Maximum a Posteriori Estimation

What is the Maximum a Posteriori Estimation?

The maximum a posteriori estimation, also known as a MAP estimate, is the mode (most frequent value) of a statistical distribution. In terms of a classification problem, this value would represent the most probable class label for a given piece of data. 

This definition is an oversimplification of the concept because it does not address the most common application. In general, when we look for the MAP estimation, we are assessing continuous functions that discretely we may not have enough data to fully represent. Thus, we start to look at distributions and probabilities with random variables. The MAP estimation becomes more of a most probable estimate rather than a concrete answer. For example, when we look at classifying objects, the MAP estimate would give us the most probable class of an object based off of the observable data as well as any prior belief/information.