This imaginary exercise is to illustrate a point I have been making for some time about the Shirley McKie perjury allegation. A fingerprint investigation is normally started because a crime has taken place. In the McKie case the match between her and "latent" (crime scene) print Y7 came first, then a new previously unimagined offence - that she entered the crime scene without permission - was suggested to explain the match. Statistical theory suggests that if the error rate is not zero then using fingerprints to find acts of wrongdoing (rather than to solve pre-existing crimes) is asking for trouble. A few minutes with some "back of envelope" type calculations will make this clear.
Imagine we know that the error rate of fingerprinting, after verification, is one per million identifications. A fingerprint team walks the streets of towns going into every location and identifying people from latent prints. If any identified person denies having deposited a print they will be accused of lying.
The first town they go to is Innocentville where very few crimes occur. When identified nearly everyone is happy to agree that they deposited the print so most of the 999,999 good identifications are used up identifying innocent people. At the end of 1 million identifications they have only found 5 people who deny having deposited a print. It doesn’t seem much to account for all that work and they are uncomfortable to think that they have wrongly accused one of the 5 of lying.
For the next million identifications the fingerprint team go to Badville. Crime is rife here so instead of finding 5 people denying depositing a print they find 25. In Badville the error rate of accusations is 1 in 25 compared with 1 in 5 for Innocentville. Same fingerprint team, same quality of fingerprint work, same identification error rate but different accusation error rate. What is different between the two towns is the proportion of latent prints where the person who deposited it will lie because they have something to hide (this is the “prior probability” of Bayes Theorem).
To reduce the error rate of accusations to a safe level we need to further increase the number of identifications of people who will deny depositing their print because they have something to hide. The places where you are most likely to find latent prints of people who lie are crime scenes. Even in Badville only one location in every two hundred recently had a crime occur in it so if the fingerprint team restrict their activities to crime scenes their error rate of accusations will drop from one in 25 to one in 5,000.
If we are in a crime scene and an identification leads to someone being accused of something other than the crime which originated the investigation, we don’t know for sure that this new alleged act of wrongdoing has happened. This is the equivalent of walking the streets looking for crimes to become apparent out of fingerprint identifications. The error rate for this type of accusation could be as low as 1 in 5 rather than 1 in 5,000 for accusations connected with the crime under investigation (with the same identification error rate). The next stage will be to look for independent evidence about the alternative act of wrongdoing - including whether it has occurred. If no evidence emerges then I would say that the odds of 1 in 5 come down even further, to 1 in 2 or maybe we should just accept that the most likely explanation for the person denying having deposited the print is that they are telling the truth.
Accusing Shirley McKie of lying with no independent evidence to suggest that the act she is accused of has happened represents an unauthorised and untested departure from standard fingerprint practise. If someone involved in the case had been trained to be aware of the risks, then an intervention would have been possible to prevent costly mistakes.
Steve Horn
Computer Programmer working in the field of statistics for industry
West Lothian
Last update 10 August 2007
Bayes Theorem and the Shirley McKie case explains the theorem as it applies to this case. You can see how simple statistical theory arrives at the same conclusions as the above.
Another non-mathematical essay about the case is here
The Prosecutor’s Fallacy is another route to the same conclusion.
I have distilled out six logical points relevant to this case.
Some thoughts about verification.