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Disclaimer: I haven't had a quality Bayesian training.

I understand how, for the frequentist, the "normal" error is a smoke-in-mirrors things, where randomness arises from lack of precise measurement - hundreds of unmeasured contributors that are averaged across all their variations to produce a variable we refer to as an "error" term. Bayesians, like quantum theorists, conceptualize "randomness" differently. It may be unmeasured factors, or one may allow it to be an intrinsic "noise".

As I browse questions tagged "uncertainty" I find many reference the aleatoric and epistemic distinction. There are other examples where a poster is "uncertain" if their distribution is platykurtic or skewed - in which case the tag should probably be deleted.

Is the epistemic/aleatoric distinction the crux of "uncertainty" on the whole? Or are there broader considerations? If the distinction boils down to epistemic vs aleatoric, are there any further practical considerations so we can be sure this is actually a statistics topic, rather than a philosophy topic? Note: many fundamental probability questions loop into philosophy for which adequate notation may not exist, and it may not be applicable to modeling. An example to the opposite might be Pearl's causality where there are implications for structural equation modeling.

Can the following tag description be improved:

A broad concept concerning lack of knowledge, especially the absence or imprecision of quantitative information about a process or population of interest.

And how can we improve the tagging on prior questions?

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    $\begingroup$ Trite but I think true: We can't control how OPs add tags (although we can edit out mistaken or useless tags) or know quite what they understand by a tag (unless they comment). I will guess that uncertainty seems a relevant tag to many (else why use it) -- but fewer people than use it would be familiar with terms like epistemic or aleatoric. Then again, there are many other ways to express the same or other related distinctions. $\endgroup$
    – Nick Cox
    Commented Dec 10, 2024 at 11:26
  • $\begingroup$ Curiously, my understanding of the conceptualization of the error term in frequentism and Bayesianism is the opposite of yours: Frequentists are fine w/ there being some irreducible uncertainty in the world, whereas Bayesians believe this is just a lack of current knowledge. I've certainly seen many comments to that effect (although who knows if I can track any down right now). It may well be that there are people with both viewpoints in both camps. $\endgroup$
    – gung - Reinstate Monica
    Commented Dec 10, 2024 at 12:52
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    $\begingroup$ @NickCox, we certainly can't control how OPs add tags, but we can eliminate tags that tend to lead to worse organization of the site's content. If there is any merit in the tag, we could try to improve its usage by editing the excerpt, etc. I do agree that using the terms "epistemic" and "aleatoric" is less likely to lead OPs to better usage, though. $\endgroup$
    – gung - Reinstate Monica
    Commented Dec 10, 2024 at 13:00
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    $\begingroup$ I should have checked earlier but I note 3 people watching the tag and 1416 questions. I think that's consistent with it not being very useful -- but I have to be uncertain. $\endgroup$
    – Nick Cox
    Commented Dec 10, 2024 at 13:09
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    $\begingroup$ I don't want to call myself frequentist or Bayesian: it's a matter of fact that I don't often use Bayesian methods, not one of principle. I would say, both seriously and facetiously, that usually our data are wrong (in some sense: inadequate if not incorrect) and our models are wrong (in some sense; ditto). Whether to blame nature, society or ourselves for what is wrong in some analysis is sometimes interesting, even entertaining, as a topic for discussion, but more rarely helpful. $\endgroup$
    – Nick Cox
    Commented Dec 10, 2024 at 14:03

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