Difference between revisions of "DiV MaxEnt"

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==MaxEnt General 2==
==MaxEnt General 2==
*Sattin, F. '''Bayesian approach to superstatistics''' European Physical Journal B -- Condensed Matter;Jan2006, Vol. 49 Issue 2, p219

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Electron Spectrum Reconstruction

  • Alexei V. Chvetsov and George A. Sandison Reconstruction of electron spectra using singular component decomposition Med. Phys. 29, 578 (2002)
  • Robert L. Wolpert; Katja Ickstadt Reflecting uncertainty in inverse problems: A Bayesian solution using Lévy processes Inverse Problems 2004;20(6):1759-1771
  • Wei J, Sandison GA, Chvetsov AV Reconstruction of electron spectra from depth doses with adaptive regularization. Med Phys. 2006 Feb;33(2):354-9.
  • Chvetsov AV, Sandison GA Angular correction in reconstruction of electron spectra from depth dose distributions. Med Phys. 2003 Aug;30(8):2155-8.
  • technical memorandum High energy electron beam energy determination through depth dose distribution June 26, 2002
  • T. Tabata and R. Ito, The Passage of fast electrons through matter: The work at the Radiation Center of Osaka Prefecture and related topics
  • E.T. Jaynes Predictive Statistical Mechanics
  • E.T. Jaynes Information theory and statistical mechanics


  • H. M. Franca, A. Maia, Jr., and C. P. Malta Maxwell Electromagnetic Theory, Planck's Radiation Law, and Bose-Einstein Statistics Foundations... 26, 1996
  • J. Aitchison On Coherence in Parametric Density Estimation Vol. 77, No. 4, Dec., 1990 > On Coherence in Para...
  • Anand G. Dabak , Don H. Johnson Relations between Kullback-Leibler distance and Fisher information (2002)
  • S. Kullback; R. A. Leibler. On Information and Sufficiency The Annals of Mathematical Statistics, Vol. 22, No. 1 (Mar., 1951), 79-86.
  • J. Tersoff and David Bayer Quantum Statistics for Distinguishable Particles Phys. Rev. Lett. 50, 2038–2038 (1983)
  • Shore, J., Johnson, R. Properties of cross-entropy minimization IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. IT-27, NO, 4, JULY
  • Edwin T. Jaynes Prior Probabilities IEEE Transactions On Systems Science and Cybernetics, vol. sec-4, no. 3, 1968, pp. 227-241
  • M. Grendar, Jr., M. Grendar Maximum Probability and Maximum Entropy methods: Bayesian interpretation arXiv:physics/0308005v2 [physics.data-an] 9 Sep 2005
  • R E Nettleton Fisher information as thermodynamic entropy model in a classical fluid 2003 J. Phys. A: Math. Gen. 36 2443
  • Harremoes, P. Binomial and Poisson distributions as maximum entropy distributions IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 47, NO. 5, JULY 2001
  • E. T. Jaynes Information Theory and Statistical Mechanics Phys. Rev. 106, 620–630 (1957)
  • Robert K. Niven Combinatorial Information Theory: I. Philosophical Basis of Cross-Entropy and Entropy arXiv:cond-mat/0512017v5 [cond-mat.stat-mech] 20 Apr 2007
  • Robert L. Wolpert , Katja Ickstadt Reflecting Uncertainty in Inverse Problems: A Bayesian Solution using Lévy Processes INVERSE PROBLEMS 2004 1759--1771
  • ROBERT L. WOLPERT, KATJA ICKSTADT, MARTIN B. HANSEN A Nonparametric Bayesian Approach to Inverse Problems BAYESIAN STATISTICS 7, pp. 000–000 Oxford University Press, 2003
  • Ariel Caticha, Roland Preuss Maximum entropy and Bayesian data analysis: Entropic prior distributions Physical Review E - PHYS REV E , vol. 70, no. 4, 2004
  • R. Fischer, M. Mayer, W. von der Linden, and V. Dose Enhancement of the energy resolution in ion-beam experimentswith the maximum-entropy method Phys. Rev. E 55, 6667–6673 (1997)
  • Fischer, R.; Mayer, M.; von der Linden, W.; Dose, V. Energy resolution enhancement in ion beam experiments with Bayesian probability theory Nuclear Instruments and Methods in Physics Research Section B, Volume 136, Issue 1-4, p. 1140-1145.
  • W. Von der Linden , R. Preuss , V. Dose The Prior-Predictive Value: A Paradigm of Nasty Multi-Dimensional Integrals (1999)
  • R Fischer, W. Von Der Linden, V. Dose Adaptive Kernels And Occam's Razor In Inversion Problems Proceeding of the MaxEnt Conference 1996 South Africa


