Adaptive importance sampling in monte carlo integration

Man Suk Oh, James O. Berger

Research output: Contribution to journalArticlepeer-review

108 Scopus citations


An Adaptive Importance Sampling (AIS) scheme is introduced to compute integrals of the form [Formula Omitted] as a mechanical, yet flexible, way of dealing with the selection of parameters of the importance function. AIS starts with a rough estimate for the parameters λ of the importance function [Formula Omitted], and runs importance sampling in an iterative way to continually update λ using only linear accumulation. Consistency of AIS is established. The efficiency of the algorithm is studied in three examples and found to be substantially superior to ordinary importance sampling.

Original languageEnglish
Pages (from-to)143-168
Number of pages26
JournalJournal of Statistical Computation and Simulation
Issue number3-4
StatePublished - 1 Jul 1992

Bibliographical note

Funding Information:
"Research was supported by the National Science Foundation, grants DMS-8702620 and DMS-8717799, and by a David Ross Fellowship from Purdue University, as part of the first author's Ph.D. thesis. Parts of the work were also done while the authors were visiting at Duke University. The authors thank Arup Bose for his help with the convergence proofs.


  • Monte Carlo integration
  • adaptive importance sampling
  • approximate normality
  • basic importance sampling
  • importance function
  • linear accumulation
  • martingale limit theorem


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