Difference between revisions of "Bayes' theorem"

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m (Undo revision 7619 by Nosovicki (Nope, the previous version was right. Discuss on the talk page if in doubt.))
(Removed "Odds, evidence, and an intuitive form of Bayes’ theorem" because it's private)
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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 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".
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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]] 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]]
  
==Main article==
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==Blog posts==
  
* [http://yudkowsky.net/rational/bayes An Intuitive Explanation 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]].
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*[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]
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*[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]]
 
==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://blog.oscarbonilla.com/2009/05/visualizing-bayes-theorem/ Visualizing Bayes' theorem] by Oscar Bonilla
 
  
 
[[Category:Theorems]]
 
[[Category:Theorems]]
 
[[Category:Bayesian]]
 
[[Category:Bayesian]]

Revision as of 21:46, 17 March 2012

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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

Bayes.png

Blog posts

External links

See also