near-repeat burglary effects. Journal of Quantitative Criminology 25 (3): 325–339.CrossRefGoogle Scholar
  59. Short, M.B. et al (2008) A statistical model of criminal behavior. Mathematical Models and Methods in Applied Sciences 18 (S1): 1249–1267.CrossRefGoogle Scholar
  60. Silverman, B. (1998) Density Estimation for Statistics and Data Analysis. London: Chapman & Hall.Google Scholar
  61. Taniguchi, T.A., Rengert, G.F. and Mccord, E.S. (2009) Where size matters: Agglomeration economies of illegal drug markets in Philadelphia. Justice Quarterly 26 (4): 670–694.CrossRefGoogle Scholar
  62. Townsley, M., Homel, R. and Chaseling, J. (2003) Infectious burglaries – A test of the near repeat hypothesis. British Journal of Criminology 43 (3): 615–633.CrossRefGoogle Scholar
  63. Townsley, M., Johnson, S.D. and Ratcliffe, J.H. (2008) Space time dynamics of insurgent activity in Iraq. Security Journal 21 (3): 139–146.CrossRefGoogle Scholar
  64. Trickett, A., Osborn, D.R., Seymour, J. and Pease, K. (1992) What is different about high crime areas. British Journal of Criminology 32 (1): 81–89.Google Scholar
  65. Vere-Jones, D. (2009) Some models and procedures for space-time point processes. Environmental and Ecological Statistics 16: 173–195.CrossRefGoogle Scholar
  66. Wortley, R. and McFarlane, M. (2011) The role of territoriality in crime prevention: A field experiment. Security Journal 24 (2): 149–156.CrossRefGoogle Scholar
  67. Wright, R.T. and Decker, S.H. (1994) Burglars on the Job: Streetlife and Residential Breaking. Boston, MA: Northeastern University Press.Google Scholar
  68. Wuthnow, R. (2005) Democratic renewal and cultural inertia: Why our best efforts fall short. Sociological Forum 20 (3): 343–367.CrossRefGoogle Scholar
  69. Zhuang, J., Ogata, Y. and Vere-Jones, D. (2002) Stochastic declustering of space-time earthquake occurrences. Journal of the American Statistical Association 97 (458): 369–380.CrossRefGoogle Scholar

Copyright information

© Palgrave Macmillan, a division of Macmillan Publishers Ltd 2011

Authors and Affiliations

  • Erik Lewis
    • 1
  • George Mohler
    • 2
  • P Jeffrey Brantingham
    • 3
  • Andrea L Bertozzi
    • 1
  1. 1.Department of MathematicsUniversity of California – Los AngelesUSA
  2. 2.Department of Mathematics and Computer ScienceSanta Clara UniversitySanta ClaraUSA
  3. 3.Department of AnthropologyUniversity of CaliforniaLos AngelesUSA

Personalised recommendations