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An individual's belief in the occurrence of an event prior to any additional collection of evidence related to .

Later, the analyst gets access to the data , which contains information about event . She can now use Bayes formula to state her updated belief, in light of the evidence , expressed by the conditional probability

(2.4)

that is a simple consequence of the multiplication rule for probabilities

The analyst's updated belief about , after she has access to the evidence , is called the posterior probability .