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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. 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.
    2. 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.
    3. Marco Ratto, 2008. "Analysing DSGE Models with Global Sensitivity Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 115-139, March.
    4. 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.
    5. 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.
    6. 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.
    7. Snyder, William C, 2000. "Accuracy estimation for quasi-Monte Carlo simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(1), pages 131-143.
    8. 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.
    9. 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.
    10. 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.
    11. Pierre L'Ecuyer & Christiane Lemieux, 2000. "Variance Reduction via Lattice Rules," Management Science, INFORMS, vol. 46(9), pages 1214-1235, September.
    12. James Risk & Michael Ludkovski, 2015. "Statistical Emulators for Pricing and Hedging Longevity Risk Products," Papers 1508.00310, arXiv.org, revised Sep 2015.
    13. 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.
    14. 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.

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