Comparing Objective and Subjective Bayes Factors for the Two-Sample Comparison: The Classification Theorem in Action

Area of Science:

• Statistics
• Bayesian inference
• Statistical modeling

Background:

• Numerous Bayes factors (BFs) exist for comparing population means in independent two-sample studies.
• Recent work includes objective BFs (Wang & Liu, 2015) versus subjective BFs (Gönen et al., 2005).
• The choice of priors significantly influences BF performance in Bayesian models.

Purpose of the Study:

• To discuss desirable properties (desiderata) of proposed BFs for two-sample problems.
• To propose a novel criterion for comparing BFs, regardless of their subjective or objective determination.
• To evaluate BFs based on their ability to correctly classify data, minimizing misclassification probability.

Main Methods:

• Review and discussion of existing desiderata for Bayes factors.
• Proposal of a new classification-based criterion for BF evaluation.
• Verification of the proposed criterion through simulation studies.
• Analysis of the impact of prior choices on BF performance.

Main Results:

• The proposed criterion offers an objective method for comparing BFs.
• Simulations can clearly demonstrate the effects of different prior specifications.
• The criterion provides new insights into the general appropriateness of various BFs.
• It offers a framework for determining the "best" BF for a given problem.

Conclusions:

• A new, objective criterion based on minimizing misclassification probability is proposed for evaluating Bayes factors.
• This criterion enhances understanding of prior selection effects and BF utility.
• It provides a robust method for selecting the most appropriate Bayes factor in two-sample studies.