# Bayes' theorem

Bayes' theorem a theorem establishing a method of calculating conditional (adjective) statistical probabilities, in which a known probability is modified in the light of later events that affect the data under consideration (Ex.: the probability of selecting a heart from a deck of cards is 13/52; if a card is selected from a full deck and that card is a heart, the probability that the next card selected will also be a heart becomes 12/51, but if that first selected card is not a heart, the probability for the next card becomes 13/51)

Origin of Bayes' theorem

after T.*Bayes*(1702-61), Eng theologian and mathematician known for his early work in modern probability theory

## bayes-theorem

Noun

(*uncountable*)

- A theorem which states that an already-known unconditioned probability (the "prior") of some target event can be multiplied by a "likelihood ratio" — the conditional probability of a certain factor event (given the pri) divided by the marginal probability of that factor — in order to obtain the ("posterior", i.e., the) conditional probability of the target given the factor.

Usage notes

- The "marginal probability" is the unconditioned probability of the factor, which can be expanded, by means of the law of total probability, into a sum of terms. Each term is the product of the conditional probability of the factor given some event which shares the same sample space as the target, and the unconditioned probability of that event.

Origin

Named after Thomas Bayes (1701–1761), English mathematician.