Posterior Odds
Definition
The ratio of the probability of the prosecution hypothesis to the probability of the defence hypothesis after the forensic evidence is taken into account. Calculated as prior odds multiplied by the likelihood ratio. This is the updated belief state, which the fact-finder uses alongside all other case evidence.
- Formula
- Prior odds multiplied by the likelihood ratio
- Represents
- Updated belief after considering forensic evidence
- Set by
- Fact-finder, not the forensic scientist
- Framework
- Bayesian evidence evaluation
Common questions
Why does the forensic scientist not calculate posterior odds directly?+
Prior odds depend on the whole body of case evidence, alibi, motive, and other non-forensic facts, which are for the court to weigh, not the scientist. The scientist's role is limited to reporting the likelihood ratio, leaving the fact-finder to combine it with the prior to reach posterior odds.
What happens if the likelihood ratio is misinterpreted as the posterior odds?+
This is the prosecutor's fallacy: treating the strength of the evidence alone as if it were the probability of guilt, while ignoring the prior odds. It overstates how conclusive the forensic finding is on its own and has led to wrongful convictions in past cases.
Can posterior odds be converted into a probability of guilt?+
Odds can be converted to a probability using odds divided by one plus odds, but posterior odds reflect only the hypotheses and evidence formally considered, not the full legal threshold of guilt beyond reasonable doubt, which remains a matter for the fact-finder.
Related terms
- 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...
- Prior Odds
- The ratio of the probability of the prosecution hypothesis to the probability of the defence hypothesis before the forensic evidence in question...
- Evaluative Reporting
- A framework for expressing forensic conclusions in terms of the probability of the evidence given the prosecution hypothesis versus the defence hypothesis...
- 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...
- Bayes' Theorem
- The mathematical rule that relates prior odds, the likelihood ratio, and posterior odds. In the odds form: O(Hp|E) = O(Hp) x LR....
- Defence Hypothesis (Hd)
- The proposition advanced by the defence, typically that the material came from an unknown unrelated individual or that the defendant was not...
- Prosecution Hypothesis (Hp)
- The proposition advanced by the prosecution, typically that the defendant is the source of the recovered material or was present at the...
- 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...
- Transposition Fallacy
- The error of treating the probability of the evidence given a hypothesis as though it were the probability of the hypothesis given...
Explained in these topics
- Bayes Theorem in Evidence Evaluation
- The Likelihood Ratio: Definition and LogicThe odds that the prosecution hypothesis is true after incorporating the forensic evidence. By Bayes' theorem, posterior odds = prior odds multiplied by the LR.
- Prior and Posterior Odds in CourtThe updated ratio after the likelihood ratio has been applied: posterior odds = prior odds x LR. The fact-finder uses posterior odds (combined with all other e...