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

Probabilistic evidential assessment of gunshot residue particle evidence (Part II): Bayesian parameter estimation for experimental count data

“…Following the arguments mentioned earlier in Part I of this series of papers [2], the numerator coincides with the probability distribution of a Poisson variable with parameter l H p ¼ a H p =b H p :…”

“…For the purpose of the current example, suppose there is a study in which samples from m = 5 individuals were examined with a total of P m i r i ¼ 29 GSR particles being found. 2 Besides these data, the scientist considersinitially -all positive values of l with equal degrees of belief. The latter standpoint can be conceptualised in terms of the positive uniform density…”

“…When applied to a case, it is crucial that the same kind of activity is considered. 2 Notice that, in order to distinguish these data from the actual data collected by the scientist, the number of samples and the number of counts per sample i are described by, respectively, m and r i . 3 It must be emphasised that the positive uniform prior is not a true density function because it does not integrate to 1 (this is also called an 'improprer' prior).…”

Statistical Challenges in the Quantification of Gunshot Residue Evidence

“… discussed in detail the use of Bayesian network (BN) models to calculate LRs and posterior probabilities in light of particular GSR evidence. In , they used the experimental data from the study conducted by Cardinetti et al. to obtain likelihood values for observed numbers of particles under a variety of settings.…”

“…The background (or secondary) exposure to GSR particles is an important factor that needs to be explicitly considered when calculating the statistical strength of evidence. In , a BN node corresponding to the status of background contamination ( B ) was suggested with the following four categories: none , low , medium , high . Here, we use the same categories and the corresponding conditional probability distributions.…”