Bayes' Theorem

Many of the methods used for dealing with uncertainty in expert systems are based on Bayes' Theorem.


P(A) Probability of event A
P(A B) Probability of events A and B occurring together
P(A | B) Conditional probability of event A
given that event B has occurred

If A and B are independent, then P(A | B) = P(A).

Expert systems usually deal with events that are not independent, e.g. a disease and its symptoms are not independent.

Bayes' Theorem

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

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