Difference between revisions of "Bayes' theorem"

From Lesswrongwiki
Jump to: navigation, search
(Added a simple visualization)
Line 6: Line 6:
 
:<math>P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}</math>
 
:<math>P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}</math>
 
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.
 
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.
 +
 +
==Visualization==
 +
 +
[[Image:Bayes.png]]
  
 
==References==
 
==References==

Revision as of 17:51, 6 May 2009

Smallwikipedialogo.png
Wikipedia has an article about


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.

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.

Visualization

Bayes.png

References

Other Resources