and was informed by expert judgement only. This is a quantify that would vary from one milking to the next, but the distribution of amounts of contamination would be uncertain.

The risk analysis may involve the use of a mechanistic model of the form $Y=f(X)$, where $X$ has a population distribution $N(\mu,\sigma^2)$, with $\mu,\sigma^2$ uncertain. Given an elicited distribution for $\mu,\sigma^2$, analysis can proceed with a ‘2D’ or ‘second-order’ Monte Carlo simulation [see, for example, @Wu:2004]: a $\mu, \sigma^2$ pair is sampled from its distribution, and then a sample $X_1,\ldots,X_n$ from $N(\mu,\sigma^2)$ is propagated through $f$ to obtain a sample $Y_1,\ldots,Y_N$. One can then examine how the distribution of model outputs changes as function of $\mu,\sigma^2$, and hence explore both the effects of aleatory uncertainty within the population, and epistemic uncertainty about the population distribution parameters. The decision-maker may consider reducing uncertainty about $\mu,\sigma^2$ if this source of uncertainty appears relatively important.

Prior families of distributions for the mean and variance \[sec:families\]
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In this paper, we suppose that the expert’s uncertainty about $\mu$ can be represented by a normal distribution $$\mu \thicksim \mbox{N} (m, v),$$ and that her uncertainty about $\sigma^2$ can be represented by an inverse gamma distribution 