Mathematics in the dock

A few years ago I met a mathematician called Norman Fenton at Queen Mary, University of London, who told me about the disturbing problem of miscarriages of justice happening in British courts because jurors, judges and lawyers were failing to understand statistics. The most famous case in recent years is that of of Sally Clark, who was sent to jail for killing her two young children, before mathematics proved that it was likelier that they were both victims of cot death. The solution to bad statistics like this sometimes comes in the form of Bayes' Theorem, a formula that forensic scientists use to calculate the odds of one event given the prior odds of other related events. Number-crunching evidence using Bayesian reasoning, Fenton said, was a much more accurate way of assessing a suspect's guilt (in fact with one of his colleagues, he invented a piece of software that does all this number crunching for you).

But while lots of mathematicians support the use of Bayesian reasoning in courts, judges have historically shown a hostility to formulae for fear of confusing jurors. Explaining Bayes' Theorem to people isn't easy, even with diagrams. Fenton has been an expert witness in some high-profile trials, including that of murderer Levi Bellfield back in 2007, and he knows first hand just how easy it is for people (including scientists) to misinterpret forensic evidence. So I ended up writing a feature about our encounter for New Scientist in 2009, explaining the common statistical fallacies that happen in courts, and how they might be avoided.

Then last year, in an appeal case known as RvT (the redacted judgment is available here), a High Court judge effectively ruled that Bayes' Theorem can't be used at all except in limited circumstances, such as with DNA evidence. Experts have told me on and off the record that this could lead to many more miscarriages of justice in the future. It has sent shockwaves through the forensic science community. Fenton has been so concerned by the ruling that he is forming a research group to figure a way to get this mathematical tool back in the courts. If you'd like to read more about the whole story, check out my feature in The Guardian today.

For anyone who would like to investigate the issue more deeply, there has been a spate of academic publications recently looking at it, including this draft paper by Fenton and his colleague Martin Neil, one in the Criminal Law Review by Redmayne, Roberts, Aitken and Jackson, and a paper in Science & Justice by Berger, Buckleton, Champod and Evett.