The Pólya information divergence

Information Sciences

Volumn 180, Issue 21, 2010, Pages 4189-4194

  Grendár, Marian ^a,b,c   Niven, Robert K ^d  

^a FPV UMB ^*  (Slovakia)

^b INSTITUTE OF CHEMISTRY   (Slovakia)

^c INSTITUTE OF MEASUREMENT SCIENCE   (Slovakia)

^d UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Anyons; Boltzmann P lya Inverse problem; Bose Einstein statistic; Conditional law of large numbers; Fermi Dirac statistic; Kullback Leibler divergence; Maximum entropy; Maximum probability; P lya urn model; Sanov's Theorem; Shannon Jensen divergence

Indexed keywords

ANYONS; BOLTZMANN; BOSE-EINSTEIN STATISTICS; FERMI-DIRAC STATISTICS; JENSEN DIVERGENCE; KULLBACK LEIBLER DIVERGENCE; LAW OF LARGE NUMBERS; MAXIMUM ENTROPY; MAXIMUM PROBABILITY; SANOV'S THEOREM; URN MODELS;

ENTROPY; INVERSE PROBLEMS; STATISTICAL MECHANICS;

STATISTICS;

EID: 77956617119     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2010.06.031     Document Type: Article

References (44)

1. R. Acharya, and P. Narayana Swamy Statistical mechanics of anyons J. Phys. A: Math. Gen. 27 1994 7247 7263
2. J.-F. Bercher, and C. Vignat On minimum Fisher information distributions with restricted support and fixed variance Inform. Sciences 179 2009 3832 3842
3. J.-F. Bercher On some entropy functionals derived from Rényi information divergence Inform. Sciences 178 2008 2489 2506
4. L. Boltzmann Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheilichkeitsrechnung respektive den Sätzen über das Wärmegleichgewicht Wiener Berichte 2 1877 373 435
5. D.E. Brown, R.L. Smith, A weak law of large numbers for rare events, Tech. Rep. 86-4, the University of Michigan, Ann Arbor, 1986.
6. P. Castell, M. Sbert, M. Chover, and M. Feixas Viewpoint-based simplification using f-divergences Inform. Sciences 178 2008 2375 2388
7. T.M. Cover, and J. Thomas Elements of Information Theory 1991 John Wiley and Sons New York
8. I. Csiszár Sanov property, generalized I-projection and a conditional limit theorem Ann. Probab. 12 1984 768 793
9. I. Csiszár Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems Ann. Statist. 19 1991 2032 2066
10. I. Csiszár MaxEnt, mathematics and information theory K.M. Hanson, R.N. Silver, Maximum Entropy and Bayesian Methods 1996 Kluwer 35 50
11. I. Csiszár The method of types IEEE Trans. Inform. Theory IT-44 1998 2505 2523
12. I. Csiszár, and P. Shields Information theory and statistics: a tutorial Foundations and Trends in Communications and Information Theory 1 2004 417 528
13. A. Dembo, and O. Zeitouni Large Deviations Techniques and Applications 1993 Jones and Bartlett Publishers Boston
14. F. Eggenberger, and G. Pólya Über die Statistik verketteter Vorgänge Z. Angew. Math. Mech. 1 1923 279 289
15. L. Golshani, E. Pasha, and G. Yari Some properties of Rényi entropy and Rényi entropy rate Inform. Sciences 179 2009 2426 2433
16. M. Grendár Jr., and M. Grendár What is the question that MaxEnt answers? A probabilistic interpretation A. Mohammad-Djafari, Bayesian Inference and Maximum Entropy Methods in Science and Engineering 2001 AIP Melville, NY 83 94 Also at arXiv:math-ph/0009020
17. M. Grendár Jr., and M. Grendár Maximum entropy method with non-linear moment constraints: challenges G. Erickson, Y. Zhai, Bayesian Inference and Maximum Entropy Methods in Science and Engineering 2004 AIP Melville, NY 97 110 Also at arXiv:physics/0308006
