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I understand how Naive Bayes' Classifier is working and I also understand Maximum a Posterior but what I don't understand is the connection between Naive Bayes' Classifier and Maximum a Posterior. I don't know what I don't see in Naive Bayes' Classifier to understand Naive Bayes' Classifier is using Maximum a Posterior. I can still calculate according to the way it is but it is not the point.
How can I show they are connected? or Naive Bayes' Classifier is based on Maximum a Posterior?
It's a MAP decision rule because it respects the class priors and decides based on the posterior, not the likelihood only, e.g. $$P(C=c|X)\propto \underbrace{P(X|C=c)}_{\text{likelihood}}\underbrace{P(C=c)}_{\text{class prior}}$$ MAP rules respect posteriors, and ML rules respect likelihood instead.
