Sensitivity Analysis of Model Input Dependencies Using Copulas

Abstract

Many important decision and risk analysis problems are complicated by dependencies between input variables. In such cases, standard one-variable-at-a-time sensitivity analysis methods are typically eschewed in favor of fully probabilistic, or n-way, analysis techniques which simultaneously model all n input variables and their interdependencies. Unfortunately, much of the intuition provided by one-way sensitivity analysis and its associated graphical output displays such as Tornado diagrams may not be available in fully probabilistic methods. It is also difficult or impossible to isolate the marginal effects of variables in an n-way analysis. In this paper, we present a dependence-adjusted approach for identifying and analyzing the impact of the input variables in a model through the use of probabilistic sensitivity analysis based on copulas. This approach provides insights about the influence of both the input variables and the dependence relationships between the input variables. A key contribution of this approach is that it facilitates assessment of the relative marginal influence of variables for the purpose of determining which variables should be modeled in applications where computational efficiency is a concern, such as in decision tree analysis of large scale problems. In addition, we also investigate the sensitivity to the magnitude of correlation in the inputs.

Keywords: Decision Analysis, Sensitivity Analysis, Correlations, Dependence, Copulas