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Correlation method for variance reduction of Monte Carlo integration in RS-HDMR.

Authors
  • Li, Genyuan
  • Rabitz, Herschel
  • Wang, Sheng-Wei
  • Georgopoulos, Panos G
Type
Published Article
Journal
Journal of computational chemistry
Publication Date
Feb 01, 2003
Volume
24
Issue
3
Pages
277–283
Identifiers
PMID: 12548719
Source
Medline
License
Unknown

Abstract

The High Dimensional Model Representation (HDMR) technique is a procedure for efficiently representing high-dimensional functions. A practical form of the technique, RS-HDMR, is based on randomly sampling the overall function and utilizing orthonormal polynomial expansions. The determination of expansion coefficients employs Monte Carlo integration, which controls the accuracy of RS-HDMR expansions. In this article, a correlation method is used to reduce the Monte Carlo integration error. The determination of the expansion coefficients becomes an iteration procedure, and the resultant RS-HDMR expansion has much better accuracy than that achieved by direct Monte Carlo integration. For an illustration in four dimensions a few hundred random samples are sufficient to construct an RS-HDMR expansion by the correlation method with an accuracy comparable to that obtained by direct Monte Carlo integration with thousands of samples.

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