MLE = Maximum Likelihood Estimation
MAP = Maximum a posteriori
MLE is intuitive/naive in that it starts only with the probability of observation given the parameter (i.e. the likelihood function) and tries to find the parameter best accords with the observation. But it take into no consideration the prior knowledge.
MAP seems more reasonable because it does take into consideration the prior knowledge through the Bayes rule.
Here is a related question, but the answer is not thorough.
So, I think MAP is much better. Is that right? And when should I use which?
Best Answer
If a prior probability is given as part of the problem setup, then use that information (i.e. use MAP). If no such prior information is given or assumed, then MAP is not possible, and MLE is a reasonable approach.