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Bayesian Inductive Inference and Maximum Entropy

  • Stephen F. Gull
Part of the Fundamental Theories of Physics book series (FTPH, volume 31-32)

Abstract

The principles of Bayesian reasoning are reviewed and applied to problems of inference from data sampled from Poisson, Gaussian and Cauchy distributions. Probability distributions (priors and likelihoods) are assigned in appropriate hypothesis spaces using the Maximum Entropy Principle, and then manipulated via Bayes’ Theorem. Bayesian hypothesis testing requires careful consideration of the prior ranges of any parameters involved, and this leads to a quantitive statement of Occam’s Razor. As an example of this general principle we offer a solution to an important problem in regression analysis; determining the optimal number of parameters to use when fitting graphical data with a set of basis functions.

Keywords

Posterior Distribution Scale Parameter BAYESIAN Inference Maximum Entropy Bayesian Method 
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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Copyright information

© Kluwer Academic Publishers 1988

Authors and Affiliations

  • Stephen F. Gull
    • 1
  1. 1.Cavendish LaboratoryMullard Radio Astronomy ObservatoryCambridgeUK

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