## Bayes’ Theorem in the Courtroom

Using Bayes’ Theorem and other statistical calculations as evidence for court trials has been a very controversial issue. The current ruling is that statistically based conclusions and evidence are not permitted. Bayes’ Theorem is a method of probability that determines the probability of an outcome and could therefore be used in many court cases to evaluate the validity of the case evidence, witness reports, or even to draw conclusions not based on given evidence.

These probabilities are, however, subjective based on the original information used. Although Bayes’ can be used to determine the probability that an event occurred, this probability will not provide the evidence to say that the event 100% did or did not occur; it can only provide the odds that the event occurred, which must then be interpreted to be in favor of one of the outcomes. Therefore, when looking at the determined probabilities, how can it be said what is a “good enough” probability that an event happened to convict a person on trial? There might be a 15 to 1 chance that the defendant was at the same place as where the murder occurred, but is this a good enough probability to charge the defendant with murder? Incorrectly calculated probabilities have been used in the past to wrongly commit innocent people.

So although astounding deductions can be made using Bayes’ Theorem, there are definitely uncertainties and bias that goes along with it. As stated by the article’s author, “Despite its potential utility, Bayes’ theorem is not trusted by much of the legal profession. There are two main reasons: subjectivity is often misunderstood, and Bayesian arguments are difficult to present in a way that everyone will comprehend.” The question becomes, is there a way to accurately and more easily present Bayes’ Theorem conclusions, and is the subjectivity of the method too biased? This question depends on many aspects of the issue. If a program that performs Bayes’ Theorem calculations can be developed, then the different outcomes based on various subjective initial assumptions can be analyzed.

Overall, there are enormous advancements that could be made using statistical evidence from Bayes’ Theorem in the courtroom. These are difficult and sometimes extremely convoluted calculations; can this become a trusted method in the legal system?

Source: http://www.nature.com/nature/journal/v479/n7371/full/479036a.html