Monte Carlo Sampling

  • Dirk P. Kroese
  • Joshua C. C. Chan
Chapter

Abstract

Monte Carlo sampling—that is, random sampling on a computer—has become an important methodology in modern statistics. By simulating random variables from specified statistical models and probability distributions one can often estimate certain statistical quantities that may otherwise be difficult to obtain.

Keywords

Covariance 

References

  1. Bishop, C. M. 2006. Pattern Recognition and Machine Learning. Springer-Verlag New York, Inc., Secaucus, NJ.MATHGoogle Scholar
  2. Botev, Z. I., J. F. Grotowski, & D. P. Kroese 2010. Kernel density estimation via diffusion. Annals of Statistics, 38(5):2916–2957.MathSciNetCrossRefMATHGoogle Scholar
  3. Chib, S. 1995. Marginal Likelihood from the Gibbs Output. Journal of the American Statistical Association, 90:1313–1321.MathSciNetCrossRefMATHGoogle Scholar
  4. Chib, S., & I. Jeliazkov 2001. Marginal Likelihood from the Metropolis-Hastings Output. Journal of the American Statistical Association, 96:270–281.MathSciNetCrossRefMATHGoogle Scholar
  5. Fair, R. C. 1978. A Theory of Extramarital Affairs. Journal of Political Economy, 86:45–61.CrossRefGoogle Scholar
  6. Feller, W. 1970. An Introduction to Probability Theory and Its Applications, volume I. John Wiley & Sons, New York, second edition.Google Scholar
  7. Gelfand, A. E., S. Hills, A. Racine-Poon, & A. F. M. Smith 1990. Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling. Journal of American Statistical Association, 85:972–985.CrossRefGoogle Scholar
  8. Kim, S., N. Shepherd, & S. Chib 1998. Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models. Review of Economic Studies, 65(3):361–393.CrossRefMATHGoogle Scholar
  9. Koop, G., D. J. Poirier, J. L., & Tobias 2007. Bayesian Econometric Methods. Cambridge University Press.Google Scholar
  10. Kroese, D. P., T. Taimre, & Z. I. Botev 2011. Handbook of Monte Carlo Methods. John Wiley & Sons, New York.CrossRefMATHGoogle Scholar
  11. L’Ecuyer, P. 1999. Good Parameters and Implementations for Combined Multiple Recursive Random Number Generators. Operations Research, 47(1):159 – 164.MathSciNetCrossRefMATHGoogle Scholar
  12. Marsaglia, G., & W. Tsang 2000. A Simple Method for Generating Gamma Variables. ACM Transactions on Mathematical Software, 26(3):363–372.MathSciNetCrossRefGoogle Scholar
  13. McLachlan, G. J., & T. Krishnan 2008. The EM Algorithm and Extensions. John Wiley & Sons, Hoboken, NJ, second edition.Google Scholar
  14. Metropolis, M., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, & E. Teller 1953. Equations of state calculations by fast computing machines. J. of Chemical Physics, 21:1087–1092.CrossRefGoogle Scholar
  15. Verdinelli, I., & L. Wasserman 1995. Computing Bayes Factors Using a Generalization of the Savage-Dickey Density Ratio. Journal of the American Statistical Association, 90(430): 614–618.MathSciNetCrossRefMATHGoogle Scholar
  16. Williams, D. 1991. Probability with Martingales. Cambridge University Press, Cambridge.CrossRefMATHGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Dirk P. Kroese
    • 1
  • Joshua C. C. Chan
    • 2
  1. 1.School of Mathematics and PhysicsThe University of QueenslandBrisbaneAustralia
  2. 2.Department of EconomicsAustralian National UniversityCanberraAustralia

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