Positive Dependence
Definition
Events are positively dependent when the occurrence of one increases the probability of the other: P(A|B) > P(A). In this case P(A and B) > P(A) x P(B). Treating positively dependent events as independent underestimates their joint probability, making the coincidence appear rarer than it is.
- Definition
- P(A given B) is greater than P(A)
- Effect on joint probability
- P(A and B) exceeds P(A) times P(B)
- Risk if ignored
- Joint probability of the events is underestimated
Common questions
Why does treating positively dependent events as independent matter in court?+
Multiplying their probabilities as if independent produces a smaller combined probability than the true figure, making a coincidence of evidence look rarer, and therefore more incriminating, than it actually is.
What is an example of positive dependence in forensic evidence?+
Two trace evidence types that tend to co-occur because they share a common source or transfer mechanism, such as fibres and glass fragments picked up together at the same scene, rather than arising from separate independent events.
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