 Bayes classifier

Under zero-one loss, a Bayes classifier assigns an observation to a class of greatest posterior probability. For two classes with prior probabilities ${\pi }_0,{\pi }_1$ and densities $f_0,f_1$, it chooses class one exactly when ${\pi }_1{f}_1(x)\ge {\pi }_0{f}_0(x)$.

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.