typically handled by modelling the treatment effects as random effects, drawn from some distribution. Although sample sizes within studies may be large, the number of studies can be small, so that there is very little information in the data about the population variance of treatment effects, and the prior distribution for this variance plays an important role. There is some discussion of priors for variances of random effects in [@Spiegelhalter:2004], Section 5.7.3, including some informal elicitation approaches when the treatment effect is measured as a log odds ratio.

Risk analysis and 2D Monte Carlo methods
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In a risk analysis, a decision-maker may have to make decisions based on expert opinion only [see, for example, the discussion of the role of expert judgement in food safety risk assessment in @EFSA:2014]. In particular, a risk analysis may need to consider both aleatory uncertainty caused by variability within a population, and epistemic uncertainty about the extent of this variability. For example, [@Clough:2006; @Clough:2009] analyse the risk of contamination of farm-pasteurised milk contamination with Vero-cytotoxigenic E.coli O157. Their analysis involves the use of a mechanistic model with various uncertain inputs. One input describes the amount of faecal contamination in bulk tank per milking, 