Advertisement

Synthese

, Volume 63, Issue 1, pp 1–34 | Cite as

Prior probabilities

  • John Skilling
Article

Abstract

The theoretical construction and practical use of prior probabilities, in particular for systems having many degrees of freedom, are investigated. It becomes clear that it is operationally unsound to use mutually consistent priors if one wishes to draw sensible conclusions from practical experiments. The prior cannot usefully be identified with a state of knowledge, and indeed it is not so identified in common scientific practice. Rather, it can be identified with the question one asks. Accordingly, priors are free constructions. Their informal, ill-defined and subjective characteristics must carry over into the conclusions one chooses to draw from experiments or observations.

Keywords

Prior Probability Practical Experiment Scientific Practice Subjective Characteristic Theoretical Construction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ash, R.: 1965, ‘Information Theory’, Wiley, New York.Google Scholar
  2. Edwards, A. W. F.: 1972, ‘Likelihood’, Cambridge Univ. Press.Google Scholar
  3. Fine, T. L.: 1973, ‘Theories of Probability’, Academic Press.Google Scholar
  4. Fisher, R. A.: 1950, ‘Contributions to Mathematical Statistics’, Wiley, New York.Google Scholar
  5. Frieden, B. R.: (1972), ‘Restoring with Maximum Likelihood and Maximum Entropy’, J. Opt. Soc. Am. 62, 511–518.Google Scholar
  6. Gull, S. F. and Daniell, G. J.: 1978, ‘Image Reconstruction from Incomplete and Noisy Data’, Nature 272, 686–690.Google Scholar
  7. Jaynes, E.: 1968, ‘Prior Probability’, IEEE Trans. Systems Sci. Cybernetics SSC-4, 227–241.Google Scholar
  8. Jeffreys, H.: 1961, ‘Theory of Probability’, Oxford Univ. Press.Google Scholar
  9. Jeffreys, H.: 1973, ‘Scientific Inference’, Cambridge Univ. Press.Google Scholar
  10. Kashyap, R.: 1971, ‘Prior Probability and Uncertainty’, IEEE Trans. Information Theory IT-17, 641–650.Google Scholar
  11. Krantz, D., Luce, R. D., Suppes, P. and Tversky, A.: 1971, ‘Foundations of Measurement’, Vol. I, Academic Press.Google Scholar
  12. Popper, K. R.: 1965, ‘The Logic of Scientific Discovery’, Hutchinson, London.Google Scholar
  13. Savage, L. J.: 1954, ‘The Foundations of Statistics’, Wiley, New York.Google Scholar
  14. Shafer, G.: 1976, ‘A Mathematical Theory of Evidence’, Princeton Univ. Press.Google Scholar
  15. Shannon, C. and Weaver, W.: 1949, ‘Mathematical Theory of Communication’, Univ. Illinois Press.Google Scholar
  16. Skilling, J., Strong, A. W. and Bennett, K.: 1979, ‘Maximum-entropy Image Processing in Gamma-ray Astronomy’, Mon. Not. R. Astr. Soc. 187, 145–152.Google Scholar
  17. Stein, C.: 1956, ‘Inadmissibility of the Usual Estimator for the Mean of a Multivariate Normal Distribution’, Proc. Symp. Math. Statist. and Probability, 3rd Berkeley 1, 197–206.Google Scholar
  18. Swinbank, E. and Pooley, G.: 1979, ‘A Study of the Crab Nebula at 2.7 GHz’, Mon. Not. R. Astr. Soc. 186, 775–778.Google Scholar
  19. Turchin, V. F. and Turovsteva, L. S.: 1974, ‘Restoration of Optical Spectra and Other Non-negative Functions by the Statistical Regularization Method’, Optics and Spectroscopy, 36, 162–165.Google Scholar

Copyright information

© D. Reidel Publishing Company 1985

Authors and Affiliations

  • John Skilling
    • 1
  1. 1.Dept. of Applied Mathematics and Theoretical PhysicsCambridge UniversityCambridgeEngland

Personalised recommendations