Sensitivity Analysis for Rare Events based on R\'enyi Divergence

TL;DR

This paper introduces a novel approach to quantify the sensitivity of rare event probabilities using Rnyi divergence, providing bounds and indices applicable across various rare event families without relying on specific simulation methods.

Contribution

It develops general uncertainty quantification bounds and new sensitivity indices for rare events based on Rnyi divergence, extending to large deviation rate functions.

Findings

Derived bounds for rare event sensitivity using Rnyi divergence

Proposed new sensitivity indices related to risk-sensitive functionals

Applicable to large deviation rate functions and various rare event families

Abstract

Rare events play a key role in many applications and numerous algorithms have been proposed for estimating the probability of a rare event. However, relatively little is known on how to quantify the sensitivity of the probability with respect to model parameters. In this paper, instead of the direct statistical estimation of rare event sensitivities, we develop novel and general uncertainty quantification and sensitivity bounds which are not tied to specific rare event simulation methods and which apply to families of rare events. Our method is based on a recently derived variational representation for the family of R\'enyi divergences in terms of risk sensitive functionals associated with the rare events under consideration. Based on the derived bounds, we propose new sensitivity indices for rare events and relate them to the moment generating function of the score function. The bounds scale in such a way that we additionally develop sensitivity indices for large deviation rate functions.