Temporal Hawkes Process for Modeling Short-Term Clustering of Crime Events in Ostrava
By: Lukáš Pospíšil, Karolina Dlouhá and Radomír Ščurek
References
- Eck, J.E., Chainey, S., Cameron, J.G., Leitner, M., & Wilson, R.E. (2005). Mapping crime: Understanding hot spots. National Institute of Justice.
- Chainey, S., Tompson, L., & Uhlig, S. (2008). The utility of hotspot mapping for predicting spatial patterns of crime. Security Journal, 21, pp. 4-28.
- Weisburd, D. (2015). The law of crime concentration and the criminology of place. Criminology, 53(2), pp. 133-157.
- Braga, A.A., Turchan, B., Papachristos, A.V., & Hureau, D.M. (2019). Hot spots policing and crime reduction: An update of an ongoing systematic review and meta-analysis. Journal of Experimental Criminology, 15(3), pp. 289-311.
- Johnson, S.D., Bernasco, W., Bowers, K.J., Elffers, H., Ratcliffe, J., Rengert, G., & Townsley, M. (2007). Space-time patterns of risk: A cross national assessment of residential burglary victimization. Journal of Quantitative Criminology, 23, pp. 201-219.
- Bowers, K.J., Johnson, S.D., & Pease, K. (2004). Prospective hot-spotting: The future of crime mapping? British Journal of Criminology, 44(5), pp. 641-658.
- Johnson, S.D., & Bowers, K.J. (2004). The burglary as clue to the future: The beginnings of prospective hot-spotting. European Journal of Criminology, 1(2), pp. 237-255.
- Perry, W.L., McInnis, B., Price, C.C., Smith, S.C., & Hollywood, J.S. (2013). Predictive policing: The role of crime forecasting in law enforcement operations. Santa Monica, CA: RAND Corporation.
- Ratcliffe, J.H. (2006). A temporal constraint theory to explain opportunity-based spatial offending patterns. Journal of Research in Crime and Delinquency, 43(3), pp. 261-291.
- Brantingham, P.L., & Brantingham, P.J. (1993). Environment, routine, and situation: Toward a pattern theory of crime. In R.V. Clarke & M. Felson (Eds.), Routine activity and rational choice: Advances in criminological theory (Vol. 5, pp. pp. 259-294). New Brunswick, NJ: Transaction Publishers.
- Daley, D.J., & Vere-Jones, D. (2003). An introduction to the theory of point processes (2nd ed.). Springer.
- Hawkes, A.G. (1971). Spectra of some self-exciting and mutually exciting point processes. Biometrika, 58(1), pp. 83-90.
- Hawkes, A.G., & Oakes, D. (1974). A cluster process representation of a self-exciting process. Journal of Applied Probability, 11(3), pp. 493-503.
- Reinhart, A. (2018). A review of self-exciting spatio-temporal point processes and their applications. Statistical Science, 33(3), pp. 299-318.
- Mohler, G.O., Short, M.B., Brantingham, P.J., Schoenberg, F.P., & Tita, G.E. (2011). Self-exciting point process modeling of crime. Journal of the American Statistical Association, 106(493), pp. 100-108.
- Short, M.B., D’Orsogna, M.R., Pasour, V.B., Tita, G.E., Brantingham, P.J., Bertozzi, A.L., & Chayes, L.B. (2008). A statistical model of criminal behavior. Mathematical Models and Methods in Applied Sciences, 18(Suppl. 1), pp. 1249-1267.
- Short, M.B., D’Orsogna, M.R., Brantingham, P.J., & Tita, G.E. (2009). Measuring and modeling repeat and near-repeat burglary effects. Journal of Quantitative Criminology, 25(3), pp. 325-339.
- Ozaki, T. (1979). Maximum likelihood estimation of Hawkes’ self-exciting point processes. Annals of the Institute of Statistical Mathematics, 31(1), pp. 145-155.
- Ogata, Y. (1988). Statistical models for earthquake occurrences and residual analysis for point processes. Journal of the American Statistical Association, 83(401), pp. 9-27.
- Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), pp. 716-723.
- Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), pp. 461-464.
- Cox, D.R., & Lewis, P.A.W. (1966). The statistical analysis of series of events. London: Methuen.
- Lima, R. (2023). Hawkes processes modeling, inference, and control: An overview. SIAM Review, 65(2), pp. 331-376.
- Bacry, E., Mastromatteo, I., & Muzy, J.-F. (2015). Hawkes processes in finance. Market Microstructure and Liquidity, 1(1), 1550005.
- Police of the Czech Republic. (2026). Crime map: Publicly available crime statistics [Online]. Available at: https://mapakriminality.cz (Accessed: 21 May 2026).
Language: English
Page range: 444 - 452
Submitted on: May 1, 2026
Accepted on: Jul 1, 2026
Published on: Aug 6, 2026
Published by: STE Group sp. z.o.o.
In partnership with: Paradigm Publishing Services
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© 2026 Lukáš Pospíšil, Karolina Dlouhá, Radomír Ščurek, published by STE Group sp. z.o.o.
This work is licensed under the Creative Commons Attribution-NonCommercial 4.0 License.