Prior Probability
Definition
The probability of guilt (or innocence) based on all evidence other than the specific forensic match under consideration. Bayes' theorem requires a prior to convert a likelihood ratio into a posterior probability. Courts, not experts, are responsible for assessing the prior in a criminal case.
- Field
- Forensic statistics, Bayesian inference
- Definition
- Probability of guilt from evidence other than the forensic match
- Combined with
- Likelihood ratio, via Bayes' theorem
- Produces
- Posterior probability
- Assessed by
- The court, not the forensic expert
Common questions
Why is it the court's job to set the prior probability rather than the expert's?+
The prior depends on the full body of case evidence such as alibi, motive, and eyewitness testimony, which is the fact-finder's role to weigh, whereas the forensic expert's proper role is limited to reporting the strength of the specific scientific evidence, expressed as a likelihood ratio.
What goes wrong when an expert states a probability of guilt directly?+
Stating guilt probability requires folding in a prior the expert has no basis to set, and doing so risks the transposed conditional error underlying both the prosecutor's fallacy and the defence fallacy, where the probability of the evidence given innocence is confused with the probability of innocence given the evidence.
Can a prior probability be zero or completely neutral?+
In principle a fact-finder could treat the prior as neutral before considering any other evidence, but in practice a case almost always involves some non-forensic evidence, so a genuinely uninformative prior is more of a theoretical starting point than a realistic courtroom scenario.
Related terms
- Defence Fallacy
- The converse error of inflating the importance of the RMP by arguing that, because many people in the population share the profile,...
- 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...
- Relevant Population
- The population of individuals who could plausibly have left the forensic sample, constrained by geography, time, and other case facts. Choosing the...
- Transposition of the Conditional
- The mathematical name for the error at the core of the prosecutor's fallacy. P(A | B) and P(B | A) are generally...
Explained in these topics
- The Defence FallacyThe probability of a hypothesis before the forensic evidence is considered, derived from all other evidence in the case: witness accounts, CCTV, alibi, motive,...
- The Prosecutor's Fallacy