A weight-bounded importance sampling method for variance reduction

Tenchao Yu, Linjun Lu, Jinglai Li

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Importance sampling (IS) is an important technique to reduce the estimation variance in Monte Carlo simulations. In many practical problems, however, the use of the IS method may result in unbounded variance, and thus fail to provide reliable estimates. To address the issue, we propose a method which can prevent the risk of unbounded variance; the proposed method performs the standard IS for the integral of interest in a region only in which the IS weight is bounded and we use the result as an approximation to the original integral. It can be verified that the resulting estimator has a finite variance. Moreover, we also provide a normality test based method to identify the region with bounded IS weight (termed as the safe region) from the samples drawn from the standard IS distribution. With numerical examples, we demonstrate that the proposed method can yield a rather reliable estimate when the standard IS fails, and it also outperforms the defensive IS, a popular method to prevent unbounded variance.
Original languageEnglish
Pages (from-to)311-319
JournalInternational Journal for Uncertainty Quantification
Issue number3
Publication statusPublished - 30 Jun 2019


  • importance sampling
  • variance reduction
  • estimator variance
  • normality test


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