I have 10 objects which can be classified as A,B,C,D with some probability. For example:
object 1: 40% A, 20% B, 30% C, 10% D
object 2: 10% A, 30% B, 40% C, 20% D ...
The question I want to ask is what fraction of my objects is A, B, C, D. I don't understand how to model the uncertainty given the discrete nature of classification and I can't find how to propagate the uncertainty to the fraction estimator afterwards. Perhaps I don't understand because the question I pose is wrong in the first place. It is important that I do it in a Bayesian way. Any help would be much appreciated.
Edit: The objects are independent.