## Bayes’ Rule in Criminal Profiling

The show Criminal Minds has brought a lot of attention to the role of criminal profiling in police investigations. The show highlights the Behavioral Analysis Unit of the FBI and their ability to determine specific characteristics of suspects based on the nature of their crimes. These characteristics are used to narrow down the list of suspects, until eventually the true culprit is detained. This strategy essentially makes use of Bayes’ Rule in an iterative manner. Bayes’ Rule allows the calculation of a probability of an event given prior knowledge of a variable that the event is conditionally dependent on. As new information regarding a crime is obtained, the probabilities of certain characteristics of the “unsub” (unidentified subject) are updated with Bayes’ Rule. In the show, these “calculations” are done empirically by specialized agents and are based solely on the agents’ past experience in the field. In their paper, Baumgartner et al. present an automated database approach to criminal profiling.

The strategy highlighted in the paper utilizes a Bayesian network. A Bayesian network can be visualized with a node map where nodes represent variables and edges depict conditional dependencies between those variables. This type of networks stems from Bayesian probability, which is the interpretation of probability in the sector of statistical theory known as – you guessed it – Bayesian statistics. Bayesian probability is based on the assumption that probabilities are dependent on prior events (read: Bayes’ Rule). It then follows that in a Bayesian network, the strengths of conditional dependencies (edges) would be calculated with the help of the Bayes’ Rule equation.

The variables that Baumgartner et el. use as nodes include “evidence” variables and “offender” variables. The evidence variables are characteristics of the crime scene, such as whether the victim was stabbed, whether arson was involved, etc.  Offender variables are characteristics of the offender, including things like sex crime history, military history, etc. The strengths of edges between nodes were calculated using a combination of expert experience from actual criminal profilers and a database of crime and offender data. The more data, the more iterations of Bayes’ rule can be applied, and the more accurate the relationships between evidence variables and offender variables. Once the preliminary conditional probabilities have been calculated, the network can be immediate used to narrow down criminal profiles in unsolved cases in an automated structure – simply enter evidence/crime scene data and then observe which characteristics are most strongly correlated to those variables. Once in use, the database engine will continue to recalculate conditional probabilities based on new data. This criminal profiling approach is a great example of just how helpful statistics, and specifically Bayes’ Rule, can be in the real world.

Source:

K. Baumgartner et al., Constructing Bayesian networks for criminal profiling from limited data, Knowl. Based Syst. (2008), doi:10.1016/j.knosys.2008.03.019