# Difference between revisions of "Bayes' theorem"

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==Other posts== | ==Other posts== | ||

+ | *[http://lesswrong.com/lw/2b0/bayes_theorem_illustrated_my_way/ Bayes' Theorem Illustrated (My Way)] by [[User:Komponisto|komponisto]]. | ||

*[http://causalityrelay.wordpress.com/2008/06/23/odds-and-intuitive-bayes/ Odds, evidence, and an intuitive form of Bayes’ theorem] by [[Vladimir Nesov]] | *[http://causalityrelay.wordpress.com/2008/06/23/odds-and-intuitive-bayes/ Odds, evidence, and an intuitive form of Bayes’ theorem] by [[Vladimir Nesov]] | ||

*[http://blog.oscarbonilla.com/2009/05/visualizing-bayes-theorem/ Visualizing Bayes' theorem] by Oscar Bonilla | *[http://blog.oscarbonilla.com/2009/05/visualizing-bayes-theorem/ Visualizing Bayes' theorem] by Oscar Bonilla |

## Revision as of 16:08, 4 June 2010

A law of probability that describes the proper way to incorporate new evidence into prior probabilities to form an updated probability estimate. Bayesian rationality takes its name from this theorem, as it is regarded as the foundation of consistent rational reasoning under uncertainty. A.k.a. "Bayes's Theorem" or "Bayes's Rule".

The theorem commonly takes the form:

where A is the proposition of interest, B is the observed evidence, P(A) and P(B) are prior probabilities, and P(A|B) is the posterior probability of A.

With the posterior odds, the prior odds and the likelihood ratio written explicitly, the theorem reads: