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An Objective Prior from a Scoring Rule.

Stephen G Walker1, Cristiano Villa2

  • 1Department of Mathematics, University of Texas at Austin, 2515 Speedway, Austin, TX 78712, USA.

Entropy (Basel, Switzerland)
|July 2, 2021
PubMed
Summary
This summary is machine-generated.

We introduce a novel objective prior distribution derived from information theory, using convex functions and Bregman divergence. This new prior offers a principled approach for statistical modeling and data analysis.

Keywords:
Bregman divergenceEuler–Lagrange equationconvex functionobjective prior

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Area of Science:

  • Statistics
  • Information Theory
  • Machine Learning

Background:

  • Objective priors are crucial for Bayesian inference, ensuring results are driven by data rather than arbitrary choices.
  • Existing methods for deriving objective priors can be complex and lack a unified theoretical foundation.
  • Information-theoretic concepts offer a promising framework for developing principled objective priors.

Purpose of the Study:

  • To develop a novel objective prior distribution grounded in information-theoretic principles.
  • To leverage the relationship between information, divergence measures, and scoring rules.
  • To establish a method for constructing objective priors that are both theoretically sound and practically applicable.

Main Methods:

  • Utilizing convex functions to represent information in density functions.
  • Employing Bregman divergence as a key tool for connecting information and scoring rules.
  • Deriving the objective prior by solving for a constant score function.

Main Results:

  • A novel objective prior distribution is introduced, based on information-theoretic concepts.
  • The derived prior naturally leads to proper local scoring rules.
  • The prior is shown to minimize a corresponding information criterion, reinforcing its objective nature.

Conclusions:

  • The proposed method provides a principled and unified approach to constructing objective priors.
  • This work bridges concepts from information theory, divergence measures, and scoring rules.
  • The novel objective prior has potential applications in various statistical modeling and machine learning tasks.