  • Alfredo Luis, Alfonso Rodil Alternative measures of metrological resolution: contradictions and possible lack of limits PACS numbers: 03.65.Ta, 42.50.St, 42.50.Dv, Dated: January 15, 2012
  • Robert E. Kass The Geometry of Asymptotic Inference Statist. Sci. Volume 4, Number 3 (1989), 188-219.
  • Harold Jeffreys An Invariant Form for the Prior Probability in Estimation Problems
  • Bernardo Reference posterior distribution for bayesian inference
  • Sýkora, Stanislav, Quantum theory and the bayesian inference problems, Journal of Statistical Physics, Volume 11, Issue 1, 1974
  • M. Raviculé, M. Casas, and A. Plastino Information and metrics in Hilbert space Phys. Rev. A 55, 1695–1702 (1997)
  • P. W. Lamberti, A. P. Majtey, A. Borras, M. Casas, and A. Plastino Metric character of the quantum Jensen-Shannon divergence Phys. Rev. A 77, 052311 (2008)
  • Samuel L. Braunstein and Carlton M. Caves Statistical distance and the geometry of quantum states Phys. Rev. Lett. 72, 3439–3443 (1994)
  • W. K. Wootters Statistical distance and Hilbert space Phys. Rev. D 23, 357–362 (1981)
  • James O. Berger, Jose M. Bernardo and Dongchu Sun THE FORMAL DEFINITION OF REFERENCE PRIORS The Annals of Statistics 2009, Vol. 37, No. 2, 905–938

Drinking Bird Toy?

  • E. T. Jaynes Note on thermal heating efficiency Am. J. Phys. 71 ~2!, February 2003
  • Richard R. Annis Radioactive Battery 111604 Part one 6th August 1952
  • Ralph Lorenz Finite-time thermodynamics of an instrumented drinking bird toy Am. J. Phys. 74 (8), August 2006
  • E. T. Jaynes The Second Law as Physical Fact and as Human Inference

Random Walk?

  • Guth, Eugene New Class of Classical Uncertainty Relations Giving Uncertainty for Long and Certainty for Short Times Phys. Rev. 126, 1213–1215 (1962)
  • Joseph B. Keller Diffusion at finite speed and random walks PNAS Feb 3, 2004, vol. 101 no. 5
  • Peter Kostädt and Mario Liu Causality and stability of the relativistic diffusion equation Phys. Rev. D 62, 023003 (2000)
  • Peter Kostädt and Mario Liu On the Causality and Stability of the Relativistic Diffusion Equation Phys. Rev. D 62, 023003 (2000)
  • Josep M. Porr`a and Jaume Masoliver, George H. Weiss When the telegrapher's equation furnishes a better approximation to the transport equation than the diffusion approximation Phys. Rev. E 55, 7771–7774 (1997)
  • J Almaguer and H Larralde A relativistically covariant random walk J. Stat. Mech. (2007) P08019
  • Jaume Masoliver and George H Weiss Finite-velocity diffusion 1996 Eur. J. Phys. 17 190
  • E. Orsingher, A. De Gregorio Random Flights in Higher Spaces J Theor Prob, December 2007, Volume 20, Issue 4, pp 769-806
  • Stadje, Wolfgang Exact probability distributions for noncorrelated random walk models J Statist Physics, Volume 56, Issue 3-4, pp. 415-435
  • V Balakrishnan and S Lakshmibala On the connection between biased dichotomous diffusion and the one-dimensional Dirac equation 2005 New J. Phys. 7 11


  • R N Silver Quantum Statistical Inference Workshop on Physics and Computation (1992) Volume: 65, Issue: 4
  • Igor Vajda On Convergence of Information Contained in Quantized Observations IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 48, NO. 8, AUGUST 2002
  • John Skilling Probability and Geometry AIP Conf. Proc. 954, pp. 39-46

Sense of QM?

