<unk>  (also known as Bayes' rule or Bayes' law) is a result in probability theory, which relates the conditional and marginal probability distributions of random variables. In some interpretations of probability,<unk>  tells how to update or revise beliefs in light of new evidence a posteriori.
The probability of an event A conditional on another event B is generally different from the probability of B conditional on A. However, there is a definite relationship between the two, and<unk>  is the statement of that relationship.
As a formal<unk> ,<unk>  is valid in all interpretations of probability. However, frequentist and Bayesian interpretations disagree about the kinds of things to which probabilities should be assigned in applications: frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole; Bayesians assign probabilities to propositions that are uncertain.  A consequence is that Bayesians have more frequent occasion to use<unk> .  The articles on Bayesian probability and frequentist probability discuss these debates at greater length.
Bayes' theorem
Bayesian inference
Gauss–Markov theorem
Rhythm method
Franck-Condon principle
Ancillary statistic
Cannon-Bard theory
Equation of state