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Objective Bayesian Inference for Bilateral Data.

Cyr Emile M'lan1, Ming-Hui Chen2

  • 1William E. Wecker Associates, Inc., 270 E Simpson Avenue, Jackson, WY 83001, USA.

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|April 9, 2016
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Summary
This summary is machine-generated.

This study introduces objective Bayesian methods for analyzing bilateral data, focusing on risk difference, risk ratio, and odds ratio. The findings offer robust statistical tools for researchers in medical and epidemiological studies.

Keywords:
Bayes factorDallal’s modelJeffreys’ priorOdds ratioProduct trinomial distributionReference priorRisk differenceRisk ratio

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Area of Science:

  • Biostatistics
  • Statistical Modeling
  • Bayesian Inference

Background:

  • Bilateral data analysis is crucial in medical research.
  • Existing models may lack objective Bayesian approaches.
  • Dallal's model and saturated models are common frameworks.

Purpose of the Study:

  • To develop and present three objective Bayesian methods for analyzing bilateral data.
  • To derive and analyze key risk measures: risk difference, risk ratio, and odds ratio.
  • To provide practical guidance on applying these methods using real-world data.

Main Methods:

  • Objective Bayesian analysis using Jeffreys' prior and Bernardo's reference prior.
  • Derivation of posterior distributions for risk difference and risk ratio.
  • Simulation studies to evaluate performance across different sample sizes.

Main Results:

  • Successfully derived functional forms for posterior distributions.
  • Demonstrated practical application with two real data examples.
  • Evaluated the performance of Bayesian methods against frequentist counterparts.

Conclusions:

  • The proposed objective Bayesian methods provide a reliable framework for bilateral data analysis.
  • The derived priors and posterior distributions offer valuable tools for statistical inference.
  • The methodology shows promise for applications in various scientific fields requiring analysis of paired data.