Not read the judgment so take this with that caveat (although the Guardian's legal reporting is usually pretty decent).
Don't see the problem with this - the CA (Court of Appeal) hasn't banned Bayesian logic or said it is wrong or anything like that. All they've said is that it shouldn't be used as evidence in (criminal?) legal proceedings (actually, they may not have gone this far and only spoken about the weight to be attached to it, but I'd have to read the judgment to check that) unless the underlying numbers used in the calculation are sound. Basically the CA's point is that if there is no confidence in the underlying numbers, then it doesn't matter how good Bayes theorem (or any other calculation) is - it's a GIGO situation, and can actually cause harm, because you get a seemingly precise number which isn't really precise at all. In that situation, it's better not to have that false certainty.. I think the broad thrust of the article - that courts should understand statistics better - is a great idea. But I'm not sure the CA has made a mistake in this instance. Badri On 3 Oct 2011, at 12:21, Udhay Shankar N wrote: > Fascinating. Will the next ruling ban inductive logic as well? > > Udhay > > http://www.guardian.co.uk/law/2011/oct/02/formula-justice-bayes-theorem-miscarriage > > A formula for justice > > Bayes' theorem is a mathematical equation used in court cases to analyse > statistical evidence. But a judge has ruled it can no longer be used. > Will it result in more miscarriages of justice? > > Angela Saini > guardian.co.uk, Sunday 2 October 2011 21.30 BST > > It's not often that the quiet world of mathematics is rocked by a murder > case. But last summer saw a trial that sent academics into a tailspin, > and has since swollen into a fevered clash between science and the law. > > At its heart, this is a story about chance. And it begins with a > convicted killer, "T", who took his case to the court of appeal in 2010. > Among the evidence against him was a shoeprint from a pair of Nike > trainers, which seemed to match a pair found at his home. While appeals > often unmask shaky evidence, this was different. This time, a > mathematical formula was thrown out of court. The footwear expert made > what the judge believed were poor calculations about the likelihood of > the match, compounded by a bad explanation of how he reached his > opinion. The conviction was quashed. > > But more importantly, as far as mathematicians are concerned, the judge > also ruled against using similar statistical analysis in the courts in > future. It's not the first time that judges have shown hostility to > using formulae. But the real worry, say forensic experts, is that the > ruling could lead to miscarriages of justice. > > "The impact will be quite shattering," says Professor Norman Fenton, a > mathematician at Queen Mary, University of London. In the last four > years he has been an expert witness in six cases, including the 2007 > trial of Levi Bellfield for the murders of Marsha McDonnell and Amelie > Delagrange. He claims that the decision in the shoeprint case threatens > to damage trials now coming to court because experts like him can no > longer use the maths they need. > > Specifically, he means a statistical tool called Bayes' theorem. > Invented by an 18th-century English mathematician, Thomas Bayes, this > calculates the odds of one event happening given the odds of other > related events. Some mathematicians refer to it simply as logical > thinking, because Bayesian reasoning is something we do naturally. If a > husband tells his wife he didn't eat the leftover cake in the fridge, > but she spots chocolate on his face, her estimate of his guilt goes up. > But when lots of factors are involved, a Bayesian calculation is a more > precise way for forensic scientists to measure the shift in guilt or > innocence. > > In the shoeprint murder case, for example, it meant figuring out the > chance that the print at the crime scene came from the same pair of Nike > trainers as those found at the suspect's house, given how common those > kinds of shoes are, the size of the shoe, how the sole had been worn > down and any damage to it. Between 1996 and 2006, for example, Nike > distributed 786,000 pairs of trainers. This might suggest a match > doesn't mean very much. But if you take into account that there are > 1,200 different sole patterns of Nike trainers and around 42 million > pairs of sports shoes sold every year, a matching pair becomes more > significant. > > The data needed to run these kinds of calculations, though, isn't always > available. And this is where the expert in this case came under fire. > The judge complained that he couldn't say exactly how many of one > particular type of Nike trainer there are in the country. National sales > figures for sports shoes are just rough estimates. > > And so he decided that Bayes' theorem shouldn't again be used unless the > underlying statistics are "firm". The decision could affect drug traces > and fibre-matching from clothes, as well as footwear evidence, although > not DNA. > > "We hope the court of appeal will reconsider this ruling," says Colin > Aitken, professor of forensic statistics at the University of Edinburgh, > and the chairman of the Royal Statistical Society's working group on > statistics and the law. It's usual, he explains, for forensic experts to > use Bayes' theorem even when data is limited, by making assumptions and > then drawing up reasonable estimates of what the numbers might be. Being > unable to do this, he says, could risk miscarriages of justice. > > "From being quite precise and being able to quantify your uncertainty, > you've got to give a completely bland statement as an expert, which says > 'maybe' or 'maybe not'. No numbers," explains Fenton. > > "It's potentially very damaging," agrees University College London > psychologist, Dr David Lagnado. Research has shown that people > frequently make mistakes when crunching probabilities in their heads. > "We like a good story to explain the evidence and this makes us use > statistics inappropriately," he says. When Sally Clark was convicted in > 1999 of smothering her two children, jurors and judges bought into the > claim that the odds of siblings dying by cot death was too unlikely for > her to be innocent. In fact, it was statistically more rare for a mother > to kill both her children. Clark was finally freed in 2003. > > Lawyers call this type of mistake the prosecutor's fallacy, when people > confuse the odds associated with a piece of evidence with the odds of > guilt. Recognising this is also what eventually quashed the 1991 > conviction for rape of Andrew Deen in Manchester. The courts realised at > appeal that a one-in-three-million chance of a random DNA match for a > semen stain from the crime scene did not mean there was only a > one-in-three-million chance that anyone other than Deen could have been > a match – those odds actually depend on the pool of potential suspects. > In a population of 20 million adult men, for example, there could be as > many as six other matches. > > Now, Fenton and his colleague Amber Marks, a barrister and lecturer in > evidence at Queen Mary, University of London, have begun assembling a > group of statisticians, forensic scientists and lawyers to research a > solution to bad statistics. "We want to do what people failed to do in > the past, which is really get the legal profession and statisticians and > probability guys understanding each other's language," says Fenton. > > Their first job is to find out how often trials depend on Bayesian > calculations, and the impact that the shoeprint-murder ruling might have > on future trials. "This could affect thousands of cases," says Marks. > > They have 37 members on their list so far, including John Wagstaff, > legal adviser to the Criminal Cases Review Commission, and David > Spiegelhalter, the Winton professor of the public understanding of risk > at the University of Cambridge. Added to these are senior statisticians > and legal scholars from the Netherlands, US and New Zealand. > > Fenton believes that the potential for mathematics to improve the > justice system is huge. "You could argue that virtually every case with > circumstantial evidence is ripe for being improved by Bayesian > arguments," he says. > > But the real dilemma is finding a way to help people make sense of the > calculations. The Royal Statistical Society already offers guidance for > forensic scientists, to stop them making mistakes. Lagnado says that > flowcharts in the style of family trees also help jurors visualise > changing odds more clearly. But neither approach has been entirely > successful. And until this complex bit of maths can be simply explained, > chances are judges will keep rejecting it. > > > -- > ((Udhay Shankar N)) ((udhay @ pobox.com)) ((www.digeratus.com)) >
