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Weyl Prior and Bayesian Statistics.

Ruichao Jiang1, Javad Tavakoli1, Yiqiang Zhao2

  • 1Department of Mathematics, The University of British Columbia Okanagan, Kelowna, BC V1V 1V7, Canada.

Entropy (Basel, Switzerland)
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This summary is machine-generated.

Researchers introduce a new Weyl prior for Bayesian inference, generalizing existing methods. This novel prior offers a more canonical choice for statistical manifold parameters, demonstrated with Gaussian distributions.

Keywords:
Bayesian statisticsconformal geometryinformation geometryprior distributions

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Area of Science:

  • Statistics
  • Differential Geometry
  • Bayesian Inference

Background:

  • Bayesian inference requires selecting prior distributions for parameters.
  • The Jeffreys prior, based on Riemann metric tensors, is a standard choice.
  • The α-parallel prior generalized Jeffreys prior using Chentsov-Amari tensors.

Purpose of the Study:

  • To propose a new prior distribution for Bayesian inference based on Weyl structure.
  • To investigate the relationship between the proposed Weyl prior and the α-parallel prior.
  • To calculate the Weyl prior for univariate and multivariate Gaussian distributions.

Main Methods:

  • Utilized the Weyl structure on statistical manifolds to define a new prior.
  • Established the proposed Weyl prior as a special case of the α-parallel prior (α = -n).
  • Computed the Weyl prior for univariate and multivariate Gaussian models.

Main Results:

  • The proposed Weyl prior is a special case of the α-parallel prior with α = -n.
  • This choice of α is more canonical due to conventions in α-connections.
  • The Weyl prior for univariate Gaussian distributions simplifies to the uniform prior.

Conclusions:

  • The Weyl prior offers a geometrically motivated and canonical prior for Bayesian inference.
  • The connection to α-parallel priors provides a unified framework for prior selection.
  • The simplification to a uniform prior for univariate Gaussians highlights its practical relevance.