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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 8, Pages 1519–1536 (Mi zvmmf434)  

Investigation and reduction of variance of a weighted estimate in numerical statistical simulation

I. N. Medvedev, G. A. Mikhailov

Institute of Computational Mathematics and Mathematical Geophysics, Siberian Division, Russian Academy of Sciences, pr. Akademika Lavrent'eva 6, Novosibirsk, 630090, Russia

Abstract: The efficiency of the “value” and “partial value” modeling related to the construction of a modeling distribution for an auxiliary random variable by multiplying the initial density by a value function is investigated. The value function usually corresponds to a solution of the adjoint equation. Conditions under which the value modeling of the initial distribution reduces the variance compared to the direct simulation are obtained. It is proved that the variance of the weighted estimate is bounded in the case of the partial value modeling. This proposition provides a basis for a method for determining whether or not the variance of the weighted estimate is bounded. This method uses the majorizing adjoint equation. Using a practically important problem in transport theory as an example, the asymptotic optimization of the distribution of the mean free path is presented. The application of the proposed method of the investigation of the variance boundedness for the analysis of the classical exponential transformation method of simulating the mean free path of a particle in the one-dimensional and the spherical variants is discussed.

Key words: value modeling, partial value mdoeling, variance of a weighted estimate, exponential transformation method.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:8, 1442–1458

Bibliographic databases:

UDC: 519.676
Received: 26.02.2006

Citation: I. N. Medvedev, G. A. Mikhailov, “Investigation and reduction of variance of a weighted estimate in numerical statistical simulation”, Zh. Vychisl. Mat. Mat. Fiz., 46:8 (2006), 1519–1536; Comput. Math. Math. Phys., 46:8 (2006), 1442–1458

Citation in format AMSBIB
\Bibitem{MedMik06}
\by I.~N.~Medvedev, G.~A.~Mikhailov
\paper Investigation and reduction of variance of a~weighted estimate in numerical statistical simulation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 8
\pages 1519--1536
\mathnet{http://mi.mathnet.ru/zvmmf434}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2287366}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 8
\pages 1442--1458
\crossref{https://doi.org/10.1134/S0965542506080136}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748307505}


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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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