# Difference between revisions of "Bayes' theorem"

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*[http://lesswrong.com/lw/2b0/bayes_theorem_illustrated_my_way/ Bayes' Theorem Illustrated (My Way)] by [[User:Komponisto|komponisto]]. | *[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 | *[http://blog.oscarbonilla.com/2009/05/visualizing-bayes-theorem/ Visualizing Bayes' theorem] by Oscar Bonilla | ||

+ | *[http://oracleaide.wordpress.com/2012/12/26/a-venn-pie/ Using Venn pies to illustrate Bayes' theorem] by [[User:oracleaide|oracleaide]] | ||

==External links== | ==External links== |

## Revision as of 05:24, 27 December 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
- Using Venn pies to illustrate Bayes' theorem by oracleaide

## External links

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