[silk] UK judge bans Bayesian logic
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
Re: [silk] UK judge bans Bayesian logic
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
Re: [silk] UK judge bans Bayesian logic
On Mon, Oct 3, 2011 at 4:51 PM, Udhay Shankar N ud...@pobox.com 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 The judgment's logic is highly malleable. I don't think it means the death of Bayesian logic. If the underlying factors for a problem are based on firm data (what appears to have been decisive here is that shoe sale data in relation to each and every pair is imprecise since it isn't otherwise calculated or estimated). So if either through the use of data or through mathematical logic it can be established in another case that a higher level of precision is possible, then I don't think the court will come in the way of the use of such a method. I don't think this judgment is a criticism of Bayesian techniques - rather it's a reinforcement of the reasonable doubt standard. If there is reasonable doubt, the court must acquit. And if the mathematical formula that determines the likelihood of a crime based on circumstantial evidence is inherently based on imprecise data, then the mathematical formula does not obviate reasonable doubt and can't be reliably employed. Regards, Nikhil Mehra Advocate, Supreme Court of India Tel: (+91) 9810776904 Res: C-I/10, AIIMS Campus, Ansari Nagar (East) New Delhi - 110029.
Re: [silk] UK judge bans Bayesian logic
On Monday 03 Oct 2011 4:51:12 pm Udhay Shankar N wrote: Fascinating. Will the next ruling ban inductive logic as well? I don't know what inductive logic means, but here are three views (at the bottom of this post) from the article. I disagree with the mathematician and agree with the psychologist and lawyer. The judge IMO is right. Statistics is abouut probability. The law is all about being innocent until proven guilty. If it was one's own ass in the firing line - or that of a dear one such as a wife or a husband one would certainly support the innocent until proven guilty attitude. We are taught to expect precision from mathematics. 2 x 2 = 4 . Period. We would never condone an airline pilot for landing in Karachi instad of Mumbai because he was unable to feed in the coordinates for navigation. 27 x 67 is exactly 1809. It is not approximately 1800, or nearly 2000 Humans continuously make guesstimates like nearly 2000 or approximately 1800. Pilots can navigate by dead reckoning and the position of the sun, but they frequently get lost. If you use mathematics the lay person expects certainty, not a propability. Any fool and his uncle would be able to come up with guesswork, hunches and probabilities. Now if a mathematician tries to convince me that his method probability and how he derives his gut feeling is mathematical and better than mine it is bullsh1t if it is not exact. I can do guesswork too. A whole lot of astrology is based on probabilities. We just don't want to believe it. It's too far fetched. But statistics is astrology based on information that we can relate to and ends up being more credible than astrology. It still deals only with probabilities and likelihoods. If you want to gamble your money, use statistics over astrology if you like. But when it comes to putting someone in jail, neither astrology nor hi funda statistics cut it. Mathematician: 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. Psychiologist: 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. Lawyer: 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.
