A Bayes classifier is a statistical classification technique based on Bayes' theorem, which provides a way to update the probability of a hypothesis as more evidence or information becomes available. In the context of classification, the Bayes classifier classes a given sample into one of several classes based on the probabilities of the sample belonging to each class.
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Under zero-one loss, a Bayes classifier assigns an observation to a class of greatest posterior probability. For two classes with prior probabilities and densities , it chooses class one exactly when .