Automatic Bayes Factors for Testing Equality- and Inequality-Constrained Hypotheses on Variances

Area of Science:

• Statistics
• Statistical Inference
• Hypothesis Testing

Background:

• Researchers often hypothesize specific structures for population variances when comparing independent populations.
• These hypotheses involve equality and/or inequality constraints on variances.
• Specifying subjective priors for variances in Bayes factor analysis is challenging.

Purpose of the Study:

• To introduce and evaluate automatic Bayes factors for testing equality- and inequality-constrained hypotheses on variances.
• To address the difficulty of specifying subjective priors in Bayesian hypothesis testing.
• To identify a recommendable method for testing variance hypotheses.

Main Methods:

• Consideration of three automatic Bayes factors: equal priors, fractional Bayes factor, and an adjusted fractional Bayes factor.
• The automatic Bayes factors use sample data for prior specification, avoiding subjective input.
• Evaluation of Bayes factors based on properties like information consistency and large sample consistency.

Main Results:

• Three automatic Bayes factors were presented for testing hypotheses on variances.
• The adjusted fractional Bayes factor properly accounts for the parsimony of inequality-constrained hypotheses.
• The adjusted fractional Bayes factor demonstrated favorable properties in evaluations.

Conclusions:

• The adjusted fractional Bayes factor is generally recommended for testing equality- and inequality-constrained hypotheses on variances.
• Automatic Bayes factors offer a practical alternative when subjective prior specification is difficult.
• The study provides a robust method for variance hypothesis testing in statistical inference.