# Does aleatoric uncertainty exist?

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?

• You would have (absolute) aleatoric uncertainty when measuring position of an electron, due to Heisenberg's uncertainty principle. Even if we disregard "a lot of assumptions" there will be fundamental "imperfection" in the data. But generally, the separation is just relative to a model. The "lot of assumptions" involved in measurements (production of data), and models utilized there, are irrelevant as far as judging imperfections of the model (under consideration) that receives them as inputs, and the uncertainty it contributes itself. Apr 23, 2020 at 10:44
• Thank you for the comment! Heisenberg's uncertainty principle, if my high-school physics memory doesn't betray me, would be similar to the quantum mechanics example I mentioned above. The electron has a true location, we just can't get it because the process of measuring it destroys the information we are after: that's what I would call a 'hard limit' of uncertainty. If this hard limit always exists, then it is impossible to find a model with zero epistemic uncertainty, as its perfection must be tested against reality. As a consequence, I would argue that the distinction is still not required. Apr 23, 2020 at 11:13
• This is not a place for arguing, just describing what is out there. That he process of measuring "destroys the information" was the initial view of Bohr, it is long discarded. There is no information to destroy, it is generated by the measurement itself, along with uncertainty. In any case, aleatoric uncertainty for a given model can be epistemic in a broader context. This is a special case of distinguishing internal from external, which is always relative. Apr 23, 2020 at 11:47
• Certainly, it wasn't my intention to argue - just to clarify the question as best as I can within a character limit. If I interpret your response correctly, then you suggest that the distinction between aleatoric and epistemic uncertainty is a subjective question of where to draw the line, to define the 'internal' against the 'external'. So with a broad enough view, everything is epistemic? Given the ubiquity of these concepts in science, I imagine this topic was discussed before: is there any mathematical or philosophical literature exploring this topic fundamentally you can recommend? Apr 23, 2020 at 12:11
• "The electron has a true location, we just can't get it because the process of measuring it destroys the information we are after" That would be a "hidden variables interpretation", one which posits a quantum system has additional properties beyond those assigned to it by the quantum state. Bell's theorem shows that no local hidden variables theory can explain quantum behavior (one where influences cannot travel faster than light), and although Bohmian mechanics replicates quantum predictions, it is fundamentally untestable because the hidden variables are not measurable even in principle. Apr 23, 2020 at 19:39