when making judgements about $X$. A possibility is that the expert instead only makes judgements about $X$ conditional on some estimate of $\sigma^2$.

[@KADANE:1980] use conjugate priors for $\mu$ and $\sigma^2$ which force the expert’s opinion about the two parameters to be dependent. However, it is possible in reality that knowledge of one parameter would not change the expert’s opinion about the other. [@Al-Awadhi:2001] argued that, unless mathematical tractability is required, then it can be better to assume independence between the two parameters, and that this helps the expert focus on the assessments of each parameter separately. They proposed an elicitation method for the multivariate normal distribution where the mean vector and covariance matrix are assumed to be independent, though their method also asks the expert to update his or her judgements in the light of hypothetical data.

We argue that the better informed the expert, the less likely a judgement of dependence between the two parameters would be required. For example, consider the distribution of running times for an individual over a distance of 5km. With no information about the ability of the runner, one might have considerable uncertainty about the mean, e.g. an interval of 15 minutes to 