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Monte Carlo Integration

  • Christian P. Robert
  • George Casella
Chapter
Part of the Use R book series (USE R)

Abstract

While Chapter 2 focused on the simulation techniques useful to produce random variables by computer, this chapter introduces the major concepts 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 by-product 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. Chapter 5 will similarly deal with the resolution of optimization problems by simulation techniques.

Keywords

Posterior Distribution Importance Sampling Monte Carlo Estimator Importance Weight Tail Probability 
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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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Université Paris Dauphine UMR CNRS 7534 CEREMADEParis cedex 16France
  2. 2.Department of StatisticsUniversity of FloridaGainesvilleUSA

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