Bayes rule is a mathematical equation that allows you to calculate conditional probabilities when you know conditional probabilities the 'other way round'. For example, if you know the probability of a patient exhibiting various symptoms if they have a particular illness, it allows you to calculate the probability that they have the illness given the symptoms they are showing. In the case of two mutually exclusive states A and B (e.g. A="has a cold", B="does not have a cold"), and an observation C (e.g. "has a runny nose"), then Bayes rule is P(A|C) = P(C|A)P(A) / ( P(C|A)P(A) + P(C|A)P(B) ). Note that for this you need to know the prior probability of each occurrence, P(A) and P(B); when these are known from data they are also known as the base rate.

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