Bayes' Theorem says that if event B has a non-zero probability of occuring, then when it does occur, we can compute the probability that event A also happened as follows:

This gives a sort of "inverse probability" calculation.

See also:

A recent use of this theorem is spam filtering. Although the application is not strictly correct, it's close enough that it can be very effective. An alternative, or even supplementary spam filtering system uses Markov Chains.
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Local neighbourhood - D3

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