Global sensitivity analysis using Monte Carlo estimation under fat-tailed distributions

Global sensitivity analysis found a widespread use in the modeling community to study the input and output relationship of typically complex numerical models. Many sensitivity analysis studies have been published over the years across different domains, from considering simple test problems to more complex case studies involving large numerical models. However, very few studies have addressed the issue of the presence of fat-tailed distributions and its implication for the sensitivity analysis. First, we recall how the law of large numbers slowly convergences depending on the extent of tails in the distributions. Then, we present some methods to study Paretianity in the data and estimate the tail index. We then apply these concepts to a real- world global sensitivity problem using a case study of long- term measurements of N₂O emissions dataset from WWTPs. We then propose a robust sensitivity metric based on mean absolute deviation for parameter importance ranking under fat- tailed distributions.