Analytic posterior distribution and bayes factor for pearson partial correlations

Area of Science:

• Statistics
• Bayesian Inference
• Correlation Analysis

Background:

• Pearson correlation is widely used but has limitations.
• Estimating partial correlations often requires complex methods.
• Bayesian approaches offer a robust alternative for statistical inference.

Purpose of the Study:

• To present a novel Bayesian approach for testing and estimating Pearson partial correlations.
• To derive analytic expressions for key Bayesian metrics.
• To simplify full Bayesian inference for partial correlations.

Main Methods:

• Generalizing a Bayesian inference procedure for Pearson's correlation coefficient.
• Deriving analytic expressions for the Bayes factor.
• Obtaining the marginal posterior distribution of the partial correlation coefficient.

Main Results:

• Analytic expressions for Bayes factor and posterior distribution are obtained.
• Full Bayesian inference is possible using minimal summary statistics.
• The method is validated with two empirical examples.

Conclusions:

• The proposed Bayesian approach offers a computationally efficient and theoretically sound method for partial correlation analysis.
• This method simplifies complex statistical inference.
• It provides a valuable tool for researchers in various fields.