Bayes' Theorem
/beɪzɪz ˈθiərəm/bayes' the·o·remnoun
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
- Bayes, T. & Price, R. (1763). An Essay towards solving a Problem in the Doctrine of Chances.Philosophical Transactions of the Royal Society, 53, 370–418.