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Part of the book series: NATO ASI Series ((NSSB,volume 135))

Abstract

This workshop is concerned with two topics, foundations of quantum theory and of irreversible statistical mechanics, which might appear quite different. Yet the current problems in both fields are basically the same, two different aspects of a deep conceptual hang up that permeates not only physics, but all fields that use probability theory.

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References

  • J. G. Abels (1974) “Maximum Entropy Spectral Analysis”, Astron. Astrophys. Suppl. 15; 383.

    Google Scholar 

  • G. Bricogne (1982), in Computational Crystallography, D. Dayre, Editor,pp. 258–264; Oxford University Press, New York.

    Google Scholar 

  • G. Bricogne (1982), in Computational Crystallography, D. Dayre, Editor,pp. 258–264; Oxford University Press, New York.

    Google Scholar 

  • G. Bricogne, ed. (1985), Proceedings of the EMBO Workshop on Maximum–Entropy Methods, Orsay, April 24–28, 1984. Applications in crystal and biological macromolecular structure determination from x-ray/ neutron scattering data.

    Google Scholar 

  • R. K. Bryan, M. Bansal, W. Folkhard, C. Nave, and D. A. Marvin, (1983), “Maximum–Entropy calculation of the electron density at 4A resolution of Pfl filamentous bacteriophage”, Proc. Nat. Acad. Sci. U.S.A. 80, 4728.

    Google Scholar 

  • S. F. Burch, S. F. Gull & J. Skilling (1983), “Image Restoration by a Powerful Maximum Entropy Method”, Comp. Vision, Graphics & Image Processing, 23, 118–123.

    Google Scholar 

  • John Parker Burg (1967), “Maximum Entropy Spectral Analysis”, Proc. 37th Annual Meeting, International Society of Exploration Geophysicists, Oklahoma City. Reprinted in Childers (1978).

    Google Scholar 

  • John Parker Burg (1975), Maximum Entropy Spectral Analysis, Ph.D. Thesis

    Google Scholar 

  • Stanford University.

    Google Scholar 

  • D. G. Childers, Editor (1978); Modern Spectrum Analysis, IEEE Press and J. Wiley & Sons, N.Y. A reprint collection.

    Google Scholar 

  • R.T. Cox (1946), “Probability, Frequency, and Reasonable Expectation” Am. J. Phys. 14 1–13. This is greatly expanded in R.T. Cox, The Algebra of Probable Interference, Johns Hopkins University Press, Baltimore (1961).

    Google Scholar 

  • R. G. Currie (1981), “Solar Cycle Signal in Earth Rotation: Non Behavior”, Science, 211, 386

    Google Scholar 

  • R. G. Currie (1981), “Evidence for 18.6 year Mn Signal in Temperature and Drought Conditions in North America Since AD 1800”, J. Geophys. Res. 86, #C11, pp. 11055–11064.

    Google Scholar 

  • R. G. Currie (1981), “Solar Cycle Signal in Air Temperature in North America: Amplitude, Gradient, Phase and Distribution”, J. Atmos. Sci., 38, 809–818.

    Google Scholar 

  • G. J. Danieli & S. F. Gull (1980), “Maximum Entropy Algorithm Applied to Image Enhancement”, I EE Proc. 127E, 170–172.

    Google Scholar 

  • A. C. Fabian, R. Willingale, J. P. Pye, S. S. Murray and G. Fabbiano (1980), “The X–Ray Structure and Mass of the Cassiopeia A Supernova Remnant”, Mon. Not. Roy. Astr. Soc., 193, 175–188.

    Google Scholar 

  • R. Frieden (1972), Restoring with Maximum Likelihood and Maximum

    Google Scholar 

  • Entropy, J. Opt. Soc. Am. 62, 511–518.

    Google Scholar 

  • B. R. Frieden (1980), “Statistical Models for the Image Restoration Problem”, Computer Graphics and Image Processing, 2, 40–59.

    Google Scholar 

  • Z. Gburski, C. G. Gray, and D. E. Sullivan, (1984), Chem. Phys. Lett. 106, 55.

    Google Scholar 

  • B. R. Frieden (1980), “StatisticalModels for the Image Restoration Problem” Computer Graphics and Image Processing, 12, 40-59.

    Google Scholar 

  • J. Willard Gibbs (1902) Elementary Principles in Statistical Mechanics, reprinted in The Collected Works of J. Willard Gibbs, Vol. 2, by Yale University Press, New Haven, Conn., 1948 and by Dover Publications, Inc., New York, 1960.

