Baye’s Rule- A formula for justice
Named after Thomas Bayes, Baye’s Rule calculates the probability of an event A given an event B. It is often know as a way to calculate the changing probabilities of events given new and updating information. The rule is described by the formula: Pr[A/B]= (pr[A] x Pr[B/A])/Pr[B]. This formula states that the probability of even A occuring if B is true = the probability of A times the probability of B if A is true divided by the probability of B. Baye’s Rule can be applied to countless probability examples such as poker, elections and more. Specifically, it makes sense that Baye’s Rule would be a perfect match for use in deciding court cases given certain changing evidence.
An article posted by “The Guardian” discusses how the mathematical calculation has been thrown out of court in the past. Although the article discusses a murder case where, “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,” it also describes the practicality and urgency to use Baye’s Rule in court. For example, Colin Aitken, a 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 describes that, “It’s usual, 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.” The support for the us of Baye’s Rule stems from the ability of the Rule to take into account changes in information and “rationally” calculates probabilities that sometime seem irrelavent.
For example, the article discusses that in the murder case involving a matching footprint, Bayes Rule proves the matching footprint to be much more convicting and relevant than it would first seem considering that there are 786,000 pairs of the same shoe sold. However Baye’s Rule points out that if you take into account, “the 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.”
In addition to professor Colin Aitken, the article mentions that the University College London psychologist, Dr. David Lagnado also agrees for similar reasons. Dr. David Lagnado points out that people often, “Like a good story to explain the evidence and this makes us use statistics inappropriately.” However, if Bayes Rule were applied in court these inappropriate uses of statistics, such as peoples first and inaccurate view about the footprint, would be corrected with mathematic reasoning. Overall, the article’s argument supporting the need for Bayes Rule in courts around the country is highlighted in the closing remarks that You could argue that virtually every case with circumstantial evidence is ripe for being improved by Bayesian arguments.”
http://www.guardian.co.uk/law/2011/oct/02/formula-justice-bayes-theorem-miscarriage