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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