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Statistical inference with exchangeability and martingales.

Chris C Holmes1, Stephen G Walker2,3

  • 1Department of Statistics, University of Oxford, Oxford, UK.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|March 27, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a parametric Bayesian bootstrap method, leveraging martingales for enhanced Bayesian inference. It explores exchangeability and predictive modeling in Bayesian approaches.

Keywords:
bootstrapparametric bootstrappredictive inferencescore function

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Area of Science:

  • Statistics
  • Probability Theory

Background:

  • Review of exchangeability and its significance in Bayesian statistics.
  • Highlighting the predictive nature of Bayesian models and symmetry assumptions.
  • Examining existing bootstrap methods and Doob's martingale-based Bayesian inference.

Purpose of the Study:

  • Introduce a novel parametric Bayesian bootstrap.
  • Demonstrate the fundamental role of martingales in this new approach.
  • Provide theoretical underpinnings and practical illustrations.

Main Methods:

  • Reviewing exchangeability and Bayesian approaches.
  • Analyzing the Bayesian bootstrap and Efron's parametric bootstrap.
  • Developing a parametric Bayesian bootstrap using martingales.

Main Results:

  • A new parametric Bayesian bootstrap method is proposed.
  • Martingales are shown to be crucial for the methodology.
  • Theoretical results and illustrative examples are presented.

Conclusions:

  • The proposed parametric Bayesian bootstrap offers a new tool for Bayesian inference.
  • Martingales are integral to understanding and applying this method.
  • The work contributes to the ongoing discourse on Bayesian inference challenges and prospects.