Crime scenes, DNA and the prosecutor’s fallacy

Although we’ve only got a small statistics research group here at the University of Edinburgh, they get up to some pretty interesting stuff. Today I met with Colin Aitken, Professor of Forensic Statistics, to see if he would be interested in being interviewed for the MOOC. Colin is interested in the application of statistics to forensic science and legal reasoning. So what does this involve?

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Consider, for example, a blood stain found at a crime scene. The police take a DNA profile, but the blood stain is degraded so the profile is not very good – 1 in 1000 people of the general population would match that blood sample. The police arrest a suspect, and their DNA matches. What is the chance that they are innocent?

The prosecution might argue that as only 1 in 1000 people would be a DNA match, there is only a 1 in 1000 chance that the suspect is innocent, or that there is only a 1 in 1000 chance that the blood at the crime scene came from someone other than the suspect. But they would be wrong in both cases – these are examples of what we call the prosecutor’s fallacy.

Say we know that the criminal comes from a town with population 50,000. One in 1000 of these people will be a DNA match for the sample, which is 50 people. The suspect is therefore 1 of these 50 people. The criminal is also one of these 50 people, and so the probability that the suspect is the criminal is actually only 1 in 50 – so the probability that they are innocent is 49 in 50, not 1 in 1000.

This is a huge difference, emphasising the importance of understanding the probabilities involved. Unfortunately, carelessness with probability in cases like this has led to huge miscarriages of justice in the past, with devastating consequences. You’ll be able to find out more from Colin in Week 4 of the course.

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