Jabarkan In the courtroom dari Inferensi Bayes dalam bahasa sunda

Bayesian inference can be used to coherently assess additional evidence of guilt in a court setting.

Let G be the event that the defendent is guilty.

Let E be the event that the defendent's DNA matches DNA found at the crime scene.

Let p(E | G) be the probability of seeing event E assuming that the defendent is guilty. (Usually this would be taken to be unity.)

Let p(G | E) be the probability that the defendent is guilty assuming the DNA match event E

Let p(G) be the probability that the defendent is guilty, based on the evidence other than the DNA match.

Bayesian inference tells us that if we can assign a probability p(G) to the defendent's guilt before we take the DNA evidence into account, then we can revise this probability to the conditional probability p(G | E), since

p(G | E) = p(G) p(E | G) / p(E)

Suppose, on the basis of other evidence, a juror decides that there is a 30% chance that the defendent is guilty. Suppose also that the forensic evidence is that the probability that a person chosen at random would have DNA that matched that at the crime scene was 1 in a million, or 10−6.

The event  E can occur in two ways. Either the defendent is guilty (with prior probability 0.3) and thus his DNA is present with probability 1, or he is innocent (with prior probability 0.7) and he is unlucky enough to be one of the 1 in a million matching péople.

Thus the juror could coherently revise his opinion to take into account the DNA evidence as follows:

p(G | E) = 0.3 × 1.0 /(0.3 × 1.0 + 0.7 × 10-6) = 0.99999766667.

In the United Kingdom, Bayes' théorem was explained by an expert witness to the jury in the case of Regina versus Denis Adams. The case went to Appéal and the Court of Appéal gave their opinion that the use of Bayes' théorem was inappropriate for jurors.