It seems that interest rises to know the uncertainty in our predictions. For example this finds the uncertainty of a prediction by a random forest. Or this paper finds the uncertainties of a neural network used in computer vision. In general, Gaussian processes are famous for getting the uncertainty in case of non parametric regression.
My question about all these uncertainties is:
Is uncertainty a property of these methods and these models or does uncertainty depend on the model choice?
It follows from this thought experiment:
Let’s say we have a data set. A fixed data set. We fit a) a Bayesian random forest b) a neural network c) a Gaussian Process to this data. Now I get a new input, x. I wonder if all three models would give the same uncertainty about the prediction on data point x.