## Bayes Theorem in Justice Systems

https://www.theguardian.com/law/2011/oct/02/formula-justice-bayes-theorem-miscarriage

In judicial systems around the world it is a common strategy for prosecutors to use statistics to bolster their claims. As described in the guardian over the years this has led to a number of misrepresentations and caused one judge to bar the use of some statistical methods in future court cases.

One of the main techniques used is Bayes theorem. A formula that gives the probability of an event, for instance the defendant being guilty, given knowledge of some other fact, such as a DNA match with a semen stain. It is easy to see how in this situation the numbers can be used to support both sides. There is only a 1 in 3 million chance that a random DNA match would occur and in the first trial this was taken to mean that there was only a 1 in 3 million chance the defendant was innocent. However, in the appeal it was pointed out that if the population who may have committed the crime was a pool of 20 million men then there would be on average about 6 men whose DNA would match.

Situations like this explain why friction has developed between many judges and the use of statistics in court cases. It is easy to stretch the data to make the situation fit the narrative you are pushing. However, in other industries Bayes’ theorem has been profoundly helpful. Bayes theorem has helped things from spam filters to code breakers. Norman Fenton, a mathematician at Queen Mary University of London, said that “virtually every case with circumstantial evidence is ripe for being improved by Bayesian arguments”. The power to be used for good and ill makes it very important that all involved are educated on basic statistical methods so that formulas like Bayes theorem can be used to better our justice system.