# Difference between revisions of "Bayes' theorem"

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− | A law of probability that describes the proper way to incorporate new [[evidence]] into [[prior probabilities]] to form an [[belief update|updated]] probability estimate. [[Bayesian | + | A law of probability that describes the proper way to incorporate new [[evidence]] into [[prior probabilities]] to form an [[belief update|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: | The theorem commonly takes the form: | ||

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[[Image:Bayes.png]] | [[Image:Bayes.png]] | ||

− | == | + | ==Blog posts== |

− | * [http://yudkowsky.net/rational/bayes An Intuitive Explanation of Bayes' Theorem] | + | *[http://lesswrong.com/lw/2b0/bayes_theorem_illustrated_my_way/ Bayes' Theorem Illustrated (My Way)] by [[User:Komponisto|komponisto]]. |

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

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+ | ==External links== | ||

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+ | *[http://yudkowsky.net/rational/bayes An Intuitive Explanation of Bayes' Theorem] | ||

+ | *[http://kruel.co/2010/02/27/a-guide-to-bayes-theorem-a-few-links/ A Guide to Bayes’ Theorem – A few links] by Alexander Kruel | ||

==See also== | ==See also== | ||

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*[[Posterior probability]] | *[[Posterior probability]] | ||

*[[Belief update]] | *[[Belief update]] | ||

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[[Category:Theorems]] | [[Category:Theorems]] | ||

[[Category:Bayesian]] | [[Category:Bayesian]] |

## Revision as of 21:46, 17 March 2012

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:

## Visualization

## Blog posts

- Bayes' Theorem Illustrated (My Way) by komponisto.
- Visualizing Bayes' theorem by Oscar Bonilla

## External links

- An Intuitive Explanation of Bayes' Theorem
- A Guide to Bayes’ Theorem – A few links by Alexander Kruel