Fisher-Rao distance between truncated distributions and robustness analysis in uncertainty quantification

TL;DR

This paper introduces a method using Fisher-Rao distance on truncated distributions to analyze the robustness of model outputs under input uncertainties, supported by theoretical results and a practical industrial case study.

Contribution

It develops a framework for robustness analysis in uncertainty quantification using Fisher-Rao distance on truncated distributions, with theoretical justification and practical implementation tools.

Findings

The approach effectively characterizes output variability under input distribution perturbations.

Theoretical results support the use of Fisher-Rao distance in robustness analysis.

Application to an industrial case demonstrates practical feasibility.

Abstract

Input variables in numerical models are often subject to several levels of uncertainty, usually modeled by probability distributions. In the context of uncertainty quantification applied to these models, studying the robustness of output quantities with respect to the input distributions requires: (a) defining variational classes for these distributions; (b) calculating boundary values for the output quantities of interest with respect to these variational classes. The latter should be defined in a way that is consistent with the information structure defined by the ``baseline'' choice of input distributions. Considering parametric families, the variational classes are defined using the geodesic distance in their Riemannian manifold, a generic approach to such problems. Theoretical results and application tools are provided to justify and facilitate the implementation of such robustness studies, in concrete situations where these distributions are truncated -- a setting frequently encountered in applications. The feasibility of our approach is illustrated in a simplified industrial case study.