would weight prior knowledge and hypothetical data precisely according to Bayes’ theorem in any case. The expert may be insensitive to the sample size, for example in accounting for the variability in a sample mean [@Tversky:1971]. We think it desirable to have alternative elicitation methods available to the expert.

[@KADANE:1980] and [@Al-Awadhi:1998] infer judgements about the parameters $\mu$ and $\sigma^2$ from judgements about the observable quantities $X_i$, by eliciting summaries from the expert’s predictive distribution. For example, suppose we wish to elicit an expert’s opinion about the variance parameter $\sigma^2$ of a random variable $X$ that follows a normal distribution with a known mean $\mu$. Since $\sigma^2$ is not directly observable then the expert is asked to make judgements about the observable quantity $X$, and we infer $p(\sigma^2)$ from these judgements. Any choice of $p(\sigma^2)$ implies a distribution $$p_X(x) = \int_{\mathbb{R}^{+}} p_X(x \mid \sigma^2) p(\sigma^2) d\sigma^2,$$ and we suppose that a particular choice of $p(\sigma^2)$ will result in the above integral (approximately) matching the expert’s beliefs about $X$, so that this choice of $p(\sigma^2)$ describes the expert’s underlying beliefs about $\sigma^2$. A concern here is whether an expert really is able to account for his or her uncertainty about $\sigma^2$ 