A Bayes classifier is a classification rule that applies the Bayes decision rule. Given probabilities 
under a posterior
distribution for classes 
, ..., 
and a loss function 
, where 
is the numerical penalty for choosing action 
when the true class is 
, the Bayes classifier chooses an action 
that minimizes the posterior expected loss
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For a zero-one loss function, this is equivalent to choosing the class having largest such probability,
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