The Annals of Applied Statistics

Self-exciting hurdle models for terrorist activity

Michael D. Porter and Gentry White

Full-text: Open access

Abstract

A predictive model of terrorist activity is developed by examining the daily number of terrorist attacks in Indonesia from 1994 through 2007. The dynamic model employs a shot noise process to explain the self-exciting nature of the terrorist activities. This estimates the probability of future attacks as a function of the times since the past attacks. In addition, the excess of nonattack days coupled with the presence of multiple coordinated attacks on the same day compelled the use of hurdle models to jointly model the probability of an attack day and corresponding number of attacks. A power law distribution with a shot noise driven parameter best modeled the number of attacks on an attack day. Interpretation of the model parameters is discussed and predictive performance of the models is evaluated.

Article information

Source
Ann. Appl. Stat. Volume 6, Number 1 (2012), 106-124.

Dates
First available in Project Euclid: 6 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1331043390

Digital Object Identifier
doi:10.1214/11-AOAS513

Mathematical Reviews number (MathSciNet)
MR2951531

Zentralblatt MATH identifier
1316.62186

Keywords
Self-exciting hurdle model shot noise terrorism Indonesia Hawkes process Riemann zeta point process probability gain

Citation

Porter, Michael D.; White, Gentry. Self-exciting hurdle models for terrorist activity. Ann. Appl. Stat. 6 (2012), no. 1, 106--124. doi:10.1214/11-AOAS513. https://projecteuclid.org/euclid.aoas/1331043390


