Rare event estimation with sequential directional importance sampling (SDIS)

Kai Cheng; Iason Papaioannou; Zhenzhou Lu; Xiaobo Zhang; Yanping Wang

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arXiv · 2202.05683

Rare event estimation with sequential directional importance sampling (SDIS)

Kai Cheng·Iason Papaioannou·Zhenzhou Lu·Xiaobo Zhang·Yanping Wang

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Abstract

In this paper, we propose a sequential directional importance sampling (SDIS) method for rare event estimation. SDIS expresses a small failure probability in terms of a sequence of auxiliary failure probabilities, defined by magnifying the input variability. The first probability in the sequence is estimated with Monte Carlo simulation in Cartesian coordinates, and all the subsequent ones are computed with directional importance sampling in polar coordinates. Samples from the directional importance sampling densities used to estimate the intermediate probabilities are drawn in a sequential manner through a resample-move scheme. The latter is conveniently performed in Cartesian coordinates and directional samples are obtained through a suitable transformation. For the move step, we discuss two Markov Chain Monte Carlo (MCMC) algorithms for application in low and high-dimensional problems. Finally, an adaptive choice of the parameters defining the intermediate failure probabilities is proposed and the resulting coefficient of variation of the failure probability estimate is analyzed. The proposed SDIS method is tested on five examples in various problem settings, which demonstrate that the method outperforms existing sequential sampling reliability methods.

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BibTeX RIS

Kai Cheng, Iason Papaioannou, Zhenzhou Lu, Xiaobo Zhang, Yanping Wang. 2022-01-12. Rare event estimation with sequential directional importance sampling (SDIS). https://arxiv.org/abs/2202.05683

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