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On quasi-Monte Carlo integrations

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  • Sobol, I.M.

Abstract

Relations between Monte Carlo and quasi-Monte Carlo methods are analysed from both theoretical and practical points of view with special emphasis on high-dimensional integration.

Suggested Citation

  • Sobol, I.M., 1998. "On quasi-Monte Carlo integrations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(2), pages 103-112.
    • Handle: RePEc:eee:matcom:v:47:y:1998:i:2:p:103-112
    DOI: 10.1016/S0378-4754(98)00096-2
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    References listed on IDEAS

    as
    1. Ilya M. Sobol’ & Boris V. Shukhman, 1995. "Integration With Quasirandom Sequences: Numerical Experience," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 263-275.
    2. Spassimir H. Paskov & Joseph F. Traub, 1995. "Faster Valuation of Financial Derivatives," Working Papers 95-03-034, Santa Fe Institute.
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    Cited by:

    1. W Y Hung & S Kucherenko & N J Samsatli & N Shah, 2004. "A flexible and generic approach to dynamic modelling of supply chains," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(8), pages 801-813, August.
    2. Marco Ratto, 2008. "Analysing DSGE Models with Global Sensitivity Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 115-139, March.
    3. Risk, J. & Ludkovski, M., 2016. "Statistical emulators for pricing and hedging longevity risk products," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 45-60.
    4. Ricardo Smith Ramírez, 2007. "FIML estimation of treatment effect models with endogenous selection and multiple censored responses via a Monte Carlo EM Algorithm," Working papers DTE 403, CIDE, División de Economía.
    5. Snyder, William C, 2000. "Accuracy estimation for quasi-Monte Carlo simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(1), pages 131-143.
    6. Stefano Balietti & Brennan Klein & Christoph Riedl, 2021. "Optimal design of experiments to identify latent behavioral types," Experimental Economics, Springer;Economic Science Association, vol. 24(3), pages 772-799, September.
    7. Sobol′ , I.M, 2001. "Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 55(1), pages 271-280.
    8. Li, Jingshi & Wang, Xiaoshen & Zhang, Kai, 2016. "Multi-level Monte Carlo weak Galerkin method for elliptic equations with stochastic jump coefficients," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 181-194.
    9. Pierre L'Ecuyer & Christiane Lemieux, 2000. "Variance Reduction via Lattice Rules," Management Science, INFORMS, vol. 46(9), pages 1214-1235, September.
    10. Yun, Wanying & Lu, Zhenzhou & Feng, Kaixuan & Li, Luyi, 2019. "An elaborate algorithm for analyzing the Borgonovo moment-independent sensitivity by replacing the probability density function estimation with the probability estimation," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 99-108.
    11. Pengfei Wei & Chenghu Tang & Yuting Yang, 2019. "Structural reliability and reliability sensitivity analysis of extremely rare failure events by combining sampling and surrogate model methods," Journal of Risk and Reliability, , vol. 233(6), pages 943-957, December.
    12. Kucherenko, Sergei & Feil, Balazs & Shah, Nilay & Mauntz, Wolfgang, 2011. "The identification of model effective dimensions using global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 440-449.
    13. Kucherenko, S. & Rodriguez-Fernandez, M. & Pantelides, C. & Shah, N., 2009. "Monte Carlo evaluation of derivative-based global sensitivity measures," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1135-1148.
    14. James Risk & Michael Ludkovski, 2015. "Statistical Emulators for Pricing and Hedging Longevity Risk Products," Papers 1508.00310, arXiv.org, revised Sep 2015.

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