Monte Carlo Integration

  • Christian P. Robert
  • George Casella
Part of the Springer Texts in Statistics book series (STS)

Abstract

While Chapter 2 focussed on developing techniques to produce random variables by computer, this chapter introduces the central concept of Monte Carlo methods, that is, taking advantage of the availability of computer generated random variables to approximate univariate and multidimensional integrals. In Section 3.2, we introduce the basic notion of Monte Carlo approximations as a byproduct of the Law of Large Numbers, while Section 3.3 highlights the universality of the approach by stressing the versatility of the representation of an integral as an expectation.

Keywords

Importance Sampling Tail Probability Finite Variance Laplace Approximation Monte Carlo Integration 
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Notes

  1. Bucklew, J. (1990). Large Deviation Techniques in Decision, Simulation and Estimation. John Wiley, New York.Google Scholar
  2. Lugannani, R. and Rice, S. (1980). Saddlepoint approximation for the distribution of the sum of independent random variables. Adv. Appl. Probab., 12: 475–490.MathSciNetMATHCrossRefGoogle Scholar
  3. DiCiccio, T. J. and Martin, M. A. (1993). Simple modifications for signed roots of likelihood ratio statistics. J. Royal Statist. Soc. Series B, 55: 305–316.MathSciNetMATHGoogle Scholar
  4. Wood, A., Booth, J., and Butler, R. (1993). Saddlepoint approximations to the CDF of some statistics with nonnormal limit distributions. J. American Statist. Assoc., 88: 680–686.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Christian P. Robert
    • 1
  • George Casella
    • 2
  1. 1.CEREMADEUniversité Paris DauphineParis Cedex 16France
  2. 2.Department of StatisticsUniversity of FloridaGainesvilleUSA

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