Rare event estimation of high dimensional problems with confidence intervals

Yanwen Xu, Pingfeng Wang

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Rare events have low probabilities of occurrence, and computation of such small probabilities is challenging, especially for high dimensional problems. Meanwhile, the robust estimation of the probability with narrow bounds is a key component for rare event estimation. Thus, confidence intervals of the estimator can be established based on the central limit theorem. Yet, the commonly used Monte Carlo simulation method is computationally inefficient as the sample size would be huge to derive a reasonably narrow confidence interval. Therefore, this paper introduces an efficient probability estimation technique that estimate the probability of rare events for high dimensional systems with smaller sample size and provide narrow estimation confidence intervals simultaneously. The asymptotic normality for the estimator has been proved theoretically without strong assumptions, and based on that, an asymptotic confidence interval has been established for the proposed probability estimator. The efficiency of the developed technique for probability estimation with confidence intervals is assessed with several engineering reliability analysis and design examples. Our numerical experiments demonstrate that a narrow confidence interval can be built efficiently with the probability estimation, and the real probability results always located within the proposed estimation bounds, which improve both efficiency and accuracy of the rare events estimation.

Original languageEnglish (US)
Title of host publicationProceedings of the 2020 IISE Annual Conference
EditorsL. Cromarty, R. Shirwaiker, P. Wang
PublisherInstitute of Industrial and Systems Engineers, IISE
Number of pages6
ISBN (Electronic)9781713827818
StatePublished - 2020
Event2020 Institute of Industrial and Systems Engineers Annual Conference and Expo, IISE 2020 - Virtual, Online, United States
Duration: Nov 1 2020Nov 3 2020

Publication series

NameProceedings of the 2020 IISE Annual Conference


Conference2020 Institute of Industrial and Systems Engineers Annual Conference and Expo, IISE 2020
Country/TerritoryUnited States
CityVirtual, Online


  • Rare events
  • Sequential importance sampling
  • The confidence interval

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Industrial and Manufacturing Engineering


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