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This study explores combining statistical evidence from multiple Bayesian inference bases. The linear opinion pool method is identified as optimal for creating a consensus measure of evidence, preserving its integrity.

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Area of Science:

  • Statistics
  • Bayesian Inference
  • Decision Theory

Background:

  • Combining evidence from multiple sources is crucial in statistical analysis.
  • Existing methods for pooling priors do not directly address combining statistical evidence.
  • The need for a consensus measure of evidence across different Bayesian inference bases is highlighted.

Purpose of the Study:

  • To discuss the problem of combining statistical evidence from k Bayesian inference bases.
  • To identify the most appropriate method for obtaining a consensus measure of statistical evidence.
  • To analyze the properties of the linear opinion pool in this context.

Main Methods:

  • The study focuses on combining measures of statistical evidence, rather than pooling priors.
  • The linear opinion pool is proposed and analyzed for its suitability.
  • Jeffrey conditionalization is identified as a key tool for more general cases.

Main Results:

  • The linear opinion pool is shown to have the most appropriate properties for combining statistical evidence.
  • Linear pooling preserves consensus with respect to the evidence, unlike other rules.
  • While not preserving prior independence, linear pooling behaves appropriately for expressing statistical evidence.

Conclusions:

  • The linear opinion pool is the recommended method for creating a consensus measure of statistical evidence.
  • Jeffrey conditionalization is important for combining evidence when priors and sampling models differ.
  • This work provides a framework for robust evidence combination in Bayesian statistics.