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In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule) describes the probability of an event, based on conditions that might be related to the event. For example, suppose one is interested in whether Addison has cancer, and that she is 65. If cancer is related to age, information about Addison's age can be used to more accurately assess the probability of her having cancer using Bayes' Theorem. When applied, the probabilities involved in Bayes' theorem may have different probability interpretations. In one of these interpretations, the theorem is used directly as part of a particular approach to statistical inference. With the Bayesian probability interpretation the theorem expresses how a subjective degree of belief should rationally change to account for evidence: this is Bayesian inference, which is fundamental to Bayesian statistics. However, Bayes' theorem has applications in a wide range of calculations involving probabilities, not just in Bayesian inference. Bayes' theorem is named after Rev. Thomas Bayes (; 1701–1761), who first showed how to use new evidence to update beliefs. It was further developed by Pierre-Simon Laplace, who first published the modern formulation in his 1812 ''Théorie analytique des probabilités''. Sir Harold Jeffreys put Bayes' algorithm and Laplace's formulation on an axiomatic basis. Jeffreys wrote that Bayes' theorem "is to the theory of probability what the Pythagorean theorem is to geometry". ==Statement of theorem== Bayes' theorem is stated mathematically as the following equation:〔.〕 : where ''A'' and ''B'' are events. * ''P''(''A'') and ''P''(''B'') are the probabilities of ''A'' and ''B'' without regard to each other. * ''P''(''A'' | ''B''), a conditional probability, is the probability of observing event ''A'' given that ''B'' is true. * ''P''(''B'' | ''A''), is the probability of observing event ''B'' given that ''A'' is true. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bayes' theorem」の詳細全文を読む スポンサード リンク
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