Modeling expert dependency in decision analysis

This research considers how a decision maker should use probability forecasts obtained from experts and in particular on how the dependence among expert opinions can be quantified. Most previous research on the aggregation of expert opinion in decision analysis has been of two types: easily implemented non-Bayesian techniques such as weighted averages, or limited Bayesian techniques based on specialized families of distributions. What is needed is an aggregation technique that efficiently and explicitly allows for a complete range of possible dependence structures among expert opinions, using a small number of reasonably assessable parameters.;From a Bayesian point of view, a decision maker's prior opinion should be updated to incorporate the forecasts of n experts through the assessment of an n-dimensional joint likelihood function. However, assessment of such joint distributions is notoriously problematic for all but the most trivial cases. This research develops a method of generating joint likelihood functions based on the theory of the copulas.;Copulas are statistical functions that act on univariate cumulative marginal distributions to create a cumulative joint likelihood function that maintains the same marginals while adding dependence information. Different copulas represent different dependence structures among the experts' opinions, while at the same time allowing the decision maker to separate the assessment of dependence from that of the quality of each individual expert.;In this dissertation, a methodology for using copulas for combining multiple probability forecasts on a binary event is developed. This methodology preserves an assessed set of general marginal likelihood functions, and allows for the use of any dependence structure. A new interpretation of copulas and their derivatives in the expert context is also presented, leading to promising practical assessment techniques for creating these general copulas and joint likelihood functions. A real-world example based on a linear conditional expectations model and a Normal copula is examined in detail. Also developed is a new property of some copulas, called self-complementarity, that may be appropriate for combining expert opinions in certain circumstances, as well as a method for creating copulas that satisfy this property.