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Drug trace evidence on banknotes Norman Fenton, July 2011 • Small quantities of drugs are found on many banknotes in distribution • But if ‘abnormally high’ trace levels are found then this is used as evidence that the person in possession of the notes is a drug dealer (or drug user). • What follows is a very simplified view of why the ‘standard’ analysis is usually flawed. The ‘standard’ approach 99 percentile (55 units) Suppose this is the distribution of levels of cocaine found on notes in possession of non drug users/dealers Units of cocaine found on notes possessed by non drug users/dealers Suppose a randomly selected banknote in the possession of Joe Bloggs is found to have 56 units of cocaine Question: Can we reject the hypothesis that Joe Bloggs is not a drug dealer/user? Answer (according to ‘standard’ approaches): Yes, as there is a less than 1% chance that a randomly selected note in the possession of a non drug user/dealer will have more than 55 units of cocaine. Additional information needed We need the distribution of levels of cocaine found on notes in possession of drug users/dealers Suppose it looks like this Units of cocaine found on notes possessed by drug users/dealers We also need to know the proportion of people who are drug users/dealers. Suppose it is 20% (in reality it is less, but even with this generous figure we can show the previous conclusion if fundamentally flawed). Hence we are assuming the following ‘prior’ probabilities for the hypothesis “Person is a non drug user/dealer” True: 80% False: 20% So, this is the ‘full’ prior model you need This is a Bayesian network In any given case these distributions actually represent our ‘prior’ probability beliefs. This is the distribution of levels of cocaine found on all banknotes. Note this is a ‘bimodal’ distribution The result with Bayesian updating 1. We observe the bank note has 56 units of cocaine 2. This results in a revised belief about the probability Joe is not a drug dealer/user. But the probability is still greater than 50% So is Joe not a drug dealer/user? (given the evidence of the banknote) • With the ‘standard’ approach we ‘reject’ the above null hypothesis with ‘high significance’ (p-value 0.01). This is also often misintepreted as meaning there is a greater than 1% chance Joe is a drug dealer/user. • But with the (proper) Bayesian approach our belief in Joe not being a drug dealer is 52% (reduced from a prior of 80%). • So the ‘evidence’ is relevant but, contrary to what the ‘standard’ approach suggests is a very long way from enabling you to ‘reject’ the hypothesis. References • • • • • • • • Sleeman, R., I. Fletcher, A. Burton, J. F. Carter and D. J. Roberts (1999). "Rapid screening of banknotes for the presence of controlled substances by thermal desorption atmospheric pressure chemical ionisation tandem mass spectrometry." Analayst 124(103-108). (2004). R v Benn and Benn, Court of Appeal (Criminal Division), EWCA Crim 2100 (2008). Smith v HM Advocate, HIGH COURT OF JUSTICIARY, HCJAC 7 (2004). Regina v Simon Fleur EWCA Crim 2372 (2002). R v Compton, Compton and Compton, EWCA Crim 2835 Carter, J. F., R. Sleeman and J. Parry (2003). "The distribution of controlled drugs on banknotes via counting machines " Forensic Science International 132 106-112. Ebejer, K. A., G. R. Lloyd, R. G. Brereton, J. F. Carter and R. Sleeman (2007). "Factors influencing the contamination of UK banknotes with drugs of abuse " Forensic Science International 171. Ebejer, K. A., J. Winn, et al. (2007). "The difference between drug money and a lifetime's savings?" Forensic Science International 167: 94-101.