Uses of Bayes' Theorem

In doing an expert task, such as medical diagnosis, the goal is to determine identifications (diseases) given observations (symptoms). Bayes' Theorem provides such a relationship.

P(A | B) = P(B | A) * P(A) / P(B)

Suppose: A = Patient has measles, B = has a rash
Then: P(measles/rash) =
         P(rash/measles) * P(measles) / P(rash)

The desired diagnostic relationship on the left can be calculated based on the known statistical quantities on the right.

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