Saturday, April 14, 2012

A Test of Empirical Bayes Journey-to-Crime Estimation in The Hague

In the article, “Finding a Serial Burglar’s Home Using Distance Decay and Conditional Origin–Destination Patterns: A Test of Empirical Bayes Journey-to-Crime Estimation in The Hague”, the authors test a new method, empirical Bayes journey-to-crime estimation, to estimate where an offender lives from where he or she commits crimes. In the new method, the profiler not only asks ‘what distances did previous offenders travel between their home and the crime scenes’ but also ‘where did previous offenders live who offended at the locations included in the crime series I investigate right now?’.

The empirical Bayes method uses not only the distance of the journey to crime, but also exploits our knowledge of origins (where did previous offenders live) and destinations (where did they offend), and the links between them to predict the home of a serial offender. It uses more specific information about past offenders. In contradistinction from previous methods, distance does not completely dictate the outcome of the prediction. Thus, given distance, if some destinations have been associated with a particular origin relatively frequently in the past, the new method will identify that particular origin as a likely home area of the offender.

The Bayes journey-to-crime estimation is an extension of its earlier distance-based. Based on connections between offenders and the incidents they committed, three risk surfaces are calculated:
  1. The first risk surface is the risk surface generated by the regular journey-to-crime/distance decay      method in CrimeStat (labeled distance decay risk surface & P(JTC)).
  2. The second is a ‘usual suspects’ risk surface by prioritizes zones where previous offenders lived, independent of where they committed their crimes and independent of the location of the crimes in the series of the offender that is being searched (labeled the general risk surface & P(O))
  3. The third risk surface is based on the origin-destination zone matrix (labeled conditional probability risk surface & P(O|JTC)).
The empirical Bayes journey-to-crime method generates two other risk surfaces by combining the above three risk surfaces. One of these two combination surfaces is the product risk surface, which explicitly recognizes both distance decay and the home-to-incident histories of prior offenders. The product surface is mathematically the numerator of the other combination surface, the Bayesian risk probability. The Bayesian risk surface is calculated by the application of the Bayes’ formula:
Thus, in addition to the three basic risk surfaces distance decay, general, and conditional, in this paper, two combination risk surfaces, product and Bayesian risk, are analyzed.

Based on the study of 62 burglars, the homes of serial burglars were more successfully estimated with the new conditional risk surface than with the other risk surfaces. The method demonstrated may seem complex, but the authors are confident that in practice it will not be. The authors do state that there are disadvantages with using Bayes method which includes that the new method requires more data, more upfront work and may only be applied to relatively common crimes such as burglary or robbery.

Block, R., & Bernasco, W. (2009). Finding a serial burglar's home using distance decay and conditional origin–destination patterns: a test of empirical Bayes journey-to-crime estimation in the Hague. Journal Of Investigative Psychology & Offender Profiling, 6(3), 187-211. doi:10.1002/jip.108. Received from


  1. Excellent article and application of Bayes. Could this be extended to not only include where the offender lived and where the offense occurred? For example could M.O. be included into the model so that it might be observed that offenders who commit crime with weapons are doing it further from where the lived?

  2. It would be interesting to see this in action. Given how some law enforcement agencies may not have the best records, the applicability may be limited. However, for larger jurisdictions, this could prove to be more accurate than other methods.

  3. I suspect this could be (and probably -is-) applied to localized terrorist/resistance activities in areas like the middle east. The crime may be a bombing rather than a burglary, but some of the patterns should still show some similarity.

  4. So I know that the method required more data than traditional methods, so as long as the bombing in the Middle East had enough data on it, then I would imagine using this method would be useful.

  5. This is a great application of Bayes, though moderately abstract and semi-freak-o-nomics-esque. It would be interesting to see this used in a real case and then brought up in court as a piece of evidence.