# A sensitivity analysis of the PAWN sensitivity index

## TL;DR

This paper investigates how the PAWN sensitivity index's robustness is affected by its design parameters, revealing potential biases and challenges in reliably ranking model inputs compared to Sobol' indices.

## Contribution

It provides a comprehensive sensitivity analysis of PAWN's design parameters and compares its robustness with Sobol' indices, highlighting limitations in input influence detection.

## Key findings

- PAWN's results are sensitive to its design parameters.
- Design uncertainties can bias PAWN's input ranking.
- PAWN may struggle to distinguish influential from non-influential inputs.

## Abstract

The PAWN index is gaining traction among the modelling community as a sensitivity measure. However, the robustness to its design parameters has not yet been scrutinized: the size ($N$) and sampling ($\varepsilon$) of the model output, the number of conditioning intervals ($n$) or the summary statistic ($\theta$). Here we fill this gap by running a sensitivity analysis of a PAWN-based sensitivity analysis. We compare the results with the design uncertainties of the Sobol' total-order index ($S_{Ti}^*$). Unlike in $S_{Ti}^*$, the design uncertainties in PAWN create non-negligible chances of producing biased results when ranking or screening inputs. The dependence of PAWN upon ($N,n,\varepsilon, \theta$) is difficult to tame, as these parameters interact with one another. Even in an ideal setting in which the optimum choice for ($N,n,\varepsilon, \theta$) is known in advance, PAWN might not allow to distinguish an influential, non-additive model input from a truly non-influential model input.