Statistics and Computing

, Volume 23, Issue 2, pp 271–285 | Cite as

Markov chain importance sampling with applications to rare event probability estimation

  • Zdravko I. Botev
  • Pierre L’Ecuyer
  • Bruno Tuffin


We present a versatile Monte Carlo method for estimating multidimensional integrals, with applications to rare-event probability estimation. The method fuses two distinct and popular Monte Carlo simulation methods—Markov chain Monte Carlo and importance sampling—into a single algorithm. We show that for some applied numerical examples the proposed Markov Chain importance sampling algorithm performs better than methods based solely on importance sampling or MCMC.


Importance sampling Nonparametric Minimum variance density Rare-event probability Variance reduction 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Zdravko I. Botev
    • 1
  • Pierre L’Ecuyer
    • 2
  • Bruno Tuffin
    • 3
  1. 1.School of Mathematics and StatisticsUniversity of New South WalesSydneyAustralia
  2. 2.Department of Computer Science and Operations ResearchUniversité de MontréalMontréalCanada
  3. 3.INRIA Rennes Bretagne-AtlantiqueRennes CedexFrance

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