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Importance Sampling in High Dimensions

Au, S. K. and Beck, J. L. (2003) Importance Sampling in High Dimensions. Structural Safety, 25 (2). pp. 139-163. ISSN 0167-4730. doi:10.1016/S0167-4730(02)00047-4.

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This paper draws attention to a fundamental problem that occurs in applying importance sampling to ‘high-dimensional’ reliability problems, i.e., those with a large number of uncertain parameters. This question of applicability carries an important bearing on the potential use of importance sampling for solving dynamic first-excursion problems and static reliability problems for structures with a large number of uncertain structural model parameters. The conditions under which importance sampling is applicable in high dimensions are investigated, where the focus is put on the common case of standard Gaussian uncertain parameters. It is found that importance sampling densities using design points are applicable if the covariance matrix associated with each design point does not deviate significantly from the identity matrix. The study also suggests that importance sampling densities using random pre-samples are generally not applicable in high dimensions.

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Additional Information:Copyright © 2002 Elsevier. This paper is based upon work partly supported by the Pacific Earthquake Engineering Research Center under National Science Foundation Cooperative Agreement No. CMS-9701568. This support is gratefully acknowledged. Part of this work was prepared when the first author was at graduate standing at the California Institute of Technology, whose generous financial support is gratefully acknowledged.
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Subject Keywords:Importance sampling; Monte Carlo simulation; Reliability; Relative entropy
Issue or Number:2
Record Number:CaltechAUTHORS:20120829-120814856
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33664
Deposited By: Carmen Nemer-Sirois
Deposited On:31 Aug 2012 20:01
Last Modified:09 Nov 2021 21:36

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