Independent Monte Carlo

Part of the Statistics and Computing book series (SCO)


Monte Carlo integration is a rough and ready technique for calculating high-dimensional integrals and dealing with nonsmooth integrands [4, 5, 6, 8, 9, 10, 11, 12, 13]. Although quadrature methods can be extended to multiple dimensions, these deterministic techniques are almost invariably defeated by the curse of dimensionality. For example, if a quadrature method relies on n quadrature points in one dimension, then its product extension to d dimensions relies on n d quadrature points. Even in one dimension, quadrature methods perform best for smooth functions. Both Romberg acceleration and Gaussian quadrature certainly exploit smoothness.


Success Probability Unbiased Estimator Importance Sampling Quadrature Method Importance Weight 


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  1. 1.
    Casella G, Robert CP (1996) Rao-Blackwellisation of sampling schemes. Biometrika 83:81-94MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Chen Y, (2005) Another look at rejection sampling through importance sampling. Prob Stat Letters 72:277-283MATHCrossRefGoogle Scholar
  3. 3.
    Doyle PG, Snell JL (1984) Random Walks and Electrical Networks. The Mathematical Association of America, Washington, DCGoogle Scholar
  4. 4.
    Gentle JE (2003) Random Number Generation and Monte Carlo Methods, 2nd ed. Springer, New YorkMATHGoogle Scholar
  5. 5.
    Hammersley JM, Handscomb DC (1964) Monte Carlo Methods. Methuen, LondonMATHGoogle Scholar
  6. 6.
    Kalos MH, Whitlock PA (1986) Monte Carlo Methods, Volume 1: Basics. Wiley, New YorkCrossRefGoogle Scholar
  7. 7.
    Lindvall T (1992) Lectures on the Coupling Method. Wiley, New YorkMATHGoogle Scholar
  8. 8.
    Liu JS (2001) Monte Carlo Strategies in Scientific Computing. Springer, New YorkMATHGoogle Scholar
  9. 9.
    Morgan BJT (1984) Elements of Simulation. Chapman & Hall, LondonMATHGoogle Scholar
  10. 10.
    Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed. Cambridge University Press, CambridgeGoogle Scholar
  11. 11.
    Robert CP, Casella G (1999) Monte Carlo Statistical Methods. Springer, New YorkMATHGoogle Scholar
  12. 12.
    Ross SM (2002) Simulation, 3rd ed. Academic Press, San DiegoGoogle Scholar
  13. 13.
    Rubinstein RY (1981) Simulation and the Monte Carlo Method. Wiley, New YorkMATHCrossRefGoogle Scholar

Copyright information

© Springer New York 2010

Authors and Affiliations

  1. 1.Departments of Biomathematics, Human Genetics, and Statistics David Geffen School of MedicineUniversity of California, Los AngelesLos AngelesUSA

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