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Bayes

The theorem that if an event B is known to have occurred as the result of some one event in a set (Ak), then the probability that it was the particular event Aj that caused B is given by P(Aj B) = P(B Aj) P(Aj)/ Sk(P(Ak) P(B Ak)), where Aj is from a set of J members. The numerator is the product of the probability of event Aj, regardless of whether B occurred or not, times the probability that B would have occurred if Ajk times the probability that B would have occurred if that Aj had. If all the conditions of the theorem are fulfilled, the theorem is certainly correct. The difficulties in applying the theorem, however, are caused by insufficient knowledge of the a priori probabilities. The theorem has gained considerable notoriety through its misuse, e.g., by mistaking prior data for a priori knowledge.

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