A simple and efficient method for global sensitivity analysis based on cumulative distribution functions. (May 2015) - Pianosi, Francesca; Wagener, Thorsten
Abstract: Variance-based approaches are widely used for Global Sensitivity Analysis (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 when it is multi-modal. 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. The key idea is to characterise output distributions by their Cumulative Distribution Functions (CDF), which are easier to derive than PDFs. We discuss and demonstrate the advantages of PAWN through applications to numerical and environmental modelling examples. We expect PAWN to increase the application of density-based approaches and to be a complementary approach to variance-based GSA. Highlights: We present a new density-based GSA method called PAWN to complement variance-based GSA. Differently from variance-based methods, PAWN can be applied to highly-skewed or multi-modal output distributions. Differently from other density-based methods, PAWN uses output CDFs, which simplifies numerical implementation. PAWN can be easily tailored to focus on output sub-ranges, for instance extreme values. Intermediate results generated in the application of PAWN can be visualized to gather insights about the model behaviour.