Bayes Decision Rule

$$x\in w_j\leftrightarrow p(x|w_j)P(w_j)=\underset{i}{\max }p(x|w_i)P(w_i)$$

All BDR-based classifiers are also called a Maximum A Posteriori Classifier.

---

The decision rule itself is given by

$$x\in w_j\leftrightarrow P(w_j|x)=\underset{i}{\max }P(w_i|x)$$