Bayes' Theorem

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

Notation:

P(A)	Probability of event A
P(A B)	Probability of events A and B occurring together
P(A | B)	Condiional probability of event A given
	that event B has occurred: P(rain|cloudy)

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

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)