A Mixture Model for the Number of Gunshot Residues Found on Suspects' Hands

Quantifying the strength of gunshot residue (GSR) evidence requires scientific knowledge about the number of particles expected to be found on individuals who were or were not involved in a shooting. However, controlled experiments demand expensive resources in terms of microscope time and labor, which restricts the data of most studies to only a small group of individuals. We suggest a novel method that exploits data collected routinely on suspects during the daily work of forensic laboratories. These observational data relate to both persons who were involved in a shooting and innocent individuals. We suggest a mixture approach with different models for the number of gunshot residue particles in each group and develop an iterative algorithm to estimate the probabilities of observing the evidence under the defense proposition that the suspect is innocent and under the prosecution assumption that he is not. The method is applied to data of more than 500 suspects collected by the Israel National Police Division of Identification and Forensic Science. The analysis shows that the probability of finding three or more GSR particles on the hands of innocent suspects is very small, less than 1.5 in 1000 cases. Our new method enables researchers to use data on real cases, possibly supplemented by experimental data, in order to estimate the probabilities of a given GSR finding under the defense and prosecution propositions.