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PhilGoetz comments on Average utilitarianism must be correct? - Less Wrong
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According to Wikipedia, that is what is meant by epistemic uncertainty. It says that one type of uncertainty is
"1. Uncertainty due to variability of input and / or model parameters when the characterization of the variability is available (e.g., with probability density functions, pdf),"
and that all other types of uncertainty are epistemic uncertainty.
And here's a quote from "Separating natural and epistemic uncertainty in flood frequency analysis", Bruno Merz and Annegret H. Thieken, J. of Hydrology 2004, which also agrees with me:
"Natural uncertainty stems from variability of the underlying stochastic process. Epistemic uncertainty results from incomplete knowledge about the process under study."
This "natural uncertainty" is a property of distributions, while epistemic uncertainty to which you refer here corresponds to what I meant. When you have incomplete knowledge about the process under study, you are working with one of the multiple possible processes, you are operating inside a wide event that includes all these possibilities. I suspect you are still confusing the prior on global state space with marginal probability distributions on variables. Follow the links I gave before.