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A.1 Bayes' theorem

The probability
*p*(, *j*) of observing both and *j* can be written in two ways,

*p*(, *j*) = *p*(| *j*)*P*(*j*) = *P*(*j*|)*p*() . |
(A.1) |

*p*() is the probability of (independent of *j*), *P*(*j*) is the probability of *j* (independent of ),
*p*(| *j*) is the probability of under the condition that *j* is given, and
*P*(*j*|) is the probability of *j* under the condition that is given. Reorganizing (A.1) about
*P*(*j*|) gives

*P*(*j*|) = . |
(A.2) |

This is Bayes' theorem.

*Heiko Hoffmann *

2005-03-22