Expert judgement combination using moment methods

Moment methods have been employed in decision analysis, partly to avoid the computational burden that decision models involving continuous probability distributions can suffer from. In the Bayes linear (BL) methodology prior judgements about uncertain quantities are specified using expectation (rather than probability) as the fundamental notion. BL provides a strong foundation for moment methods, rooted in work of De Finetti and Goldstein. The main objective of this paper is to discuss in what way expert assessments of moments can be combined, in a non-Bayesian way, to construct a prior assessment. We show that the linear pool can be justified in an analogous but technically different way to linear pools for probability assessments, and that this linear pool has a very convenient property: a linear pool of experts’ assessments of moments is coherent if each of the experts has given coherent assessments. To determine the weights of the linear pool we give a method of performance based weighting analogous to Cooke's classical model and explore its properties. Finally, we compare its performance with the classical model on data gathered in applications of the classical model.