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August 2020 Sensitivity analysis for rare events based on Rényi divergence
Paul Dupuis, Markos A. Katsoulakis, Yannis Pantazis, Luc Rey-Bellet
Ann. Appl. Probab. 30(4): 1507-1533 (August 2020). DOI: 10.1214/19-AAP1468

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 rare event’s 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 Rényi divergences in terms of risk sensitive functionals associated with the rare events under consideration. Inspired by 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.

Citation

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Paul Dupuis. Markos A. Katsoulakis. Yannis Pantazis. Luc Rey-Bellet. "Sensitivity analysis for rare events based on Rényi divergence." Ann. Appl. Probab. 30 (4) 1507 - 1533, August 2020. https://doi.org/10.1214/19-AAP1468

Information

Received: 1 May 2018; Revised: 1 January 2019; Published: August 2020
First available in Project Euclid: 4 August 2020

MathSciNet: MR4132633
Digital Object Identifier: 10.1214/19-AAP1468

Subjects:
Primary: 60F10 , 94A17

Keywords: large deviation , Rare event , Rényi divergence , risk sensitive functional , score function , sensitivity analysis , uncertainty quantification , variational representation

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 4 • August 2020
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