# Bayes Discriminant Rule

The rule to minimize the error rate by maximizing the posterior probability is the same for the
discrete and continuous case. The only difference is that probabilities are used instead of
probability densities. The following discriminant functions are equivalent decision rules:

## The 2-category case:

This is a classifier that places a pattern in one of two possible categories and is called a dichotomizer. Since we have 2 categories, we will have 2 discriminant function *g*_{1}(*x*) and *g*_{2}(*x*). As before, we would assign *x* to *w*_{1} if *g*_{1}(*x*)_{ > }g_{2}(*x*). Instead, we can define:

and decide *w*_{1} if *g*(*x*)>0. Two forms of the dIscriminant function are therefore: