Evaluation of evidence for autocorrelated data, with an example relating to traces of cocaine on banknotes

Abstract

Much research in recent years for evidence evaluation in forensic science has focussed on methods for determining the likelihood ratio in various scenarios. One proposition concerning the evidence is put forward by the prosecution and another is put forward by the defence. The likelihood of each of these two propositions is calculated, given the evidence. The likelihood ratio, or value of the evidence, is then given by the ratio of the likelihoods associated with these two propositions. The aim of this research is twofold. Firstly, it is intended to provide methodology for the evaluation of the likelihood ratio for continuous autocorrelated data. The likelihood ratio is evaluated for two such scenarios. The first is when the evidence consists of data which are autocorrelated at lag one. The second, an extension to this, is when the observed evidential data are also believed to be driven by an underlying latent Markov chain. Two models have been developed to take these attributes into account, an autoregressive model of order one and a hidden Markov model, which does not assume independence of adjacent data points conditional on the hidden states. A nonparametric model which does not make a parametric assumption about the data and which accounts for lag one autocorrelation is also developed. The performance of these three models is compared to the performance of a model which assumes independence of the data. The second aim of the research is to develop models to evaluate evidence relating to traces of cocaine on banknotes, as measured by the log peak area of the ion count for cocaine product ion m/z 105, obtained using tandem mass spectrometry. Here, the prosecution proposition is that the banknotes are associated with a person who is involved with criminal activity relating to cocaine and the defence proposition is the converse, which is that the banknotes are associated with a person who is not involved with criminal activity relating to cocaine. Two data sets are available, one of banknotes seized in criminal investigations and associated with crime involving cocaine, and one of banknotes from general circulation. Previous methods for the evaluation of this evidence were concerned with the percentage of banknotes contaminated or assumed independence of measurements of quantities of cocaine on adjacent banknotes. It is known that nearly all banknotes have traces of cocaine on them and it was found that there was autocorrelation within samples of banknotes so thesemethods are not appropriate. The models developed for autocorrelated data are applied to evidence relating to traces of cocaine on banknotes; the results obtained for each of the models are compared using rates of misleading evidence, Tippett plots and scatter plots. It is found that the hiddenMarkov model is the best choice for themodelling of cocaine traces on banknotes because it has the lowest rate of misleading evidence and it also results in likelihood ratios which are large enough to give support to the prosecution proposition for some samples of banknotes seized from crime scenes. Comparison of the results obtained for models which take autocorrelation into account with the results obtained from the model which assumes independence indicate that not accounting for autocorrelation can result in the overstating of the likelihood ratio.