Bayesian reasoning (which incorporates the likelihood ratio and Bayes’ theorem) is a logical framework for reasoning about uncertainty. Experts (including statisticians and forensic scientists) have argued for many years that Bayesian reasoning has the potential to improve the efficiency, transparency and fairness of the justice system, and to avoid the kind of fallacies in probabilistic reasoning that have not only troubled the appellate courts but are also likely to have misled tribunals of fact in many trials.
The use of Bayesian reasoning in investigative and evaluative forensic science and the law is, however, the subject of much confusion. It is deployed in the adduction of DNA evidence, but expert witnesses and lawyers struggle to articulate the underlying assumptions and results of Bayesian reasoning in a way that is understandable to lay people. The extent to which Bayesian reasoning could benefit the justice system by being deployed more widely, and how it is best presented, is unclear and requires clarification. Norman Fenton, discusses here.