  • David S. Weiss, Brenton C. Young, and Steven Chu Precision measurement of the photon recoil of an atom using atomic interferometry Phys. Rev. Lett. 70, 2706–2709 (1993)
  • Z. Haba, H. Kleinert, Schrödinger wave functions from classical trajectories Physics Letters A Volume 294, Issues 3–4, 25 February 2002, Pages 139–142
  • Piotr Garbaczewski Relativistic problem of random flights and Nelson's stochastic mechanics Physics Letters A Volume 164, Issue 1, 6 April 1992, Pages 6–16
  • John S. Bell On the Einstein Podolsky Rosen paradox
  • A.F. KRACKLAUER, La “théorie” de Bell est-elle la plus grande méprise de l’histoire de la physique? Ann. Fond. Louis de Broglie, Vol. 25, n°2, 2000.
  • J. Avendaño, L. de la Peña, Reordering of the ridge patterns of a stochastic electromagnetic field by diffraction due to an ideal slit Phys. Rev. E 72, 066605 (2005)
  • L. Fortunato, S. De Baerdemacker, K. Heyde Solution of the Bohr hamiltonian for soft triaxial nuclei Phys.Rev. C74 (2006) 014310
  • C. P. Malta, Trevor S. Marshall , Emilio Santos Wigner density of a rigid rotator Phys. Rev. E 55, 2551–2556 (1997)
  • A. Garrett Lisi Quantum mechanics from a universal action reservoir arXiv:physics/0605068v1 [physics.pop-ph] 8 May 2006
  • B. Holdom Approaching quantum behavior with classical fields J.Phys.A39:7485,2006
  • H J Hrgovcic Discrete representations of the n-dimensional wave equation 1992 J. Phys. A: Math. Gen. 25 1329
  • Kwok Sau Fa Fokker-Planck equation with variable diffusion coefficient in the Stratonovich approach arXiv:cond-mat/0503331v2 [cond-mat.soft] 15 Mar 2005

Probability Distance?

  • Anand G. Dabak , Don H. Johnson Relations between Kullback-Leibler distance and Fisher information (2002)
  • Jianhua Lin, Divergence Measures Based on the Shannon Entropy IEEE TRANSACTIONS ON INFORMATION THEORY. VOL. 37, NO. I , JANUARY 1991
  • S.M. Ali and D. Silvey. A general class of coefficients of divergence of one distribution from another. J. Roy. Stat. Soc., Ser. B, 28: 131–142, 1966.

unnamed folder

  • Tommaso Toffoli, How much of physics is just computation?, Superlattices and Microstructures, 23, 381-406 (1998)
  • Norman Margolus, Lev B. Levitin The maximum speed of dynamical evolution Physica D 120 (1998) 188-195

