I am wondering whether the distinction into epistemic and aleatoric uncertainty really makes sense. The way I have understood it (and Wikipedia seems to define it) the distinction is:
- epistemic uncertainty is inperfection of the model, which may be alleviated by improving process representation.
- aleatoric uncertainty is inperfection of the data to which we apply our model, so even a model with (hypothetical) zero epistemic uncertainty might still yield uncertain predictions due to aleatoric input uncertainty.
I wonder whether fundamentally aleatoric uncertainty isn't just another type of epistemic uncertainty. For example, if I measure the temperature with a mercury thermometer, I am not really measuring temperature: I am observing the temperature-based expansion of mercury in a glass tube, then compare its rise to a scale at its side, and convert this length into a temperature using a regression obtained by some previous experiment.
This process contains a lot of assumptions, so in a sense it constitutes a model of its own. It seems to me that any aleatoric uncertainty we obtain from repeated temperature measurements could seemingly be equally well explained with epistemic uncertainty of the thermometer model. The 'hard' uncertainty limit in the universe found in quantum mechanics might be an exception, but if this is a fundamental property of the universe, one might equally well consider it a hard limit on epistemic uncertainty.
Is there a nuance I have missed? Are there any papers or books on the topic you could recommend?