The Rule of Probabilities: A Practical Approach for Applying Bayes' Rule to the Analysis of DNA Evidence

Abstract

Bayes’ rule is not being used to guide jury decision making in the vast majority of criminal cases introducing 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 intuitive source probability is practically one hundred percent. But, in other cases, with large database trawls and random match probability at 1 in a million, jurors will have no ability to convert the random match probability or the likelihood ratio based on 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 non-source 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. In particular, focusing on the prior probability that the “database is guilty,” i.e. the probability that someone in the database is the source of the forensic evidence, is not just analytically and empirically tractable, but avoids the evidentiary limitations concerning a particular defendant’s prior bad acts. Appropriate application of Bayes’ rule, far from preempting the fact-finding and adversarial process, can guide advocates to engage the important aspects of the evidence that are still likely to be open to contestation. Perhaps most important, appropriate application of Bayes’ rule will also allow jurors to reach verdicts via a coherent path that employs sound logic and reasoning.

Keywords: Bayes’ rule, probability, jury decision-making, big data

JEL Classification: K14, K40, K49