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- Q182505 subject Q7139537.
- Q182505 subject Q7612002.
- Q182505 subject Q8794749.
- Q182505 abstract "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 a woman has cancer, and knows that she is 65. If cancer is related to age, information about her 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 (/ˈbeɪz/; 1701–1761), who first provided an equation that allows 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".".
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- Q182505 comment "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 a woman has cancer, and knows that she is 65.".
- Q182505 label "Bayes' theorem".
- Q182505 depiction Bayes_Theorem_MMB_01.jpg.