Bayes' theorem
Definition
The mathematical rule that relates prior odds, the likelihood ratio, and posterior odds. In the odds form: O(Hp|E) = O(Hp) x LR. This is the formal basis for Bayesian forensic inference and is equivalent to the probability form of the theorem but easier to apply in sequential evidence evaluation.
Related terms
- Evaluative reporting
- A framework for expressing forensic conclusions in terms of the probability of the evidence given the prosecution hypothesis versus the defence hypothesis...
- Likelihood ratio (LR)
- The ratio of two conditional probabilities: the probability of the observed evidence given the prosecution's hypothesis (same source), divided by the probability...
- Prosecutor's fallacy
- The error of treating the RMP (or its reciprocal) as the probability that the defendant is innocent, or as the probability that...
- Random match probability (RMP)
- The probability that a randomly chosen unrelated person from the relevant population would match the evidence profile by chance. A very small...
- Posterior odds
- The ratio of the probability of the prosecution hypothesis to the probability of the defence hypothesis after the forensic evidence is taken...
- Prior odds
- The ratio of the probability of the prosecution hypothesis to the probability of the defence hypothesis before the forensic evidence in question...
- Propositions (Hp / Hd)
- The two competing hypotheses in evaluative reporting. Hp is the prosecution proposition (for example, the accused is the source of the trace),...
- Transposition fallacy
- The error of treating the probability of the evidence given a hypothesis as though it were the probability of the hypothesis given...
- Validation study
- An empirical study that tests the accuracy, precision, and error rate of a forensic method under realistic conditions. Validation data are required...
Explained in these topics
- How Numbers Enter Forensic ConclusionsA mathematical rule relating prior probability, the likelihood of evidence under competing hypotheses, and posterior probability. In odds form: posterior odds...
- Prior and Posterior Odds in CourtThe mathematical rule that relates prior odds, the likelihood ratio, and posterior odds. In the odds form: O(Hp|E) = O(Hp) x LR. This is the formal basis for B...
- The Role of Statistics in Evidence EvaluationA rule relating prior probability, the likelihood ratio, and posterior probability. In forensic terms: posterior odds = prior odds multiplied by the LR. The th...