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Bayesian Folder

• 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

Informatics Folder

• 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

General

• 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

IEEE TRANSACTlIONS ON lNFORMATION THEORY, VOL. m26, NO. 1, JANUARY 1980

• 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)

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, Pages 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
• Jose M. Bioucas-Dias, Mario A. T. Figueiredo, and Joao P. Oliveira ADAPTIVE TOTAL VARIATION IMAGE DECONVOLUTION: A MAJORIZATION-MINIMIZATION APPROACH
• 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