Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification

TL;DR

This paper introduces methods to distinguish and integrate aleatoric and epistemic uncertainties in systems, using duality between risk-sensitive integrals and relative entropy, with computational efficiency achieved via polynomial chaos expansions.

Contribution

It develops a framework combining known and unknown distributional information to bound performance measures, advancing uncertainty quantification techniques.

Findings

Explicit bounds on variances and exceedance probabilities.

Effective use of polynomial chaos for computational tractability.

Unified approach for aleatoric and epistemic uncertainty analysis.

Abstract

Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the system when the distributions of some variables are known exactly, others are known only approximately, and perhaps others are not modeled as random variables at all. The main tool used is the duality between risk-sensitive integrals and relative entropy, and we obtain explicit bounds on standard performance measures (variances, exceedance probabilities) over families of distributions whose distance from a nominal distribution is measured by relative entropy. The evaluation of the risk-sensitive expectations is based on polynomial chaos expansions, which help keep the computational aspects tractable.