MaxEnt Unfolding

  • E.T. jaynes Prior information and ambiguity in inverse problem SIAM-AMS Proceeding V14 1984
  • S.F. Gull and J. Skilling, Maximum Entropy Image Reconstruction: General Algorithm, Monthly Notices of the Royal Astronomical Society, Vol. 211, NO.1, P. 111, 1984
  • S.F. Gull and J. Skilling, Maximum entropy method in image processing', IEE PROCEEDINGS, Vol. 131, Pt. F, No. 6, OCTOBER 1984
  • J. M. Borwein, A. S. Lewis and D. Noll Maximum Entropy Reconstruction Using Derivative Information, Part 1: Fisher Information and Convex Duality
  • J. M. Borwein , A. S. Lewis , M. N. Limber , D. Noll Maximum Entropy Spectral Analysis Using Derivative Information Part 2: Computational Results
  • FRÖHNER F. H. Assigning uncertainties to scientific data
  • K. Zarb Adami Variational Methods in Bayesian Deconvolution PHYSTAT2003, SLAC, Stanford, California, September 8-11, 2003
  • Marcel Reginattoa, Paul Goldhagena, Sonja Neumannb, Spectrum unfolding, sensitivity analysis and propagation of uncertainties with the maximum entropy dec*Shore, J., Johnson, R. Properties of cross-entropy minimization IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. IT-27, NO, 4, JULYonvolution code MAXED Nuclear Instruments and Methods in Physics Research Section A, Volume 476, Issues 1–2, 1 January 2002, PageAIP Conf. Proc. 954, pp. 39-46s 242–246
  • G. D'Agostini Improved iterative Bayesian unfolding arXiv:1010.0632v1 [physics.data-an] 4 Oct 2010
  • A. Mohammad-Djafari, Jérôme Idier A scale invariant Bayesian method to solve linear inverse problems arXiv:physics/0111125v1 [physics.data-an] 14 Nov 2001
  • Shikoh ITOH & Toshiharu TSUNODA Neutron Spectra Unfolding with Maximum Entropy and Maximum Likelihood Journal of Nuclear Science and Technology Volume 26, Issue 9, 1989
  • Yuan Qi, Thomas P. Minka, and Rosalind W. Picard Bayesian Spectrum Estimation of Unevenly Sampled Nonstationary Data EDICS: 2-TIFR, 2-SPEC
  • Aristidis C. Likas and Nikolas P. Galatsanos A Variational Approach for Bayesian Blind Image Deconvolution 2222 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 52, NO. 8, AUGUST 2004
  • U. Gerhardt, S. Marquardt, N. Schroeder, S. Weiss Bayesian deconvolution and analysis of photoelectron or any other spectra: Fermi-liquid versus marginal Fermi-liquid behavior of the 3d electrons in Ni Phys. Rev. B » Volume 58 » Issue 11
  • Satoh, T., Matsui, A., Hirohata, T., Matsumoto, T. A hierarchical Bayesian deconvolution with positivity constraints 0-7803-5871-6/99/$10.00 1999 IEEE
  • Georgios Choudalakis Fully Bayesian Unfolding

MaxEnt General 1

  • Cox, R. T. Probability, Frequency and Reasonable Expectation American Journal of Physics, Volume 14, Issue 1, pp. 1-13 (1946)
  • Alfréd Rényi, On Measures of Entropy and Information Proc. Fourth Berkeley Symp. on Math. Statist. and Prob., Vol. 1 (Univ. of Calif. Press, 1961), 547-561.
  • CLAUDE E. SHANNON, Communication in the Presence of Noise, PROCEEDINGS OF THE IEEE, VOL. 86, NO. 2, FEBRUARY 1998 447
  • Jaynes, E. T., The Minimum Entropy Production Principle, Ann. Rev. Phys. Chem. 31, 579, 1980
  • Jaynes, E. T., Macroscopic Prediction, in Complex Systems - Operational Approaches, H. Haken (ed.), Springer-Verlag, Berlin, p. 254, 1985
  • Jaynes, E. T., Probability in Quantum Theory, in Complexity, Entropy, and the Physics of Information, W. H. Zurek (ed.), Addison-Wesley, Redwood City, CA, p. 381, 1990
  • Ariel Caticha, From Inference to Physics, Presented at MaxEnt 2008, the 28th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (July 8-13, 2008, Boraceia Beach, Sao Paulo, Brazil)
  • Ariel Caticha, Entropic Dynamics, Presented at MaxEnt 2001, the 21th International Workshop on Bayesian Inference and Maximum Entropy Methods (August 4-9, 2001, Baltimore, MD, USA)
  • Ariel Caticha, Updating Probabilities, Presented at MaxEnt 2006, the 26th International Workshop on Bayesian Inference and Maximum Entropy Methods (July 8-13, 2006, Paris, France)
  • Ariel Caticha, Relative Entropy and Inductive Inference, Presented at MaxEnt23, the 23rd International Workshop on Bayesian Inference and Maximum Entropy Methods (August 3-8, 2003, Jackson Hole, WY, USA)
  • Skilling, John, The Canvas of Rationality, BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: Proceedings of the 28th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering. AIP Conference Proceedings, Volume 1073, pp. 67-79 (2008).
  • Sýkora, Stanislav, Quantum theory and the bayesian inference problems, Journal of Statistical Physics, Volume 11, Issue 1, 1974
  • Shore, J., Johnson, R. Axiomatic Derivation of the Principle of Maximum Entropy and the Principle of Minimum Cross-Entropy


