# Estimation in Naive Bayes

In Multinomial Naive Bayes Classifier, which parameter estimation do we use, is it Maximum Likelihood or Maximum A Posteriori?

If any one of the esteemed members may kindly help me out.

For learning the NBC, the ML estimate for feature $F_i$ given class $C_j$ is often used. That is $$P(F_i \mid C_j) \leftarrow \frac{\text{# cases from class C_j with feature F_i}}{\text{# cases from class C_j}}.$$ There are usually two options for setting the class marginals.. either $$P(C_j) \leftarrow \frac{1}{\text{# of possible classes}},$$ or $$P(C_j) \leftarrow \frac{\text{# cases from class C_j}}{\text{# of cases}}.$$ The latter is the ML estimate for the marginal, and the former is just a nameless 'objective' approach. In this setup, there is no MAP estimate unless a prior is incorporated, but that is nonstandard.