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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.

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99 percentile (55 units) Units of cocaine found on notes possessed by non drug users/dealers Suppose this is the distribution of levels of cocaine found on notes in possession of 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. The standard approach

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Units of cocaine found on notes possessed by drug users/dealers We need the distribution of levels of cocaine found on notes in possession of drug users/dealers Suppose it looks like this 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% Additional information needed

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So, this is the full prior model you need This is a Bayesian network This is the distribution of levels of cocaine found on all banknotes. Note this is a bimodal distribution In any given case these distributions actually represent our prior probability beliefs.

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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%

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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.

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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.

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