Transposition of the conditional
Definition
The mathematical name for the error at the core of the prosecutor's fallacy. P(A | B) and P(B | A) are generally not equal; their relationship is given by Bayes' theorem. In court contexts, A is often 'innocence' and B is 'the observed evidence'.
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...
- Prior probability
- The probability of guilt (or innocence) based on all evidence other than the specific forensic match under consideration. Bayes' theorem requires a...
- Product rule (probability)
- The rule that P(A and B) = P(A) x P(B) holds only when A and B are independent. Applying it to correlated...
- 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...
- Reference class
- The population against which a probability or frequency is calculated. Choosing the wrong reference class, for example using general population allele frequencies...
Explained in these topics
- History of Statistical Evidence in CourtsThe logical error of swapping a conditional probability with its converse: claiming that P(E|H) = P(H|E). This is formally equivalent to the prosecutor's falla...
- The Prosecutor's FallacyThe mathematical name for the error at the core of the prosecutor's fallacy. P(A | B) and P(B | A) are generally not equal; their relationship is given by Baye...