Controling Monte Carlo Variance

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


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.


Importance Sampling Monte Carlo Estimator Monte Carlo Sequence Monte Carlo Integration Acceleration Method 
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  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.MathSciNetzbMATHGoogle 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.zbMATHGoogle Scholar
  4. Loh, W. (1996). On latin hypercube sampling. Ann. Statist., 24: 2058–2080.MathSciNetzbMATHCrossRefGoogle Scholar
  5. Stein, M. (1987). Large sample properties of simulations using latin hypercube sampling. Technometrics, 29: 143–151.MathSciNetzbMATHCrossRefGoogle 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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