**Definition of Bayes' Theorem:**

In probability theory as well as statistics, Bayes' theorem (also called Bayes' law and/or Bayes' rule) is a result that is of great importance in the mathematical manipulation of conditional probabilities. It is a result that derives from the more basic axioms of probability.

When applied, the probabilities involved in Bayes' theorem may have any of a number of probability interpretations. In one of these interpretations, Bayes' theorem is used directly as part of a particular approach to statistical inference. In particular, with the Bayesian interpretation of probability,

*the theorem expresses how a subjective degree of belief should rationally change to account for evidence*: this is Bayesian inference, and it is fundamental to Bayesian statistics. Keep in mind, however, that Bayes' theorem has applications in a wide range of calculations involving probabilities, not just in Bayesian inference.

See Also: Wikipedia Bayes' Theorem.

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