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I found this quotation, which I don't have time at the moment to properly integrate into the article, but which explains the distinction between these two types better than the current text:
"Epistemic uncertainty,... represents a lack of knowledge about the appropriate value to use for a quantity. Epistemic uncertainty is sometimes referred to as state of knowledge uncertainty, subjective uncertainty, Type B, or reducible uncertainty, meaning that the uncertainty can be reduced through increased understanding (research), or increased and more relevant data. [7,8] Epistemic quantities are sometimes referred to as quantities which have a fixed value in an analysis, but we do not know that fixed value. For example, the elastic modulus for the material in a specific component is presumably fixed but unknown or poorly known. In contrast, uncertainty characterized by inherent randomness which cannot be reduced by further data is called aleatory uncertainty. Some examples of aleatory uncertainty are weather or the height of individuals in a population: these cannot be reduced by gathering further information. Aleatory uncertainty is also called stochastic, variability, irreducible and type A uncertainty. Aleatory uncertainties are usually modeled with probability distributions, but epistemic uncertainty may or may not be modeled probabilistically. Regulatory agencies, design teams, and weapon certification assessments are increasingly being asked to specifically characterize and quantify epistemic uncertainty and separate its effect from that of aleatory uncertainty" [1]Kmote (talk) 22:08, 22 June 2015 (UTC)[reply]
It seems the distinction is that between the uncertainty about one particular realization versus the uncertainty over an ensemble of realizations. In the example given, the elastic modulus may be fixed for a single manufactured part, but it certainly would exhibit a statistical distribution over a lot of such parts. Fgnievinski (talk) 00:33, 23 June 2015 (UTC)[reply]
Even on its own terms, I do not see the distinction being made as being between 'one particular realization' and 'an ensemble of realizations' (which after all is just one realization in a bigger space). More generally, there is no difference between the weather and the other 'aleatory' examples given, and the examples for 'epistemic' uncertainty, except perhaps the amount of extra knowledge required to reduce this uncertainty significantly. After all, if uncertainty about the weather was 'irreducible', why would we be spending millions on weather forecasting. The whole distinction between 'aleatory' and 'epistemic' is illusory, and should be removed from this page as not being encyclopaedic, but research (although it does not really merit the latter label either). illywhacker; (talk) 13:08, 3 December 2015 (UTC)[reply]
Not quite attributable
"Sources of uncertainty" cites a reference at the top of the list, but the list in the cited reference is different. Section 2.1 of Kennedy & O'Hagan lists Parameter uncertainty, Model inadequacy, Residual variability, Parametric variability, Observation error, and Code uncertainty. — Preceding unsigned comment added by 129.6.59.205 (talk) 15:29, 24 February 2015 (UTC)[reply]
