1 hour may be judged plausible, with smaller variances of running times associated with smaller means within this interval. But if one already has ‘expert’ knowledge about the particular runner’s ability, a much smaller interval may be judged plausible for the mean, and one’s beliefs about the variance may not change appreciably given different plausible means.

In this paper, we propose a new elicitation method for quantifying opinions about an uncertain population mean and variance. Our method does not elicit judgements using hypothetical data and Bayes’ theorem, it does not use predictive elicitation and it assumes independence between the mean and variance. The article is organised as follows. In the next section we briefly discuss some motivating applications where the prior distributions will be important. In Section \[sec:families\] we discuss the choice of prior families of distributions for the uncertain mean and variance. In Section \[sec:method\], we present a detailed procedure of eliciting judgements using our proposed elicitation method. In Section \[sec:example\], we present a real elicitation example to illustrate the use of our proposed method in practice.

Motivating applications
=======================

Bayesian clinical trial design
------------------------------

Various authors have proposed a Bayesian alternative to a power calculation in the design 