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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. http://resolver.caltech.edu/CaltechAUTHORS:20120829-120814856

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/S0167-4730(02)00047-4DOIUNSPECIFIED
http://www.sciencedirect.com/science/article/pii/S0167473002000474PublisherUNSPECIFIED
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.
Funders:
Funding AgencyGrant Number
NSFCMS-9701568
CaltechUNSPECIFIED
Subject Keywords:Importance sampling; Monte Carlo simulation; Reliability; Relative entropy
Record Number:CaltechAUTHORS:20120829-120814856
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120829-120814856
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33664
Collection:CaltechAUTHORS
Deposited By: Carmen Nemer-Sirois
Deposited On:31 Aug 2012 20:01
Last Modified:31 Aug 2012 20:01

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