Is it practical to distinguish aleatoric uncertainty from epistemic uncertainty? I know the difference between the two, but don't know if it is practical to tell them apart technically.

Say, I have trained a deep neural network and I use some techniques to get the posterior predictive distribution and capture both the two types of uncertainty. But without knowing if the input features have left the knowing grounds(extrapolation) or not, how do I determine two distributions(CPDs) with the same variance belonging to aleatoric or epistemic uncertainty?

Imagine that I train a classification model with 10 classes. I run a MC dropout model tens of times. The aleatoric uncertainty is expressed in the distribution across the classes, which is zero if one class gets a probability of one. The epistemic uncertainty is expressed in the spread of the predicted probabilities of one class.
