Bayes' Theorem

/beɪzɪz ˈθiərəm/bayes' the·o·remnoun
Probability CoreFoundational

Definition

1.[in probability] the identity that converts the likelihood of evidence given a hypothesis into the probability of the hypothesis given that evidence, by weighting it with the hypothesis's prior probability.

Applying Bayes' theorem to a positive test result requires the disease's base rate, not just the test's accuracy.

Formal statement

P(A|B) = P(B|A) * P(A) / P(B)

P(A) is the prior, P(B|A) the likelihood, P(A|B) the posterior.

Etymology

An eponym (Rule 519) after Thomas Bayes (c. 1701–1761), the English Presbyterian minister whose essay on the problem was published posthumously by Richard Price in 1763.

Synonyms

  • Bayes' rulesense 1 · Absolute

See also

References