    MATH  Google Scholar 

  • S. F. Gull & G. J. Daniel (1978), “Image Reconstruction from Incomplete and Noisy Data”, Nature 272, 686–690.

    Article  ADS  Google Scholar 

  • S. F. Gull & G. J. Daniell (1979J, “The Maximum Entropy Method”, in Image Formation from Coherent Functions in Astronomy, C. van Schooneveld, Ed., D. Reidel Pub. Co.

    Google Scholar 

  • S. F. Gull & J. Skilling (1983), “The Maximum Entropy Method”, IAU/URSI Symposium on Indirect Imaging, Sydney Australia.

    Google Scholar 

  • S. Gull and J. Skilling (1984), “The Entropy of an Image”, in J. A. Roberts, ed., Indirect Imaging, Cambridge U. Press.

    Google Scholar 

  • S. Haykin, Editor (1979), Nonlinear Methods of Spectral Analysis, Topics in Applied Physics, Vol. 34; Springer-Verlag, New York.

    Google Scholar 

  • S. Haykin, Editor (1982). The September 1982 IEEE Proceedings, Vol. 70, is a special issue devoted to spectrum analysis.

    Google Scholar 

  • W. Heisenberg (1958), Daedalus 87, 100.

    Google Scholar 

  • K. D. Home (1982), “Eclipse Mapping of Accretion Disks in Cataclysmic Binaries”, Ph.D. Thesis, CalTech. PME with “prior prejudice” favoring circular symmetry.

    Google Scholar 

  • E. T. Jaynes (1967), “Foundations of Probability Theory and Statistical Mechanics”, in Del aware Seminar in the Foundations of Physics, M. Bunge, Ed., Springer-Verlag, Berlin.

    Google Scholar 

  • E. T. Jaynes (1976), “Confidence Intervals vs. Bayesian Intervals”, in Foundations of Probability Theory, Statistical Inference, and StatisticalTheories of Science, W. L. Harper and C. A. Hooker, Eds. Reidel Publishing Co., Dordrecht–Holland. Reprinted in Jaynes (1983).

    Google Scholar 

  • E. T. Jaynes (1978), “Where do we Stand on Maximum Entropy?”, in The Maximum Entropy Formalism, R. D. Levine and M. Tribus, Eds., M.I.T. Press, Cambridge Mass. Reprinted in Jaynes, (1983).

    Google Scholar 

  • E. T. Jaynes (1980), “The Minimum Entropy Production Principle”, in

    Google Scholar 

  • Annual Review of Physical Chemistry, S. Rabinovitch, Ed., Annual Reviews, Inc., Palo Alto Calif. Reprinted in Jaynes, (1983).

    Google Scholar 

  • E. T. Jaynes (1983), Papers on Probability, Statistics, and Statistical Physics, R. D. Rosenkrantz, Editor, D. Reidel Publishing Co., Dordrecht–Holland. Contains reprints of the preceding four articles and nine others.

    Google Scholar 

  • E. T. Jaynes, (1984), “Prior Information and Ambiguity in Inverse Problems”, SIAM–AMS Proceedings, 14, 151–166.

    MathSciNet  Google Scholar 

  • E. T. Jaynes, (1985), “The Evolution of Carnot’s Principle”, in Bricogne (1985).

    Google Scholar 

  • H. Jeffreys (1961), Theory of Probability, Oxford University Press.

    Google Scholar 

  • R. W. Johnson & J. E. Shore~Tl983), “Minimum-Cross-Entropy Spectral Analysis of Multiple Signals”, IEEE Trans. Acoust. Speech & Signal Processing ASSP-31, 574–582.

    Google Scholar 

  • J. H. Justice, Ed., (1985), Proceedings of the Workshop on Bayesian/ Maximum Entropy Methods, University of Calgary, August 1984. In Press.

    Google Scholar 

  • M. C. Kemp (1980), “Maximum Entropy reconstructions in emission tomography”, Medical Radionuclide Imaging, 1, 313–323.

    Google Scholar 

  • P. S. Laplace (1814), Essai Philosophique sur les Probabilités, Courcier Imprimeur, Paris; reprints of this work and of Laplace’s much larger Theorie Analytique des Probabilités are available from Editions Culture et Civilisation, 115, Ave. Gabriel Lebron, 1160 Brussels, Belgium.

