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Correlation method for variance reduction of Monte Carlo integration in RS‐HDMR
Author(s) -
Li Genyuan,
Rabitz Herschel,
Wang ShengWei,
Georgopoulos Panos G.
Publication year - 2003
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.10172
Subject(s) - monte carlo method , monte carlo integration , variance reduction , quasi monte carlo method , control variates , orthonormal basis , numerical integration , mathematics , importance sampling , hybrid monte carlo , statistics , markov chain monte carlo , physics , mathematical analysis , quantum mechanics
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. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 277–283, 2003