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Methods of Reducing Sample Size in Monte Carlo Computations

Author

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  • H. Kahn

    (The Rand Corporation, Santa Monica, California)

  • A. W. Marshall

    (The Rand Corporation, Santa Monica, California)

Abstract

This paper deals with the problem of increasing the efficiency of Monte Carlo calculations. The methods of doing so permit one to reduce the sample size required to produce estimates of a fixed level of accuracy or, alternatively, to increase the accuracy of the estimates for a fixed cost of computation. Few theorems are known with regard to optimal sampling schemes, but several helpful ideas of very general applicability are available for use in designing Monte Carlo sampling schemes. Three of these ideas are discussed and illustrated in simple cases. These ideas are (1) correlation of samples, (2) importance sampling, and (3) statistical estimation. Operations Research , ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.

Suggested Citation

  • H. Kahn & A. W. Marshall, 1953. "Methods of Reducing Sample Size in Monte Carlo Computations," Operations Research, INFORMS, vol. 1(5), pages 263-278, November.
    • Handle: RePEc:inm:oropre:v:1:y:1953:i:5:p:263-278
    DOI: 10.1287/opre.1.5.263
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    Cited by:

    1. Koopman, Siem Jan & Shephard, Neil & Creal, Drew, 2009. "Testing the assumptions behind importance sampling," Journal of Econometrics, Elsevier, vol. 149(1), pages 2-11, April.
    2. Víctor Elvira & Luca Martino & Christian P. Robert, 2022. "Rethinking the Effective Sample Size," International Statistical Review, International Statistical Institute, vol. 90(3), pages 525-550, December.
    3. Rahimiyan, Morteza, 2014. "A statistical cognitive model to assess impact of spatially correlated wind production on market behaviors," Applied Energy, Elsevier, vol. 122(C), pages 62-72.
    4. Bodendorf, Frank & Xie, Qiao & Merkl, Philipp & Franke, Jörg, 2022. "A multi-perspective approach to support collaborative cost management in supplier-buyer dyads," International Journal of Production Economics, Elsevier, vol. 245(C).
    5. Youngjun Choe & Henry Lam & Eunshin Byon, 2018. "Uncertainty Quantification of Stochastic Simulation for Black-box Computer Experiments," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1155-1172, December.
    6. Jean-Francois Richard, 2007. "Efficient High-Dimensional Importance Sampling," Working Paper 321, Department of Economics, University of Pittsburgh, revised Jan 2007.
    7. Hopmans, A.C.M. & Kleijnen, J.P.C., 1978. "Importance sampling in systems simulation : A practical failure?," Research Memorandum FEW 73, Tilburg University, School of Economics and Management.
    8. Rossi, Roberto & Chen, Zhen & Tarim, S. Armagan, 2024. "On the stochastic inventory problem under order capacity constraints," European Journal of Operational Research, Elsevier, vol. 312(2), pages 541-555.
    9. Geweke, John, 1996. "Monte carlo simulation and numerical integration," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 15, pages 731-800, Elsevier.
    10. Tito Homem-de-Mello, 2007. "A Study on the Cross-Entropy Method for Rare-Event Probability Estimation," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 381-394, August.
    11. Geweke, John, 2001. "Bayesian econometrics and forecasting," Journal of Econometrics, Elsevier, vol. 100(1), pages 11-15, January.
    12. Mie Augier & James G. March & Andrew W. Marshall, 2015. "Perspective—The Flaring of Intellectual Outliers: An Organizational Interpretation of the Generation of Novelty in the RAND Corporation," Organization Science, INFORMS, vol. 26(4), pages 1140-1161, August.
    13. Cao, Quoc Dung & Choe, Youngjun, 2019. "Cross-entropy based importance sampling for stochastic simulation models," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    14. Hopmans, A.C.M. & Kleijnen, J.P.C., 1979. "Importance sampling in systems simulation: a practical failure?," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 21(2), pages 209-220.
    15. Hatem Çoban & İpek Deveci Kocakoç & Şemsettin Erken & Mehmet Akif Aksoy, 2019. "Reducing Variation of Risk Estimation by Using Importance Sampling," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 7(2), pages 173-184, December.
    16. Agnieszka Borowska & Lennart Hoogerheide & Siem Jan Koopman, 2019. "Bayesian Risk Forecasting for Long Horizons," Tinbergen Institute Discussion Papers 19-018/III, Tinbergen Institute.
    17. Li, Yong & Zhang, Mingzhi & Zhang, Yonghui, 2022. "Sequential Bayesian bandwidth selection for multivariate kernel regression with applications," Economic Modelling, Elsevier, vol. 112(C).

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