Multicanonical sequential Monte Carlo sampler for uncertainty quantification

Robert Millar*, Hui Li, Jinglai Li

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Abstract

In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar variable. The distribution of this performance variable is important in many uncertainty quantification problems, ranging from risk management to utility optimisation. In practice, this distribution usually cannot be derived analytically and has to be obtained numerically by simulations. To this end, standard Monte Carlo simulations are often used, however, they cannot efficiently reconstruct the tail of the distribution which is essential in many applications. One possible remedy is to use the Multicanonical Monte Carlo method, an adaptive importance sampling scheme. In this method, one draws samples from an importance sampling distribution in a nonstandard form in each iteration, which is usually done via Markov chain Monte Carlo (MCMC). MCMC is inherently serial and therefore struggles with parallelism. In this paper, we present a new approach, which uses the Sequential Monte Carlo sampler to draw from the importance sampling distribution, which is particularly suited for parallel implementation. With both mathematical and practical examples, we demonstrate the competitive performance of the proposed method.
Original languageEnglish
Article number109316
JournalReliability Engineering & System Safety
Volume237
Early online date20 Apr 2023
DOIs
Publication statusPublished - 1 Sept 2023

Keywords

  • Multicanonical Monte Carlo
  • Sequential Monte Carlo sampler
  • Rare event simulation
  • Uncertainty quantification

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