# Global sensitivity analysis in the context of imprecise probabilities (p-boxes) using sparse polynomial chaos expansions

arXiv: https://arxiv.org/abs/1705.10061 · HTML: https://mlsanity.com/paper/1705.10061/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2017.

## Built on by (most cited first, 3 of 3)

- [Deep Adaptive Arbitrary Polynomial Chaos Expansion: A Mini-data-driven Semi-supervised Method for Uncertainty Quantification](https://mlsanity.com/paper/2107.10428/) (2021)
- [Consistency regularization-based Deep Polynomial Chaos Neural Network Method for Reliability Analysis](https://mlsanity.com/paper/2203.15655/) (2022)
- [Data-driven sparse polynomial chaos expansion for models with dependent inputs](https://mlsanity.com/paper/2101.07997/) (2021)

## Abstract (arXiv)

Global sensitivity analysis aims at determining which uncertain input parameters of a computational model primarily drives the variance of the output quantities of interest. Sobol' indices are now routinely applied in this context when the input parameters are modelled by classical probability theory using random variables. In many practical applications however, input parameters are affected by both aleatory and epistemic (so-called polymorphic) uncertainty, for which imprecise probability representations have become popular in the last decade. In this paper, we consider that the uncertain input parameters are modelled by parametric probability boxes (p-boxes). We propose interval-valued (so-called imprecise) Sobol' indices as an extension of their classical definition. An original algorithm based on the concepts of augmented space, isoprobabilistic transforms and sparse polynomial chaos expansions is devised to allow for the computation of these imprecise Sobol' indices at extremely low cost. In particular, phantoms points are introduced to build an experimental design in the augmented space (necessary for the calibration of the sparse PCE) which leads to a smart reuse of runs of the original computational model. The approach is illustrated on three analytical and engineering examples which allows one to validate the proposed algorithms against brute-force double-loop Monte Carlo simulation.