Classifier with the Lowest Error Probability

$\text{arg max}$ selects for $s$ that gives the biggest Posteriori.

$$\boxed{s^{\ast }=\arg \underset{i\in \mathcal{S}}{\max }p(s=i\mid \mathbf{x})}$$

Note: maximum Posteriori gives lesser Error than maximum Likelihood because the Prior plays a very important role in the classification.