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Objective Bayesianism and Geometry

  • Carlos C. Rodriguez
Part of the Fundamental Theories of Physics book series (FTPH, volume 39)

Abstract

We suggest in this paper that the concepts of utility, prior probability and entropy are not independent but must be related through the following formula: “The expected utility of a Theory is an increasing funetion of its entropy.” It follows that associated to each regular class of theories (i.e. parametric statistical model) there is a unique one parameter family of densities able to act as prior distributions. These entropic priors form the exponential family generated by the invariant measure in the class, that has the entropy of each theory as sufficient statistic.

Keywords

Invariant Measure Prior Distribution Prior Probability Maximum Entropy Exponential Family 
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.

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References

  1. Amari, S., 1985, Differentual Geometrical Methods in Statistics. Lecture Notes in Statistics, 28 Springer-Verlag.Google Scholar
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  3. Rodriguez, C., 1988. The metrics induced by the Kullback Number. Maximum Entropy and Bayesian Methods, 415–422. (J. Skilling, Ed.) Kluwer Academic Publishers.Google Scholar
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Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • Carlos C. Rodriguez
    • 1
  1. 1.Department of Mathematics and StatisticsState University of New York at AlbanyAlbanyUSA

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