Yes, epistemic uncertainty (that is, uncertainty due to a lack of knowledge) is likely the biggest thorn in the side of a modeler/computational physicist/ computational engineer (I would make a bolder statement, but, at the risk of being redundant, I just don’t know man). One way of dealing with this is the concept of Probability Boxes. The basic idea is to treat aleatory uncertainties as distributional and epistemic as to be an interval. On the one hand, this is conservative because we have no assumptions about the underlying distribution, but the actual distribution is not likely to be completely flat.
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In this post we’ll look at some actual experimental data (crazy, I know) and use simulation data from the code Hyades2D to try and produce calibrated results. The data is the very same used in Stripling, McClarren, et al., and we show how Gaussian process models can be used to make sense of simulation and experimental data.

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If you’re in the business of sampling from a distribution that you only know up to a constant normalization, Markov-Chain Monte Carlo (and the Metropolis Algorithm) are for you.  The Metropolis algorithm is name after a scientist, and not the adopted hometown of an illegal alien, but it can leap unruly distributions in a (burn-in + n) bound.  In particular, Bayes’ Theorem gives us an unnormalized distribution we would like to sample from.

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