18. M. Grendár, Maximum Probability and Relative Entropy Maximization. Bayesian Maximum Probability and Empirical Likelihood. In: Proceedings of the International Workshop on Applied Probability, IWAP 2008, Compiegne, France. Also at arXiv:0804.3926.
19. M. Grendár, R.K. Niven, The Pólya urn: limit theorems, Pólya divergence, Maximum Entropy and Maximum Probability, arXiv:cond-mat/0612697, 2006.
20. E.T. Jaynes Papers on Probability, Statistics and Statistical Physics 1979 D. Reidel Dordrecht
21. N.L. Johnson, S. Kotz, and N. Balakrishnan Discrete Multivariate Distributions 1997 John Wiley and Sons New York
22. J.D. Kečkić, and P.M. Vasić Some inequalities for the gamma function Publ. Inst. Math. (Beograd) (N.S.) 11 1971 107 114
23. S. Khudanpur Information theoretic methods in statistics Lecture Notes 1999 The Johns Hopkins University
24. S. Kullback Information Theory and Statistics 1959 John Wiley and Sons New York
25. S. Kullback, and R.A. Leibler On information and sufficiency Annals Math. Stat. 22 1951 79 86
26. J. Lin, and S.K.M. Wong A new directed divergence measure and its characterization Int. J. General Systems 7 1990 73 81
27. H. Mahmoud Pólya Urn Models 2008 Chapman & Hall/CRC
28. M.M. Mayoral, and J.A. Pardo Simulation study of the tests of uniform association based on the power-divergence Inform. Sciences 177 2007 5024 5032
29. R.K. Niven, Combinatorial information theory: I. philosophical basis of cross-entropy and entropy, arXiv:cond-mat/0512017, 2005.
30. R.K. Niven Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics Phys. Lett. A 344 2005 286 293
31. R.K. Niven Cost of s-fold decisions in exact Maxwell-Boltzmann Bose-Einstein and Fermi-Dirac statistics Physica A 365 2006 142 149
32. R.K. Niven Origins of the combinatorial basis of entropy K.H. Knuth, A. Caticha, J.L. Center, Bayesian Inference and Maximum Entropy Methods in Science and Engineering 2007 AIP Melville, NY 133 142
33. R.K. Niven Non-asymptotic thermodynamic ensembles EPL 86 2009 20010
34. R.K. Niven Combinatorial entropies and statistics European Physics Journal B 70 2009 49 63
35. R.K. Niven, and M. Grendár Generalized classical, quantum and intermediate statistics and the Pólya urn model Phys. Lett. A 373 2009 621 626
36. I.N. Sanov On the probability of large deviations of random variables Mat. Sbornik 42 1957 11 44 (In Russian)
37. H.S. Steyn On discrete multivariate probability functions Proceedings Koninklijke Nederlandse Akademie van Wetenschappen, Ser. A 54 1951 23 30
38. L. Tan, and D. Taniar Adaptive estimated maximum-entropy distribution model Inform. Sciences 177 2007 3110 3128
39. J.M. van Campenhout, and T.M. Cover Maximum entropy and conditional probability IEEE Trans. Inform. Theory 27 1981 483 489
40. O.A. Vasicek A conditional law of large numbers Ann. Probab. 8 1980 142 147
41. I. Vincze, On the Maximum Probability principle in Statistical Physics, In Progress in Statistics (European Meeting of Statisticians, Budapest, Hungary, 1972), vol. 2, 1974, pp. 869-895.
42. I. Vincze Indistinguishability of particles or independence of the random variables? J. Math. Sci. 84 1997 1190 1196
43. F. Wilczek Anyons, Sci. Am. 264 1991 58 65
44. A.K.C. Wong, and M. You Entropy and distance of random graphs with application to structural pattern recognition IEEE Trans. Pattern Anal. Machine Intell. 7 1985 599 609