Let's say that I have a problem that is basicly classification. That is, given some input and a number of possible output classes, find the correct class for the given input. Neural networks and decision trees are some of the algorithms that may be used to solve such problems. These algorithms typically only emit a single result however: the resulting classification.

Now what if I weren't only interested in one classification, but in the posterior probabilities that the input belongs to each of the classes. I.E., instead of the answer "This input belongs in class A", I want the answer "This input belongs to class A with 80%, class B with 15% and class C with 5%".

My question is not on how to obtain these posterior probabilities, but rather on the correct terminology to describe the process of finding them. You could call it regression, since we are now trying to estimate a number of real valued numbers, but I am not quite sure if that's right. I feel it's not exactly classification either, it's something in between the two.

Is there a word that describes the process of finding the class conditional posterior probabilities that some input belongs in each of the possible output classes?

P.S. I'm not exactly sure if this question is enough of a programming question, but since it's about machine learning and machine learning generally involves a decent amount of programming, let's give it a shot.