    Google Scholar 

  • A. K. Livesey (1984), “Structural Investigations of Metallic Glasses”, Ph.D. Thesis, Cambridge University.

    Google Scholar 

  • A. K. Livesey & J. Skilling (1984), “Maximum Entropy Theory”, Submitted to Acta Cryst.

    Google Scholar 

  • L. R. Mead & N. Papanicolaou (1984), “Maximum Entropy in the Problem of Moments”, J. Math. Phys. 25, 2404–2417.

    Google Scholar 

  • G. Minerbo (1979), “MENT: A maximum entropy algorithm for reconstructing a source from projection data”, Comp. Grap. & Image Processing, 10, 48–68.

    Google Scholar 

  • L. H. Schick and R. Inguva (1981), “Information Theoretic Processing of Seismic Data”, Geophys. Res. Lett. 8, 1199.

    Google Scholar 

  • P. F. Scott (1981), “A 31 GHz map of W3(0H) with a resolution of 0.3 arsec”, Mon. Not. R. Astr. Soc. 194, 25P–29 P.

    ADS  Google Scholar 

  • J. E. Shore & R. W. Johnson (1980), “Axiomatic Derivation of Maximum Entropy and the Principle of Minimum Cross–Entropy”, IEEE Trans. Inform. Theory IT–26, 26–37.

    Google Scholar 

  • J. E. Shore (1981), “Minimum Cross–Entropy Spectral Analysis”, IEEE Trans. Acoust. Speech & Signal Processing ASSP–29, 230–237.

    Google Scholar 

  • S. Sabisi (1983), “Two-Dimensional Reconstructions from One-Dimensional Data by Maximum Entropy”, Nature 301, 134–136. S. Sibisi, J. Skilling, R. Brereton, E. D. Laue, J. Staunton (1984), “Maximum Entropy Method in 13C–NMR Spectroscopy” (in preparation for Chemical Communications).

    Google Scholar 

  • J. Skilling, A. W. Strong, K. Bennett (1979), “Maximum Entropy Image Processing in Gamma–Ray Astronomy”, Mon. Not. Roy. Astron. Soc., 187, 145–152.

    Google Scholar 

  • J. Skilling (1983), “Maximum Entropy Image Reconstruction from Phaseless Fourier Data”, presented at Optical Soc. Am. meeting on Signal Recovery with Incomplete Information and Partial Constraints Incline Village, Nevada, Jan. 1983.

    Google Scholar 

  • J. Skilling and S. Gull (1983), “Algorithms and Applications”, in C. R.

    Google Scholar 

  • Smith & W. T. Grandy (1985). J. Skilling & S. Gull (1984), “The Entropy of an Image”, Am. Math. Soc. SIAM Proceedings, Vol. 14. J. Skilling & R. K. Bryan, (1984), “Image Reconstruction by Maximum–Entropy: General Algorithms”, Mon. Not. Roy. Astr. Soc. In Press.

    Google Scholar 

  • R. Smith & W. T. Grandy, Editors (1985); Proceedings of the 1981, 1982 1983 Workshops on Maximum Entropy and Bayesian Methods in Inverse Problems; University of Wyoming, Laramie WY 92071 (2 Volumes; in press).

    Google Scholar 

  • E. Smylie, G. K. C. Clarke, and T. J. Ulrych, (1973), “Analysis of Irregularities in the Earth’s Rotation”, in Computational Physics, B. A. Bolt, B. Alder, & S. Feinbach, Eds., Academic Press, New York.

    Google Scholar 

  • R. J. Tuffs (1984), Secular Changes in the Supernova Remnant Cassiopeia A,Ph.D. Thesis, Cambridge University, U.K. S. W.

    Google Scholar 

  • Wilkins, J. N. Varghese & M. S. Lehmann (1983), “Statistical Geometry. I: A Self–Consistent Approach to the Crystallographic Inversion Problem Based on Information Theory”, Acta Cryst. A39, 49–60.

    Google Scholar 

  • R. Willingale, “Use of the Maximum Entropy Method in X–Ray Astronomy”, Mon. Not. R. Astr. Soc. 194, 359–364.

    Google Scholar 

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© 1986 Plenum Press, New York

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Jaynes, E.T. (1986). Predictive Statistical Mechanics. In: Moore, G.T., Scully, M.O. (eds) Frontiers of Nonequilibrium Statistical Physics. NATO ASI Series, vol 135. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2181-1_3

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  • DOI: https://doi.org/10.1007/978-1-4613-2181-1_3

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