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Markov Chain Monte Carlo

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Numerical Analysis for Statisticians

Part of the book series: Statistics and Computing ((SCO))

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References

  1. Brualdi RA (1977) Introductory Combinatorics. North-Holland, New York

    MATH  Google Scholar 

  2. Casella G, George El (1992) Explaining the Gibbs sampler. Amer Statistician 46:167–174

    Article  MathSciNet  Google Scholar 

  3. Chib S, Greenberg E (1995) Understanding the Metropolis-Hastings algorithm. Amer Statistician 49:327–335

    Article  Google Scholar 

  4. Diaconis, P (1988) Group Representations in Probability and Statistics. Institute of Mathematical Statistics, Hayward, CA

    MATH  Google Scholar 

  5. Gelfand AE, Smith AFM (1990) Sampling-based approaches to calculating marginal densities. J Amer Stat Assoc 85:398–409

    Article  MathSciNet  MATH  Google Scholar 

  6. Gelman A, Carlin JB, Stern HS, Rubin DB (1995) Bayesian Data Analysis. Chapman & Hall, London

    Google Scholar 

  7. Gelman A, Rubin DB (1992) Inference from iterative simulation using multiple sequences (with discussion). Stat Sci 7:457–511

    Article  Google Scholar 

  8. Geman S, Geman D (1984) Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans Pattern Anal Machine Intell 6:721–741

    Article  MATH  Google Scholar 

  9. Geyer CJ (1991) Markov chain Monte Carlo maximum likelihood. Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface, Keramidas EM, editor, Interface Foundation, Fairfax, VA pp 156–163

    Google Scholar 

  10. Gidas B (1995) Metropolis-type Monte Carlo simulation and simulated annealing. Topics in Contemporary Probability and its Applications, Snell JL, editor, CRC Press, Boca Raton, FL, pp 159–232

    Google Scholar 

  11. Gilks WR, Richardson S, Spiegelhalter DJ (editors) (1996) Markov Chain Monte Carlo in Practice. Chapman & Hall, London

    MATH  Google Scholar 

  12. Hastings WK (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57:97–109

    Article  MATH  Google Scholar 

  13. Jennison C (1993) Discussion on the meeting of the Gibbs sampler and other Markov chain Monte Carlo methods. J Bay Stat Soc B 55:54–56

    Google Scholar 

  14. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680

    Article  ADS  MathSciNet  Google Scholar 

  15. Liu JS (1996) Metropolized independent sampling with comparisons to rejection sampling and importance sampling. Stat and Computing 6:113–119

    Article  ADS  Google Scholar 

  16. Metropolis N, Rosenbluth A, Rosenbluth M, Teller A, Teller E (1953) Equations of state calculations by fast computing machines. J Chem Physics 21:1087–1092

    Article  CAS  Google Scholar 

  17. Nachbin L (1965) The Haar Integral, Van Nostrand, Princeton, NJ

    MATH  Google Scholar 

  18. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed. Cambridge University Press, Cambridge

    Google Scholar 

  19. Rosenthal JS (1995) Convergence rates of Markov chains. SIAM Review 37:387–405

    Article  MATH  MathSciNet  Google Scholar 

  20. Tanner MA (1993) Tools for Statistical Inference: Methods for Exploration of Posterior Distributions and Likelihood Functions, 2nd ed. Springer-Verlag, New York

    MATH  Google Scholar 

  21. Tanner M, Wong W (1987) The calculation of posterior distributions (with discussion). J Amer Stat Assoc 82:528–550

    Article  MathSciNet  MATH  Google Scholar 

  22. Tierney L (1994) Markov chains for exploring posterior distributions (with discussion). Ann Stat 22:1701–1762

    Article  MATH  MathSciNet  Google Scholar 

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© 1999 Springer-Verlag New York, Inc.

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(1999). Markov Chain Monte Carlo. In: Numerical Analysis for Statisticians. Statistics and Computing. Springer, New York, NY. https://doi.org/10.1007/0-387-22724-5_24

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  • DOI: https://doi.org/10.1007/0-387-22724-5_24

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94979-6

  • Online ISBN: 978-0-387-22724-5

  • eBook Packages: Springer Book Archive

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