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Adaptive Significance Levels in Tests for Linear Regression Models: The e-Value and P-Value Cases.

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The full Bayesian significance test (FBST) offers a Bayesian approach to hypothesis testing. This study introduces a method to determine optimal e-value cutoffs for FBST, balancing error probabilities in regression models.

Keywords:
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Area of Science:

  • Statistics
  • Bayesian Inference
  • Hypothesis Testing

Background:

  • Traditional significance tests rely on p-values, lacking a direct Bayesian interpretation.
  • The full Bayesian significance test (FBST) uses the e-value to quantify evidence for the null hypothesis (H).
  • Determining rejection criteria for H in FBST is a practical challenge.

Purpose of the Study:

  • To develop a method for establishing e-value cutoffs in FBST.
  • To minimize combined type-I and type-II error probabilities for FBST.
  • To compare the proposed FBST cutoff method with adaptive significance level tests.

Main Methods:

  • Minimizing a linear combination of averaged type-I and type-II error probabilities.
  • Applying the method for specific sample sizes and parameter space dimensions.
  • Considering linear regression models with unknown variance within a Bayesian framework.

Main Results:

  • A novel method for determining FBST e-value cutoffs was presented.
  • The methodology allows for balancing error rates based on sample size and model complexity.
  • Comparisons were made against adaptive significance level tests using the P-value.

Conclusions:

  • The proposed method provides a principled way to set rejection thresholds in FBST.
  • This approach enhances the practical application of FBST in statistical decision-making.
  • The study contributes to robust Bayesian hypothesis testing methodologies.