Title: Dependent Decision Analysis
Authors: Robert T. Clemen Duke University and Terence Reilly Babson College
Date: November 1996
Status: working paper

Although any given decision analysis may unfold in a problem-specific way, a number of steps are commonly found in an analysis, including creating a deterministic model, performing a sensitivity analysis to identify critical variables, modeling uncertainty, evaluating the model by calculating expected value, expected utility, or risk profiles, and refining the model on the basis of expected-value-of-information or further sensitivity-analysis results. In fact, the steps in a conventional decision analysis have been formalized along precisely these lines.

In this paper, we describe how the conventional approach can be enhanced by introducing dependence assessments (Spearman's rho) for the input variables in the initial sensitivity analysis, which in turn provide flexibility in the uncertainty-modeling stage. By leveraging the information in the dependence assessments, conditional relations and conditional distributions can be approximated with no further judgmental assessments. Alternatively, a complete joint distribution can be constructed. Such a model is based on the use of the dependence assessments to construct an appropriate copula representation of the joint distribution. We demonstrate how pairwise judgments of correlations, along with fractile assessments from the initial sensitivity analysis, can be used with the multivariate-normal copula to create a joint distribution for the critical random variables in a simple example.

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