Journal of Quantitative Criminology

, Volume 30, Issue 1, pp 57–78 | Cite as

Bayesian Spatio-Temporal Modeling for Analysing Local Patterns of Crime Over Time at the Small-Area Level

  • Jane Law
  • Matthew Quick
  • Ping Chan
Original Paper



Explore Bayesian spatio-temporal methods to analyse local patterns of crime change over time at the small-area level through an application to property crime data in the Regional Municipality of York, Ontario, Canada.


This research represents the first application of Bayesian spatio-temporal modeling to crime trend analysis at a large map scale. The Bayesian model, fitted by Markov chain Monte Carlo simulation using WinBUGS, stabilized risk estimates in small (census dissemination) areas and controlled for spatial autocorrelation (through spatial random effects modeling), deprivation, and scarce data. It estimated (1) (linear) mean trend; (2) area-specific differential trends; and (3) (posterior) probabilities of area-specific differential trends differing from zero (i.e. away from the mean trend) for revealing locations of hot and cold spots.


Property crime exhibited a declining mean trend across the study region from 2006 to 2007. Variation of area-specific trends was statistically significant, which was apparent from the map of (95 % credible interval) differential trends. Hot spots in the north and south west, and cold spots in the middle and east of the region were identified.


Bayesian spatio-temporal analysis contributes to a detailed understanding of small-area crime trends and risks. It estimates crime trend for each area as well as an overall mean trend. The new approach of identifying hot/cold spots through analysing and mapping probabilities of area-specific crime trends differing from the mean trend highlights specific locations where crime situation is deteriorating or improving over time. Future research should analyse trends over three or more periods (allowing for non-linear time trends) and associated (changing) local risk factors.


Probability mapping Crime trends Hot spots Bayesian hierarchical models Spatio-temporal Spatial 



This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) through grant number RGPIN-371625-2009. We gratefully acknowledge the York Regional Police for the crime data. Without their support and understanding in providing the necessary crime data, this research would not be possible. Analysis was based on data and digital maps from the Statistics Canada Canadian Census 2006. We express thanks to the anonymous referees for their very constructive comments.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of PlanningUniversity of WaterlooWaterlooCanada
  2. 2.School of Public Health and Health SystemsUniversity of WaterlooWaterlooCanada
  3. 3.Trinity Hall CollegeUniversity of CambridgeCambridgeUK

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