Jeremy E. Oakley, Alireza Daneshkhah and Anthony O'Hagan
University of Sheffield, U.K. and Shahid Chamran University, Iran
Publication details: Submitted to Bayesian Analysis. 2010.
We consider the use of the roulette method for eliciting an expert's prob- ability density function. In the roulette method, the expert provides prob- abilities of the uncertain quantity of interest lying in a particular `bin' by allocating `gaming chips' to that bin. This method can be appealing to some experts, given the graphical representation of their beliefs that it provides. Given the judgements made by the expert, we then quantify the uncertainty about their density function, given the fact the expert has only specified a limited number of probability judgements, and that these judgements are forced to be rounded. Uncertainty about the expert's density is quantified using a Gaussian process model, and we investigate the effect of the number of bins and chips used on this uncertainty.
Keywords: Expert elicitation, Gaussian process, imprecise probabilities, trial roulette.