Calculation of likelihood ratios for gunshot residue evidence-statistical aspects

Recently published articles have proposed the use of likelihood ratios (LRs) in determining the evidential value of finding a given number of gunshot residue (GSR) particles on a suspect. LRs depend on the probabilistic models assumed for the defence proposition (the suspect was not involved in a shooting) and the prosecutor's proposition (the suspect was involved), and should be calculated based on data obtained in well designed experiments. However, statistical aspects of the analysis that select the appropriate model and provide uncertainty measures are rarely considered. In this article, data from Cardinetti et al. (2006, A proposal for statistical evaluation of the detection of gunshot residues on a suspect. Scanning, 28(3):142-147) are used to demonstrate the sensitivity of calculated LRs to the assumed model. It is shown that the Poisson model, considered by Cardinetti and others, is inappropriate and that a Negative Binomial model fits the data much better. The statistical error arising from the fact that models are estimated based on small sampled data is discussed, as well as the importance of accounting for this error. We conclude that only with a large database can statistical models be estimated accurately and LR's be treated as valid scientific measures.