# Extremum Sensitivity Analysis with Polynomial Monte Carlo Filtering

## TL;DR

This paper enhances global sensitivity analysis by introducing efficient computation methods for sensitivity indices using polynomial ridge approximations and proposes a novel extremum Sobol' index based on Monte Carlo filtering, with empirical exploration of their relationship.

## Contribution

It introduces a new approach to compute sensitivity indices efficiently with polynomial ridge approximations and proposes extremum Sobol' indices based on Monte Carlo filtering.

## Key findings

- Sensitivity indices can be computed with fewer model evaluations using ridge approximations.
- Extremum Sobol' indices based on Monte Carlo filtering are effective near output extrema.
- Empirical analysis shows a relationship between MCF-based indices and skewness-based indices.

## Abstract

Global sensitivity analysis is a powerful set of ideas and heuristics for understanding the importance and interplay between uncertain parameters in a computational model. Such a model is characterized by a set of input parameters and an output quantity of interest, where we typically assume that the inputs are independent and their marginal densities are known. If the output quantity is smooth, polynomial chaos can be used to extract Sobol' indices. In this paper, we build on these well-known ideas by examining two different aspects of this paradigm. First, we study whether sensitivity indices can be computed efficiently if one leverages a polynomial ridge approximation -- a polynomial fit over a subspace. Given the assumption of anisotropy in the dependence of a function, we show that sensitivity indices can be computed with a reduced number of model evaluations. Second, we discuss methods for evaluating sensitivities when constrained near output extrema. Methods based on the analysis of skewness are reviewed and a novel type of indices based on Monte Carlo filtering (MCF) -- extremum Sobol' indices -- is proposed. We combine these two ideas by showing that these indices can be computed efficiently with ridge approximations, and explore the relationship between MCF-based indices and skewness-based indices empirically.