of clinical trials, in which a prior distribution is elicited for a treatment effect, and then the unconditional probability of a ‘successful trial’ (e.g. rejection of a null hypothesis as required by a regulator) is calculated via an integral of the power function with respect to the elicited prior [@SpiegelhalterFreedman:1986; @O'Hagan:2005; @Ren:2014]. Power functions typically depend on population variances of patient responses, and hence a prior distribution for this variance required.

Note that the main role of this prior is in the design stage: the calculation of the unconditional probability of a successful trial *before* the data have been observed (and this calculation may assume that the trial data will be analysed using a frequentist approach). [@O'Hagan:2005] considered uncertain variances, but did not propose or use formal elicitation methods.

Bayesian random-effects meta-analysis
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A common scenario in a meta-analysis is that we have a number of studies, each of which has attempted to estimate the effect of some ‘treatment’ in a randomised controlled experiment, and the aim is to synthesise the data from all the studies to infer an overall treatment effect. Often, unobserved differences in the study populations cause the treatment effects to vary between studies, and this is 