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Maximum-Entropy Priors with Derived Parameters in a Specified Distribution.

Will Handley1,2,3, Marius Millea4,5

  • 1Astrophysics Group, Cavendish Laboratory, J.J.Thomson Avenue, Cambridge CB3 0HE, UK.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary

We developed a novel method to transform probability distributions, ensuring key parameters align with a desired distribution. This maximum-entropy approach is demonstrated with an example in neutrino-hierarchy inference.

Keywords:
Bayesian inferencederived distributionmaximum entropyneutrino hierarchyprior

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Area of Science:

  • Statistics
  • High Energy Physics

Background:

  • Probability distributions are fundamental in statistical inference.
  • Parameter estimation often requires aligning observed data with theoretical distributions.

Purpose of the Study:

  • To introduce a novel method for transforming probability distributions.
  • To ensure that parameters of interest conform to a specified target distribution.
  • To establish this method as the maximum-entropy choice.

Main Methods:

  • Development of a transformation technique for probability distributions.
  • Mathematical proof demonstrating the maximum-entropy property of the proposed method.
  • Application to a specific problem in neutrino-hierarchy inference.

Main Results:

  • A provably maximum-entropy method for probability distribution transformation.
  • Successful application demonstrated through a neutrino-hierarchy inference example.

Conclusions:

  • The proposed transformation method offers a principled way to shape probability distributions.
  • This technique has practical implications for complex inference problems, such as determining neutrino mass ordering.