Advertisement

Quantified Maximum Entropy

  • John Skilling
Part of the Fundamental Theories of Physics book series (FTPH, volume 39)

Abstract

This tutorial paper discusses the theoretical basis of quantified maximum entropy, as a technique for obtaining probabilistic estimates of images and other positive additive distributions from noisy and incomplete data. The analysis is fully Bayesian, with estimates always being obtained as probability distributions from which appropriate error bars can be found. This supersedes earlier techniques, even those using maximum entropy, which aimed to produce a single optimal distribution.

Keywords

Maximum Entropy Continuum Limit Maximum Entropy Method Prior Expectation Bayesian Probability 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Cox, R.P. (1946) “Probability, frequency and reasonable expectation”, Am. J. Phys. 17, 1–13CrossRefGoogle Scholar
  2. Frieden, B.R. (1972) “Restoring with maximum likelihood and maximum entropy”, J. Opt. Soc. Am., 62, 511–518CrossRefGoogle Scholar
  3. Gull, S.F. (1989) “Developments in maximum entropy data analysis” in Maximum Entropy and Bayesian Methods, ed. J. Skilling, 53–71. Kluwer.Google Scholar
  4. Gull, S.F. & Daniell, G.J. (1978) “Image reconstruction from incomplete and noisy data”, Nature, 272, 686–690CrossRefGoogle Scholar
  5. Gull, S.F. & Skilling, J. (1984) “Maximum entropy method in image processing” IEE Proc. 131(F). 646–659Google Scholar
  6. Jaynes, E.T. (1968) “Prior probabilities?” Reprinted in E.T. Jaynes: Papers on Probability, Statistics, and Statistical Physics, (page 124) ed. R. Rosenkrantz, 1983. Reidel.Google Scholar
  7. Jaynes, E.T. (1978) “Where do we stand on maximum entropy?” Reprinted in E.T. Jaynes: Papers on Probability, Statistics, and Statistical Physics, (page 240) ed. R. Rosenkrantz, 1983. Reidel.Google Scholar
  8. Levine, R.D. (1986) “Geometry in classical statistical thermodynamics”, J. Chem. Phys., 84, 910–916MathSciNetCrossRefGoogle Scholar
  9. Rodriguez, C. (1989) “The metrics induced by the Kullback number” in Maximum Entropy and Bayesian Methods, ed. J. Skilling, 415–422. Kluwer.Google Scholar
  10. Shore, J.E. & Johnson, R.W. (1980) “Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy” IEEE Trans. Info. Theory IT-26, 26–39 and IT-29, 942–943MathSciNetCrossRefGoogle Scholar
  11. Skilling, J. & Bryan, R.K. (1984) “The maximum entropy algorithm”, Monthly Notices Royal Astronomical Soc., 211, 111–124zbMATHGoogle Scholar
  12. Skilling, J. (1988) “The axioms of maximum entropy” in Maximum Entropy and Bayesian Methods in Science and Engineering, vol 1. Foundations, ed. G.J. Erickson and C.R. Smith. Kluwer.Google Scholar
  13. Skilling, J. (1989) “Classic maximum entropy” in Maximum Entropy and Bayesian Methods, ed. J. Skilling, 45–52. Kluwer.Google Scholar
  14. Tikochinsky, Y., Tishby, N.Z. & Levine, R.D. (1984) “Consistent inference of probabilities for reproducible experiments” Phys Rev Lett, 52, 1357–1360CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • John Skilling
    • 1
  1. 1.Department of Applied Mathematics and Theoretical PhysicsCambridgeEngland

Personalised recommendations