Adaptive importance sampling in monte carlo integration

Man Suk Oh; James O. Berger

doi:10.1080/00949659208810398

Adaptive importance sampling in monte carlo integration

Man Suk Oh, James O. Berger

Department of Statistics

Research output: Contribution to journal › Article › peer-review

96 Scopus citations

Abstract

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 language	English
Pages (from-to)	143-168
Number of pages	26
Journal	Journal of Statistical Computation and Simulation
Volume	41
Issue number	3-4
DOIs	https://doi.org/10.1080/00949659208810398
State	Published - 1 Jul 1992

Keywords

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

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10.1080/00949659208810398

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title = "Adaptive importance sampling in monte carlo integration",

abstract = "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.",

keywords = "Monte Carlo integration, adaptive importance sampling, approximate normality, basic importance sampling, importance function, linear accumulation, martingale limit theorem",

author = "Oh, {Man Suk} and Berger, {James O.}",

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.",

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AU - Berger, James O.

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N2 - 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.

AB - 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.

KW - Monte Carlo integration

KW - adaptive importance sampling

KW - approximate normality

KW - basic importance sampling

KW - importance function

KW - linear accumulation

KW - martingale limit theorem

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JO - Journal of Statistical Computation and Simulation

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Adaptive importance sampling in monte carlo integration

Abstract

Keywords

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