The Bayes decision rule chooses an action, meaning one of the decisions available to a decision maker, that minimizes the expected
value of a loss function with respect to the
posterior distribution. If 
is an action, 
is the unknown state, 
is the loss, and 
is the posterior
distribution after observing 
, the Bayes action minimizes the posterior
risk
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For classification with the zero-one loss function, which assigns loss 0 to a correct result and loss 1 to an incorrect result, the rule chooses the class having the largest probability under the posterior distribution.
