Statistics Dictionary
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Bayes Rule
Bayes' theorem (also known as Bayes' rule) is a useful tool for calculating
conditional probabilities. Bayes' theorem can be stated as follows:
Bayes' theorem.. Let A1, A2,
... , An be a set of mutually exclusive events that together form
the sample space S. Let B be any event from the same sample space, such that
P(B) > 0. Then,
| P( Ak | B ) =
|
P( Ak
∩ B )
[ P( A1 ∩
B ) + P( A2 ∩
B ) + . . . + P( An ∩ B ) ]
|
Note: Invoking the fact that P( A
k ∩
B ) = P( A
k )P( B | A
k ), Baye's theorem can
also be expressed as
| P( Ak | B ) =
|
P( Ak ) P( B | Ak )
[ P( A1 ) P( B | A1 ) + P( A2 ) P( B | A2 )
+ . . . + P( An ) P( B | An ) ]
|