Sensitivity analysis for rare events based on Rényi divergence
| Autor: | Markos A. Katsoulakis, Yannis Pantazis, Paul Dupuis, Luc Rey-Bellet |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Rényi divergence large deviation uncertainty quantification Score Scale (descriptive set theory) Rare event 94A17 Moment-generating function sensitivity analysis Rare events Statistical physics Sensitivity (control systems) Statistics Probability and Uncertainty Uncertainty quantification score function Divergence (statistics) variational representation risk sensitive functional Mathematics Event (probability theory) 60F10 |
| Zdroj: | Ann. Appl. Probab. 30, no. 4 (2020), 1507-1533 |
| Popis: | 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 Renyi 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. |
| Databáze: | OpenAIRE |
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