A proposal for statistical evaluation of the detection of gunshot residues on a suspect

The possibility of accidental contamination of a suspect by gunshot residues (GSRs) is considered. If two hypotheses are taken into account ("the suspect has shot a firearm" and "the suspect has not shot a firearm"), the likelihood ratio of the conditional probabilities of finding a number n of GSRs is defined. Choosing two Poisson distributions, the parameter lambda of the first one coincides with the mean number of GSRs that can be found on a firearm shooter, while the parameter mu of the second one is the mean number of GSRs that can be found on a nonshooter. In this scenario, the likelihood ratio of the conditional probabilities of finding a number n of GSRs in the two hypotheses can be easily calculated. The evaluation of the two parameters lambda and mu and of the goodness of the two probability distributions is performed by using different sets of data: "exclusive" lead-antimony-barium GSRs have been detected in two populations of 31 and 28 police officers at diverse fixed times since firearm practice, and in a population of 81 police officers who stated that they had not handled firearms for almost 1 month. The results show that the Poisson distributions well fit the data for both shooters and nonshooters, and that the probability of detection of two or more GSRs is normally greater if the suspect has shot firearms.