A general framework for probabilistic sensitivity analysis with respect to distribution parameters

TL;DR

This paper introduces a unified, eigenvalue-based framework for probabilistic sensitivity analysis with respect to distribution parameters, enabling comprehensive insights into influential uncertainties in engineering models.

Contribution

It develops a general, analytically derived sensitivity framework that unifies various measures, including information-theoretic metrics, and simplifies implementation via likelihood ratio methods.

Findings

Provides new insights into combined sensitivity of correlated metrics

Demonstrates robustness with entropic constraints

Enables approximation of deterministic sensitivities

Abstract

Probabilistic sensitivity analysis identifies the influential uncertain input to guide decision-making. We propose a general sensitivity framework with respect to the input distribution parameters that unifies a wide range of sensitivity measures, including information theoretical metrics such as the Fisher information. The framework is derived analytically via a constrained maximization and the sensitivity analysis is reformulated into an eigenvalue problem. There are only two main steps to implement the sensitivity framework utilising the likelihood ratio/score function method, a Monte Carlo type sampling followed by solving an eigenvalue equation. The resulting eigenvectors then provide the directions for simultaneous variations of the input parameters and guide the focus to perturb uncertainty the most. Not only is it conceptually simple, but numerical examples demonstrate that the proposed framework also provides new sensitivity insights, such as the combined sensitivity of multiple correlated uncertainty metrics, robust sensitivity analysis with an entropic constraint, and approximation of deterministic sensitivities. Three different examples, ranging from a simple cantilever beam to an offshore marine riser, are used to demonstrate the potential applications of the proposed sensitivity framework to applied mechanics problems.