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Data & Analytics · Intermediate

Bayes' Theorem

A rule for updating the probability of a hypothesis given evidence: P(A|B) = P(B|A) × P(A) / P(B).

Definition

Bayes' theorem combines a prior probability with the likelihood of the evidence to produce a posterior. It explains why tests for rare conditions produce many false positives, a consequence of low base rates.

Example

A 99%-accurate test for a 1-in-1,000 condition: most positive results are false positives.

Exam tip

Ignoring the base rate (prior) is the classic error Bayes' theorem corrects.

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