Expert judgments are key inputs in important decision-making problems, and the elicitation and modeling of such judgments are formalized in methodologies such as decision analysis, risk analysis, and expert systems. As problems grow in complexity (e.g., multi-systems modeling for regional and global environmental change), with many variables of interest, assessing and modeling expert knowledge about relationships among variables becomes more crucial. Up to this point, conditional distributions have provided the only formal, rigorous, and fully general way to represent an expert's knowledge about a set of interrelated random variables. However, this approach becomes unwieldy and infeasible unless the number of variables is very small, and it may pose cognitive problems. An alternative approach involves representing joint distributions in terms of copulas, which are functions of the marginal distributions and encode the dependence among the variables. The overall goal of the proposed research is to develop procedures for dependence assessment in practical expert-knowledge encoding situations. In this one-year pilot project, the researchers will focus primarily on the mathematical development and dependence assessments. They will also begin an investigation into the behavioral issues involved in the elicitation of expert knowledge via marginal distributions and dependence measures (as compared to marginal and conditional distributions). This initial work will provide the basis for the future development of sound assessment procedures and implementable protocols as well as an analytical framework for using those assessments.
