~~Bayes'~~Bayes' Theorem (also known as ~~Bayes'~~Bayes' Law) is a law of probability that describes the proper way to incorporate new evidence into prior probabilities to form an updated probability estimate. It is commonly regarded as the foundation of consistent rational reasoning under uncertainty. Bayes Theorem is named after Reverend Thomas Bayes who proved the theorem in 1763.

~~See also: ~~~~Bayesian probability~~~~, ~~~~Priors~~~~, ~~~~Likelihood ratio~~~~, ~~~~Belief update~~~~, ~~~~Probability and statistics~~~~, ~~~~Epistemology~~~~, ~~~~Bayesianism~~

~~Bayes'~~Bayes' theorem commonly takes the form:

P(A|B)=P(B|A)P(A)P(B)

P(A|B)P(~~¬~~¬A|B)=P(A)P(~~¬~~¬A)~~⋅~~⋅P(B|A)P(B|~~¬~~¬A)

~~ Visualization~~Visualisation of ~~Bayes'~~Bayes' Rule

~~External links~~

(also known as~~Bayes'~~Bayes' Theorem~~Bayes'~~Bayes' Law) is a law of probability that describes the proper way to incorporate new evidence into prior probabilities to form an updated probability estimate. It is commonly regarded as the foundation of consistent rational reasoning under uncertainty. Bayes Theorem is named after Reverend Thomas Bayes who proved the theorem in 1763.~~See also:~~~~Bayesian probability~~~~,~~~~Priors~~~~,~~~~Likelihood ratio~~~~,~~~~Belief update~~~~,~~~~Probability and statistics~~~~,~~~~Epistemology~~~~,~~~~Bayesianism~~~~Bayes'~~Bayes' theorem commonly takes the form:~~P(A|B)=P(B|A)P(A)P(B)~~~~¬~~¬A|B)=P(A)P(~~¬~~¬A)~~⋅~~⋅P(B|A)P(B|~~¬~~¬A)~~Visualization~~Visualisation of~~Bayes'~~Bayes' Rule~~External links~~~~Arbital Guide to Bayes' Rule~~~~An Intuitive Explanation of Bayes' Theorem~~~~by Eliezer Yudkowsky~~~~Visualizing Bayes' theorem~~~~by Oscar Bonilla~~~~Using Venn pies to illustrate Bayes' theorem~~~~by~~~~oracleaide~~~~A Guide to Bayes’ Theorem – A few links~~~~by Alexander Kruel~~~~Bayes' Theorem~~~~, Wikipedia~~