#### Document Type

Article

#### Abstract

Bayes' rule is not being used to guide jury decisionmaking in the vast majority of criminal cases involving evidence of DNA testing. Instead of telling juries the "source probability"-the probability that the individual whose DNA matches was the source of the forensic evidence found at the crime scene-experts only present pieces of the puzzle. They provide the probability that a randomly selected innocent person would have a match or the expected number of innocent matches in the database. In some cases, the random match probability will be so low (one in a quadrillion) that the resulting source probability is practically one hundred percent. But, in other cases, with large database trawls and random match probability at one in a million, jurors will have no ability to convert the random match probability or the likelihood ratio based on the expected number of matches into relevant data that will help them address the question of guilt. This Article shows that a correct application of Bayes' rule should lead fact finders and litigants to focus on the size of two variables that influence the source probability: the probability that a nonsource in the DNA database would have an alibi, and the probability that the source of the DNA is included in the database. This Article suggests practical means of estimating these two variables and argues that, as a legal matter, these parameters as well as the Bayesian posterior source probability are admissible in court.

#### Date of Authorship for this Version

2015

#### Recommended Citation

Ayres, Ian, "THE RULE OF PROBABILITIES: A PRACTICAL APPROACH FOR APPLYING BAYES' RULE TO THE ANALYSIS OF DNA EVIDENCE" (2015). *Faculty Scholarship Series*. 4871.

https://digitalcommons.law.yale.edu/fss_papers/4871