Export citation

References

  • Baddeley, A. J., Møller, J. and Waagepetersen, R. (2000). Non- and semi-parametric estimation of interaction in inhomogeneous point patterns. Stat. Neerl. 54 329–350.
  • Barros, C. P. (2003). An intervention analysis of terrorism: The Spanish ETA case. Defence and Peace Economics 6 401–412.
  • Belasco, A. (2010). The cost of Iraq, Afghanistan, and other Global War on Terror Operations Since 9/11. Technical Report RL33110, Congressional Research Services. Available at http://www.fas.org/sgp/crs/natsec/RL33110.pdf.
  • Clauset, A., Shalizi, C. R. and Newman, M. E. J. (2009). Power-law distributions in empirical data. SIAM Rev. 51 661–703.
  • Clauset, A., Young, M. and Gleditsch, K. S. (2007). On the frequency of severe terrorist events. Journal of Conflict Resolution 51 58–87.
  • Daley, D. J. and Vere-Jones, D. (2003). An Introduction to the Theory of Point Processes. I, 2nd ed. Springer, New York.
  • Daley, D. J. and Vere-Jones, D. (2004). Scoring probability forecasts for point processes: The entropy score and information gain. J. Appl. Probab. 41A 297–312.
  • Diggle, P. J. (1979). On parameter estimation and goodness-of-fit testing for spatial point patterns. Biometrics 35 87–101.
  • Diggle, P. (1985). A kernel method for smoothing point process data. J. R. Stat. Soc. Ser. C. Appl. Stat. 34 138–147.
  • Dixon, P. M. (2002). Ripley’s K function. In Encyclopedia of Econometrics (A. H. El-Shaarawi and W. W. Piegorsch, eds.) 2 1796–1803. Wiley, Chichester.
  • Dugan, L., LaFree, G. and Piquero, A. (2005). Testing a rational choice model of airline hijiackings. Criminology 43 1031–1066.
  • Enders, W. and Sandler, T. (1993). The effectiveness of antiterrorism policies: A vector-autoregression-intervention analysis. The American Political Science Review 4 829–844.
  • Enders, W. and Sandler, T. (2000). Is transnational terrorism becoming more threatening? Journal of Conflict Resolution 44 307–332.
  • Enders, W. and Sandler, T. (2002). Patterns of transnational terrorism, 1970–1999: Alternative time-series estimates. International Studies Quarterly 2 145–165.
  • Enders, W. and Sandler, T. (2006). The Polictical Economy of Terrorism. Cambridge Univ. Press, New York.
  • Goldstein, M. L., Morris, S. A. and Yen, G. G. (2004). Problems with fitting to the power-law distribution. Eur. Phys. J. B 41 255–258.
  • Hawkes, A. G. (1971). Spectra of some self-exciting and mutually exciting point processes. Biometrika 58 83–90.
  • Hawkes, A. G. and Oakes, D. (1974). A cluster process representation of a self-exciting process. J. Appl. Probab. 11 493–503.
  • Heard, N. A., Weston, D. J., Platanioti, K. and Hand, D. J. (2010). Bayesian anomaly detection methods for social networks. Ann. Appl. Stat. 4 645–662.
  • Heilbron, D. C. (1994). Zero-altered and other regression models for count data with added zeros. Biom. J. 36 531–547.
  • Holden, R. T. (1986). The contagiousness of aircraft hijacking. The American Journal of Sociology 91 874–904.
  • Holden, R. T. (1987). Time series analysis of a contagious process. J. Amer. Statist. Assoc. 82 1019–1026.
  • Jones, A. M. (1994). Health, addiction, social interaction and the decision to quit smoking. Journal of Health Economics 13 93–110.
  • LaFree, G. and Dugan, L. (2007). Introducing the global terrorism database. Terrorism and Political Violence 19 181–204.
  • LaFree, G., Dugan, L. and Korte, R. (2009). The impact of British counter terrorist strategies on political violence in Northern Ireland: Comparing deterrence and backlash models. Criminology 47 17–45.
  • LaFree, G., Morris, N. A. and Dugan, L. (2010). Cross-national patterns of terrorism: Comparing trajectories for total, attributed and fatal attacks, 1970–2006. British Journal of Criminology 50 622–649.
  • Lambert, D. (1992). Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics 34 1–14.
  • Li, R. P. and Thompson, W. R. (1975). The “Coup contagion” hypothesis. The Journal of Conflict Resolution 19 63–88.
  • Lum, C., Kennedy, L. W. and Sherley, A. J. (2006). Are counter-terrorism strategies effective? The results of the Campbell systematic review on counter-terrorism evaluation research. Journal of Experimental Criminology 2 489–516.
  • Marschall, M. J., Ruhil, V. S. Anirudh and Shah, P. R. (2010). The new radical calculus: Electoral institutions and black representation in local legislatures. American Journal of Political Science 54 107–124.
  • Midlarsky, M. I. (1978). Analyzing diffusion and contagion effects: The urban disorders of the 1960s. The American Political Science Review 72 996–1008.
  • Midlarsky, M. I., Crenshaw, M. and Yoshida, F. (1980). Why violence spreads: The contagion of international terrorism. International Studies Quarterly 24 341–365.
  • Mohler, G. O., Short, M. B., Brantingham, P. J., Schoenberg, F. P. and Tita, G. E. (2011). Self-exciting point process modeling of crime. J. Amer. Statist. Assoc. 106 100–108.
  • Mullahy, J. (1986). Specification and testing of some modified count data models. J. Econometrics 33 341–365.
  • Myers, D. J. (2000). The diffusion of collective violence: Infectiousness, susceptibility, and mass media networks. American Journal of Sociology 106 178–208.
  • Nagin, D. (2005). Group-Based Modeling of Development. Harvard Univ. Press, Cambridge, MA.
  • Ozaki, T. (1979). Maximum likelihood estimation of Hawkes’ self-exciting point processes. Ann. Inst. Statist. Math. 31 145–155.
  • Perl, R. (2007). Combating terrorism: The challenge of measuring effectiveness. Technical Report RL33160, Congressional Research Services. Available at http://fpc.state.gov/documents/organization/57513.pdf.
  • Price, J. C. and Forrest, J. S. (2009). Practical Aviation Security: Predicting and Preventing Future Threats. Butterworth-Heinemann, Oxford, UK.
  • R Development Core Team. (2011). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.
  • Rice, J. (1977). On generalized shot noise. Adv. in Appl. Probab. 9 553–565.
  • Seal, H. L. (1952). The maximum likelihood fitting of the discrete Pareto law. Journal of the Institute of Actuaries 78 115–121.
  • Townsley, M., Johnson, S. D. and Ratcliffe, J. H. (2008). The time dynamics of insurgent activity in Iraq. Security Journal 21 139–146.
  • Veen, A. and Schoenberg, F. P. (2006). Assessing spatial point process models using weighted K-functions: Analysis of California earthquakes. In Case Studies in Spatial Point Process Modeling (A. Baddeley, P. Gregori, J. Mateu, R. Stoica and D. Stoyan, eds.). Lecture Notes in Statist. 185 293–306. Springer, New York.
  • Welsh, A., Cunninham, R. B., Donnelly, C. F. and Lindenmayer, D. B. (1996). Methods for analysing data with extra zero: ZIP regression models with application for surveys of rare species. Ecological Modelling 88 297–308.