Global sensitivity analysis using a new approach based on cumulative distribution functions

Abstract:

Global Sensitivity Analysis (GSA) has become a key tool for the analysis of environmental models. Objectives for GSA include model simplification to support calibration, diagnostic analysis of model controls and subsequent comparison with underlying perceptual models, or decision-making analysis to understand over what range of uncertainty a specific action is robust. Variance-based approaches are most widely used for GSA of environmental models. However, methods that consider the entire Probability Density Function (PDF) of the model output, rather than its variance only, are preferable in cases where variance is not an adequate proxy of uncertainty, e.g. when the output distribution is highly-skewed or multi-modal. Additionally, in contrast to variance-based strategies, they might allow for the mapping of the output on the input space, e.g. a prerequisite for the use of GSA in robust decision-making under uncertainty. Still, the adoption of density-based methods has been limited so far, possibly because they are relatively more difficult to implement. Here we present a novel GSA method, called PAWN, to efficiently compute density-based sensitivity indices, while also enabling the necessary input-output space mapping. The key idea is to characterize output distributions by their Cumulative Distribution Functions, which are easier to derive than PDFs. We discuss and demonstrate the advantages of PAWN by application to numerical and environmental examples. We expect PAWN to increase the application of density-based approaches and to be a necessary complimentary approach to variance-based GSA.