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

Abstract

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.

Probabilistic evidential assessment of gunshot residue particle evidence (Part I): Likelihood ratio calculation and case pre-assessment using Bayesian networks

“…The study of Cardinetti et al [11] covers essentially two points. One part of the study argues that GSR evidence should be assessed through the use of a likelihood ratio.…”

“…Probability assignments of this kind are commonly used for specifying the components of likelihood ratios that provide a measure of the degree to which particular evidence allows one to discriminate between a set of target propositions. Section 3 will begin by considering an existing formative likelihood ratio approach for GSR evidence assessment, proposed by Cardinetti et al [11]. This approach will be used for initiating the discussion of probabilistic reasoning about GSR particle evidence and the use of Bayesian networks for this purpose, introduced later in Section 4.…”

“…In order to obtain a value for V, assessments are needed for PrðyjH p Þ and PrðyjH d Þ. Cardinetti et al [11] suggest that the number y of GSR particles may be modelled through a Poisson distribution, that is: The subscript t in l p;t;s is an indicator for the time (in hours) elapsed between the discharge of the firearm and the moment at which the sample is collected. The subscript s refers to a particular experimental setting (abbreviated here A and B) for which data are available and on the basis of which the Poisson parameter is estimated (see also below).…”

“…Cardinetti et al [11] conducted a series of experiments in order to obtain estimates for l p;t;s and l d . In particular, the authors report two series of experiments (referred to as 'Setting A' and 'Setting B' 3 ) in which samples were taken -after various intervals of time t-from individuals that discharged firearms under controlled conditions.…”

“…Details are given in Table 2. The authors in [11] chose the sample means (that is, maximum likelihood estimates) as point estimators of the Poisson parameter.…”