Statistical modelling of forensic evidence

Abstract

The evaluation of evidence found at a crime scene is primarily conducted through comparison of two competing statistical hypotheses. In forensic science, there is currently no consensus on the formulation of the competing hypotheses. A main point of discussion is the difference between common source and specific source problems. In a common source problem, all evidence is assumed to come from unknown sources, whereas the specific source problem states that one of the sources is fixed. Since the value of evidence is affected by the choice of hypotheses, this thesis tries to shed more light on the statistical framework underlying the common and specific source problem. Both a frequentist and a Bayesian approach can be followed to quantify the value of evidence, resulting in the likelihood ratio and the Bayes Factor, respectively. The theoretical framework is put into practice through two frequently used models in forensic science, namely the continuous two-level normal-normal model and the discrete one-level Bernoulli model. Since calculation of the Bayes Factor for the two-level normal-normal model cannot be done analytically, Markov Chain Monte Carlo methods are proposed and the theoretical convergence properties of the resulting methods are discussed. An explicit expression of the Bayes Factor does exist for the one-level Bernoulli model. For both models, more conservative values of the Bayes Factor are observed within the common source problem than in the specific source problem. Two approaches are considered to calculate the posterior probability of guilt and explicit bounds are derived for the difference between both techniques applied to the one-level Bernoulli model. The opportunities and challenges of a copula-based method and permutation tests are discussed as alternatives to the models generally used in evaluating forensic evidence.