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Bayesian Model Selection: Examples Relevant to NMR

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Maximum Entropy and Bayesian Methods

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 36))

Abstract

The model selection problem is one of the most basic problems in data analysis. Given a data set one can always expand the model almost indefinitely. How does one pick a model which explains the data, but does not contain spurious features relating to the noise? Here we present the results of a Bayesian model selection calculation started in [1] and then extended in [2], and show that the Bayesian answer to this question is essentially a quantitative statement of Occams razor: When two models fit the evidence in the data equally well, choose the simpler model.

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References

  1. Bretthorst G. L., (1987), Bayesian Spectrum Analysis and Parameter Estimation, Ph.D. thesis, Washington University, St. Louis, MO.; available from University Microfilms Inc., Ann Arbor, Mich.

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  2. Bretthorst, G. L., (1988), Bayesian Spectrum Analysis and Parameter Estimation, in Lecture Notes in Statistics, Vol. 48, Springer-Verlag, New York, New York

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  3. Jeffreys, H., (1939), Theory of Probability, Oxford University Press, London, (Later editions, 1948, 1961).

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  4. Zellner, A., (1980), in Bayesian Statistics, J. M. Bernardo, ed., Valencia University Press, Valencia, Spain.

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Author information

Authors and Affiliations

  1. Department of Chemistry, Washington University, Campus Box 1134, 1 Brookings Drive, St. Louis, MO, 63130, USA

    G. Larry Bretthorst

Authors
  1. G. Larry Bretthorst
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Editor information

Editors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

    J. Skilling

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© 1989 Springer Science+Business Media Dordrecht

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Bretthorst, G.L. (1989). Bayesian Model Selection: Examples Relevant to NMR. In: Skilling, J. (eds) Maximum Entropy and Bayesian Methods. Fundamental Theories of Physics, vol 36. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7860-8_39

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  • DOI: https://doi.org/10.1007/978-94-015-7860-8_39

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4044-2

  • Online ISBN: 978-94-015-7860-8

  • eBook Packages: Springer Book Archive

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