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Controling Monte Carlo Variance

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

Abstract

In Chapter 3, the Monte Carlo method was introduced (and discussed) as a simulation-based approach to the approximation of complex integrals. There has been a considerable body of work in this area and, while not all of it is completely relevant for this book, in this chapter we discuss the specifics of variance estimation and control. These are fundamental concepts, and we will see connections with similar developments in the realm of MCMC algorithms that are discussed in Chapters 7–12.

Keywords

Importance Sampling Monte Carlo Estimator Monte Carlo Sequence Monte Carlo Integration Acceleration Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. McKay, M., Beckman, R., and Conover, W. (1979). A comparison of three methods for selecting values of output variables in the analysis of output from a computer code. Technometrics, 21: 239–245.MathSciNetMATHGoogle Scholar
  2. Mead, R. (1988). The Design of Experiments. Cambridge University Press, Cambridge.Google Scholar
  3. Kuehl, R. (1994). Statistical Principles of Research Design and Analysis. Duxbury, Belmont.MATHGoogle Scholar
  4. Loh, W. (1996). On latin hypercube sampling. Ann. Statist., 24: 2058–2080.MathSciNetMATHCrossRefGoogle Scholar
  5. Stein, M. (1987). Large sample properties of simulations using latin hypercube sampling. Technometrics, 29: 143–151.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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