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Principles of Bayesian Inference Using General Divergence Criteria.

Jack Jewson1, Jim Q Smith1, Chris Holmes2

  • 1Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.

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

This study introduces a new Bayesian updating method that minimizes general divergence criteria, not just Kullback-Leibler divergence. This approach enhances statistical inference robustness by allowing flexible model choices and subjective divergence measure selection.

Keywords:
Bayesian updatingKullback–Leibler divergenceM-open inferenceminimum divergence estimationrobustness

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Area of Science:

  • Statistics
  • Bayesian Inference
  • Decision Theory

Background:

  • Statistical models are inherently misspecified relative to the true data generating process.
  • Minimizing Kullback-Leibler (KL)-divergence heavily weights tail distributions, posing robustness challenges for decision makers.
  • Existing Bayesian minimum divergence estimation methods have limitations in motivation and statistical foundation.

Purpose of the Study:

  • To develop a statistically principled Bayesian updating method targeting general divergence criteria beyond KL-divergence.
  • To improve the theoretical and motivational underpinnings of Bayesian minimum divergence estimation.
  • To provide decision-theoretic rationale for selecting divergence measures in statistical analysis.

Main Methods:

  • Leveraging recent advancements in general Bayesian updating.
  • Proposing a framework for Bayesian updating that minimizes arbitrary divergence measures.
  • Developing a principled approach to Bayesian minimum divergence estimation.

Main Results:

  • A novel Bayesian updating methodology is presented, allowing for the minimization of general divergence criteria.
  • The proposed method enhances the statistical foundations and motivation for Bayesian minimum divergence estimation.
  • The framework accommodates a broader range of divergence measures, including subjective choices.

Conclusions:

  • The developed method alleviates concerns about model misspecification and tail robustness in Bayesian inference.
  • Targeting alternative divergence measures can significantly impact statistical inference outcomes.
  • The approach offers potential applications for complex, high-dimensional statistical models.