Graphical Modelling and Statistical Learning for Sex-related Homicides

Abstract

We present a twofold analysis in the domain of sex–related homicides. Police profilers often help in criminal investigation of high profile cases, but empirical evidence in the domain is incomplete. We therefore at first apply a structural learning approach and secondly, try explicitly to predict the age of an unknown offender from information obtained from the crime scene. We apply graphical modelling to obtain a factorisation of the probability function which governs the domain. This factorisation allows us to infer dependencies and independencies between the variables and therefore describes the domain. We apply several structure learning algorithms for Bayesian Networks and combine them to a final graphical model. In the second part, we compare several prediction techniques concerning their error rate in predicting the offender’s age. The graphical model broadly presents a distinction between an offender and a situation driven crime. A situation driven crime may be characterised by an offender lacking preparation and typically attacking a known victim in familiar surroundings. The offender tends to apply blunt force to gain control over the victim and does not show a high level of forensic awareness. In contrast offender driven crimes may be identified by the high level of forensic awareness demonstrated by the offender and the sophisticated measures applied to control the victim. Furthermore the graphical model indicates that these offenders are more likely to attack an unknown victim in unfamiliar surroundings and prepare their attack. Applying several prediction techniques to the date results in a significant decrease in the root mean square error, if compared with a simple baseline model. However the actual performance of the best model, namely the lasso, is still not applicable in criminal investigation, as it its average error of 8 years is too high.