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Probability Models

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Abstract

The basic notion in probability is that of a random experiment: an experiment whose outcome cannot be determined in advance, but which is nevertheless subject to analysis. Examples of random experiments are:

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References

  • Bishop, C. M. 2006. Pattern Recognition and Machine Learning. Springer-Verlag New York, Inc., Secaucus, NJ.

    MATH  Google Scholar 

  • Botev, Z. I., J. F. Grotowski, & D. P. Kroese 2010. Kernel density estimation via diffusion. Annals of Statistics, 38(5):2916–2957.

    Article  MathSciNet  MATH  Google Scholar 

  • Chib, S. 1995. Marginal Likelihood from the Gibbs Output. Journal of the American Statistical Association, 90:1313–1321.

    Article  MathSciNet  MATH  Google Scholar 

  • Chib, S., & I. Jeliazkov 2001. Marginal Likelihood from the Metropolis-Hastings Output. Journal of the American Statistical Association, 96:270–281.

    Article  MathSciNet  MATH  Google Scholar 

  • Fair, R. C. 1978. A Theory of Extramarital Affairs. Journal of Political Economy, 86:45–61.

    Article  Google Scholar 

  • Feller, W. 1970. An Introduction to Probability Theory and Its Applications, volume I. John Wiley & Sons, New York, second edition.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Kim, S., N. Shepherd, & S. Chib 1998. Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models. Review of Economic Studies, 65(3):361–393.

    Article  MATH  Google Scholar 

  • Koop, G., D. J. Poirier, J. L., & Tobias 2007. Bayesian Econometric Methods. Cambridge University Press.

    Google Scholar 

  • Kroese, D. P., T. Taimre, & Z. I. Botev 2011. Handbook of Monte Carlo Methods. John Wiley & Sons, New York.

    Book  MATH  Google Scholar 

  • L’Ecuyer, P. 1999. Good Parameters and Implementations for Combined Multiple Recursive Random Number Generators. Operations Research, 47(1):159 – 164.

    Article  MathSciNet  MATH  Google Scholar 

  • Marsaglia, G., & W. Tsang 2000. A Simple Method for Generating Gamma Variables. ACM Transactions on Mathematical Software, 26(3):363–372.

    Article  MathSciNet  Google Scholar 

  • McLachlan, G. J., & T. Krishnan 2008. The EM Algorithm and Extensions. John Wiley & Sons, Hoboken, NJ, second edition.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • Williams, D. 1991. Probability with Martingales. Cambridge University Press, Cambridge.

    Book  MATH  Google Scholar 

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Kroese, D.P., Chan, J.C.C. (2014). Probability Models. In: Statistical Modeling and Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8775-3_1

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