Quantified Maxent: An NMR Application

  • Sibusiso Sibisi
Part of the Fundamental Theories of Physics book series (FTPH, volume 39)

Abstract

‘Classic MaxEnt’ is a Bayesian derivation of the MaxEnt treatment of inverse problems leading to a posterior probability ‘bubble’ over the solution. This probability bubble—which is maximised at the optimal regularised solution—provides the framework for quantitative inferences about the solution. In particular, the framework allows the computation of fluxes and associated error bars over the solution. This is an important advance in the general theory of inverse problems which has thus far lacked a quantitative reliability treatment of the computed solution. This paper discusses this quantification procedure and applies it to practical NMR spectroscopy.

Keywords

Inverse Problem Maximum Entropy MaxEnt Spectrum Negative Line True Flux 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Skilling J., (1989). Classic Maximum Entropy. Maximum Entropy and Bayesian Methods (ed. J. Skilling), 45–52, Kluwer.Google Scholar
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    Gull S.F., (1989). Developments in Maximum Entropy Data Analysis. Maximum Entropy and Bayesian Methods (ed. J. Skilling), 53–71, Kluwer.Google Scholar
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    Laue E.D., Skilling J., Staunton J., (1985). Maximum Entropy Reconstruction of Spectra Containing Antiphase Peaks. J. Mag. Res., 63, 418–424Google Scholar
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    Bretthorst G.L., (1989) Bayesian Model Selection: Examples Relevant to NMR. Maximum Entropy and Bayesian Methods (ed. J. Skilling), 377–388, Kluwer.Google Scholar
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    Sibisi S., Skilling J., Brereton R.G., Laue E.D., Staunton J., (1984). Maximum Entropy Signal Processing in Practical NMR Spectroscopy. Nature, 311, 446–447CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • Sibusiso Sibisi
    • 1
  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeEngland

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