  • Shore, J., Johnson, R. Properties of cross-entropy minimization IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. IT-27, NO, 4, JULY
  • Kevin H. Knuth, John Skilling, Foundations of Inference, Axioms 2012, 1(1):38-73
  • Kevin H. Knuth, The Origin of Probability and Entropy, Bayesian inference and Maximum Entropy Methods in Science and Engineering, Sao Paulo, Brazil, 2008
  • Y. Tikochinsky, Feynman Rules for Probability Amplitudes, International Journal of Theoretical Physics, Vol. 27, No. 5, 1988
  • Y. Tikochinsky*, N. Z. Tishby*, and R. D. Levine ,Consistent Inference of Probabilities for Reproducible Experiments, Phys. Rev. Lett. 52, 1357–J. M. Borwein, A. S. Lewis and D. Noll1360 (1984)
  • P. Ván Unique additive information measures - Boltzmann-Gibbs-Shannon, Fisher and beyond Physica A, 2006, V365, p28-33
  • Jos Uffink, The Constraint Rule of the Maximum Entropy Principle, Studies of the History and Philosophy of Modern Physics, 27, 47-49, 1996
  • Jos Uffink, Can the Maximum Entropy Principle Be Explained as a Consistency Requirement?, Stud.Hist.Phil.Mod.Phys. 26, 223-261, 1995
  • Tommaso Toffoli, How much of physics is just computation?, Superlattices and Microstructures, 23, 381-406 (1998)
  • Tommaso Toffoli, Action, Or the Fungibility of Computation, Feynman and Computation, 349-392 (1999)
  • Tommaso Toffoli, Occam, Turing, von Neumann, Jaynes: How much can you get for how little?, proceedings of the conference ACRI '94: Automi Cellulari per la Ricerca e l'Industria, Rende (CS), Italy, September 29--30, 1994
  • Plastino, A.; Plastino, A. R., On the universality of thermodynamics' Legendre transform structure, Physics Letters A 226 (1997) 257-263
  • A. Plastino, E. M. F. Curado, Equivalence between maximum entropy principle and enforcing dU=TdS, Phys. Rev. E 72, 047103 (2005)
  • A. Plastino, A. R. Plastino, B H Soffer, Fisher information and thermodynamics' 1st. law, arXiv:cond- mat/0509697 v2 28 Sep 2005
  • F. Pennini, A. Plastino, Heisenberg-Fisher thermal uncertainty measure, Phys. Rev. E 69, 057101 (2004)
  • F. Pennini and A. Plastino, Reciprocity relations between ordinary temperature and the Frieden-Soffer Fisher temperature, Phys. Rev. E 71, 047102 (2005)
  • A. Hernando, A. Plastino, A. R. Plastino, MaxEnt and dynamical information, arXiv:1201.0889v1 [physics.data-an] 4 Jan 2012
  • Michael E. Fisher Solution of a Combinatorial Problem—Intermediate Statistics American Journal of Physics -- January 1962 -- Volume 30, Issue 1, pp. 49
  • B. Roy Frieden and Bernard H. Soffer Lagrangians of physics and the game of Fisher-information transfer Phys. Rev. E 52, 6917–6917 (1995)
  • Humphrey J. Maris and Leo P. Kadanoff Teaching the renormalization group American Journal of Physics -- June 1978 -- Volume 46, Issue 6, pp. 652
  • W. K. Wootters Statistical distance and Hilbert space Phys. Rev. D 23, 357–362 (1981)
  • Kurt Wiesenfeld Resource Letter: ScL-1: Scaling laws American Journal of Physics -- September 2001 -- Volume 69, Issue 9, pp. 938
  • V Dose Bayesian inference in physics: case studies 2003 Rep. Prog. Phys. 66 1421
  • Anand G. Dabak , Don H. Johnson Relations between Kullback-Leibler distance and Fisher information (2002)

MaxEnt General 2

  • Sattin, F. Bayesian approach to superstatistics European Physical Journal B -- Condensed Matter;Jan2006, Vol. 49 Issue 2, p219