Vose (in Risk analysis a quantitative guide, 2008) argues that it is preferable to use non-parametric distributions when eliciting knowledge about an unknown distribution from experts. The argument is that experts may not be familiar with e.g. the shape parameter of a Weibull distribution and would perform better if using other methods of describing a distribution that would then be non-parametric.
Let’s consider a triangular distribution. Let’s say I ask one expert about the lowest, most likely and highest value a stochastic variable can take and derive a simple triangular distribution from this. Next I ask another expert with slightly differing views on the three values, leading me to the question of how to aggregate / combine these estimates (assuming that both have real expertise and are unbiased / reasonably well calibrated). Would it be valid to assume that the expert’s estimates follow some stochastic distribution (e.g. normal, gamma) and can be combined through a Bayesian update? To stick to the closed form solution I would further assume conjugate priors for the distribution of the expert's estimates. In this update the first expert’s estimates would constitute the prior, the second expert’s would constitute the likelihood from which the posterior for each estimate (low, most likely, high) would be derived. Are there any established methods for this application?
