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Error estimates on averages of correlated data

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Advances in Computer Simulation

Part of the book series: Lecture Notes in Physics ((LNP,volume 501))

Abstract

We describe how the true statistical error on an average of correlated data can be obtained with ease and efficiency by a renormalization group method. The method is illustrated with numerical and analytical examples having finite as well as infinite range correlations.

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References

  1. Wilson, K., Monte Carlo calculations for the lattice gauge theory. In’ t Hooft G. et al., editor, Recent Developments in Gauge Theories, (Cargése, 1979. Plenum, New York, 1980).

    Google Scholar 

  2. Whitmer, C., Phys. Rev. D 29 306 (1984).

    ADS  Google Scholar 

  3. Jacucci, G. and Rahman, A., Nuovo Cimento D 4 341 (1984).

    Article  ADS  Google Scholar 

  4. Gottlieb, S., Mackenzie, P. B., Thacker, H. B., Weingarten, D., Nucl. Phys. B 263 704 (1986).

    Article  ADS  Google Scholar 

  5. Allen, M. P. and Tildesley, D. J., Computer simulation of liquids. (Clarendon Press, Oxford. 1987).

    MATH  Google Scholar 

  6. Flyvbjerg, H. and Petersen, H. G., J. Chem. Phys. 91 461 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  7. Binder, K., Monte Carlo investigations. In Domb, C. and Green, M., editors, Phase Transitions and Critical Phenomena, volume 5. (Academic, New York, 1976).

    Google Scholar 

  8. Binder, K., Theory and “technical” aspects of Monte Carlo simulations. In Binder, K., editor, Monte Carlo Methods in Statistical Physics, volume 7 of Topics in Current Physics. 2nd ed. (Springer-Verlag, New York, 1979, 1986).

    Google Scholar 

  9. Binder, K. and Stauffer, D., A simple introduction to Monte Carlo simulation and some specialized topics. In Binder, K., editor, Applications of the Monte Carlo Method in Statistical Physics, volume 36 of Topics in Current Physics. 2nd ed. (Springer, New York, 1984, 1987).

    Google Scholar 

  10. Daniell, G. J., Hey, A. J. G., and Mandula, J. E., Phys. Rev. D 30 2230 (1984).

    ADS  Google Scholar 

  11. Pollock, E. L. and Alder, B. J., Physica A 102 1 (1980).

    ADS  Google Scholar 

  12. de Leeuw, S. W., Perram, J. W., and Smith, E. R., Proc. R. Soc. London Ser. A 373 27 (1980).

    Article  ADS  Google Scholar 

  13. Petersen, H. G., de Leeuw, S. W., and Perram, J. W., Mol. Phys. 66 637 (1989).

    Article  ADS  Google Scholar 

  14. Miller, R. G., Biometrika 61 1 (1974).

    MATH  MathSciNet  Google Scholar 

  15. Efron, B., SIAM Review 21 460 (1979).

    Article  MATH  MathSciNet  Google Scholar 

  16. Efron, B., The Jackknife, the Bootstrap and Other Resampling Plans, volume 38 of Regional Conference Series in Applied Mathematics. (SIAM, 1982).

    Google Scholar 

  17. Efron, B. and Tibshirani, R. J., An introduction to the bootstrap. (Chapman & Hall, London, 1993).

    MATH  Google Scholar 

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János Kertész Imre Kondor

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© 1998 Springer-Verlag

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Flyvbjerg, H. (1998). Error estimates on averages of correlated data. In: Kertész, J., Kondor, I. (eds) Advances in Computer Simulation. Lecture Notes in Physics, vol 501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105461

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  • DOI: https://doi.org/10.1007/BFb0105461

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63942-8

  • Online ISBN: 978-3-540-69675-9

  • eBook Packages: Springer Book Archive

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