Download Drug trace evidence on banknotes Norman Fenton, July 2011

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
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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.