Difference between revisions of "Bayes' theorem"

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The theorem commonly takes the form:
 
The theorem commonly takes the form:
 
:<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|B is the proposition of interest, A and B are the observed evidence, P(A) and P(B) are prior probabilities, and P(A|B) is the posterior probability of A|B.
  
 
With the posterior odds, the prior odds and the [[likelihood ratio]] written explicitly, the theorem reads:
 
With the posterior odds, the prior odds and the [[likelihood ratio]] written explicitly, the theorem reads:

Revision as of 16:45, 5 September 2011

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

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

Visualization

Bayes.png

Main article

See also

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