Constructing Priors in Maximum Entropy Methods

  • N. Rivier
  • R. Englman
  • R. D. Levine
Part of the Fundamental Theories of Physics book series (FTPH, volume 39)


We show how to construct the best prior for a Maximum Entropy procedure when two or more priors are conceivable or are proposed. The prior is a weighed sum of the conceivable priors with weights that depend exponentially on the overlap of the prior with the exponential part of the maximum entropy probability. With additional information, one can iteratively improve the prior and sharpen the choice between alternative priors. Our construction can be used to predict in some physical cases the probability distribution functions, and to make quantitative decisions in the presence of conflicting expert opinions.


Maximum Entropy Thought Experiment Expert Advice Maximum Entropy Method Posterior Probability Distribution 
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  1. Englman, R., Levine, R.D. and Rivier, N. (1989) ‘On the construction of priors in maximum entropy methods’, submitted to IEEE Trans. Info. Theory; preprint, Imperial College (1987).Google Scholar
  2. Englman, R., Rivier, N. and Jaeger, Z. (1988 a) ‘Fragment-size distribution in disintegration by maximum-entropy formalism’, Phil. Mag.B 56, 751–769.Google Scholar
  3. Englman, R., Rivier, N. and Jaeger, Z. (1988b) ‘Size-distribution in sudden breakage by the use of entropy maximization’, J. Appl. Phys. 63, 4766–4768.CrossRefGoogle Scholar
  4. Grady, D.E. and Kipp, M.E. (1985) ‘Geometric statistics and dynamic fragmentation’, J. Appl. Phys. 58, 1210–1222.CrossRefGoogle Scholar
  5. Gull, S. (1987), seminar, Imperial College (private communication).Google Scholar
  6. Holian, B.L. and Grady, D.E. (1988) ‘Fragmentation by molecular dynamics: The microscopic “big bang”’ Phys. Rev. Letters 60, 1355–1358.CrossRefGoogle Scholar
  7. Hopfield, J.J. and Tank, D.W. (1985)‘“Neural” computation of decisions in optimization problems’, Biol. Cybern. 52, 141–152.MathSciNetzbMATHGoogle Scholar
  8. Jaynes, E.T. (1968) ‘Prior probabilities’, IEEE Trans. Syst. Sci. Cybernetics SSC-4, 227–241.CrossRefGoogle Scholar
  9. Jaynes, E.T. (1973) ‘The well-posed problem’, Found. Physics 3, 477–492.MathSciNetCrossRefGoogle Scholar
  10. Jeffreys, H. (1961) Theory of Probability, 3rd. ed., Oxford Univ. Press.zbMATHGoogle Scholar
  11. Khinchin, A.I. (1957) Mathematical Foundations of Information Theory, Dover, NY.zbMATHGoogle Scholar
  12. Levine, R.D. (1986) ‘The theory and practice of the maximum entropy formalism’, in J.H. Justice (ed.), Maximum Entropy and Bayesian Methods in Applied Statistics, Cambridge Univ. Press, 59–84.CrossRefGoogle Scholar
  13. Levine, R.D. and Kosloff, R. (1979) ‘The well-reasoned choice: An information-theoretic approach to branching ratios in molecular rate processes’, Chem. Phys. Letters 28, 300–304.CrossRefGoogle Scholar
  14. Levine, R.D. and Tribus, M. (eds.) (1971) The Maximum Entropy Formalism, M.I.T. Press, Cambridge, MA.Google Scholar
  15. Mott, N.F. and Linfoot E.H. (1943), Ministry of Supply, AC 3348Google Scholar
  16. Renyi, A. (1970) Probability Theory, North-Holland, Amsterdam, ch. IX 5.Google Scholar
  17. Rivier, N. (1986) ‘Distribution of shapes and sizes by maximum entropy methods’, Ann. Isr. Phys. Soc. 8, 560–567.Google Scholar
  18. Rosenkrantz, R.D. (ed.) (1983) E.T. Jaynes, Papers on Probability Statistics and Statistical Physics, Reidel, Dordrecht.Google Scholar
  19. Shannon, C.E and Weaver, W. (1949) The Mathematical Theory of Communication, Univ. of Illinois Press, Urbana.zbMATHGoogle Scholar
  20. Stoppard, T. (1967) Rosenkrantz and Guildenstern are Dead, Faber, London.Google Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • N. Rivier
    • 1
  • R. Englman
    • 2
  • R. D. Levine
    • 3
  1. 1.Argonne National LaboratoryArgonneUSA
  2. 2.Soreq Nuclear Research CenterYavneIsrael
  3. 3.Fritz Haber Research Center for Molecular DynamicsThe Hebrew UniversityJerusalemIsrael

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