Sensitivity Analysis with Correlated Inputs – an Environmental Risk Assessment Example

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Courtesy of Oracle Crystal Ball GBU

ABSTRACT
Crystal Ball® calculates sensitivities by computing rank correlation coefficients between model inputs (assumptions) and outputs (forecasts) – an approach that is known to provide inaccurate results for correlated assumptions. This  paper describes the Partial Correlation Coefficient (PCC) concept for sensitivity analysis of probabilistic models with correlated inputs. PCCs quantify the strength of a linear relationship between input-output pairs after eliminating the linear influence of other input variables, and can be readily calculated from the input-input correlation matrix and the input-output correlation vector. The methodology is illustrated using an analytical model of environmental health risk arising from groundwater-borne ra-dionuclide migration from a nuclear waste repository.

1 INTRODUCTION
Sensitivity analysis, in its simplest sense, involves quantification of the change in model output corresponding to a change in one or more of the model inputs. In the context of probabilistic models, however, sensitivity analysis is generally taken to imply identification of input parameters that have the greatest influence on the spread (variance) of model results (Helton, 1993). This is also referred to as global sensitivity or uncertainty importance analysis to distinguish it from the classical sen-sitivity measures obtained as partial derivatives of the output with respect to inputs of interest (Saltelli et al., 2000).

The contribution to output uncertainty (variance) by an input is a function of both the uncertainty of the input variable and the sensitivity of the output to that particular input. In general, input variables identified as important in global sensitiv-ity analysis have both characteristics; they demonstrate significant variance and are characterized by large sensitivity coeffi-cients. Conversely, variables which do not show up as important per these metrics are either restricted to a small range in the probabilistic analysis, and/or are variables to which the model outcome does not have a high sensitivity.

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