= Bayes' Rule =

'''Bayes' rule''' is a probability formulation.

<<TableOfContents>>

----



== Formulation ==

The straightforward statement of Bayes' rule is:

{{attachment:bayes1.svg}}

This is the formulation with the most intuitive interpretation. The probability of event A given event B has already happened is the same as the probability of both events A and B happening divided by the probability of B already having happened. If the probability of event B having happened is 0, then the equation does not hold, but then the conditional and joint probabilities are also necessarily 0.

This can be rewritten, substituted into itself, and decomposed into several other formulations that are generally useful.

{{attachment:bayes2.svg}}

{{attachment:bayes3.svg}}

{{attachment:bayes4.svg}}

{{attachment:bayes5.svg}}

It's also important to note that, in contexts where all events are binary, the following notations are often used instead.

{{attachment:bayes6.svg}}

{{attachment:bayes7.svg}}



----
CategoryRicottone