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Analytic posteriors for Pearson's correlation coefficient.
Alexander Ly1, Maarten Marsman1, Eric-Jan Wagenmakers1
1Department of Psychological MethodsUniversity of AmsterdamPO Box 15906Amsterdam1001 NKThe Netherlands.
Statistica Neerlandica
|January 23, 2018
Summary
This study demonstrates that Bayesian analysis of Pearson
Area of Science:
- Statistics
- Bayesian inference
- Correlation analysis
Background:
- Pearson's correlation is a widely used measure of linear association.
- Bayesian methods offer a probabilistic framework for statistical inference.
- Prior distributions significantly influence Bayesian analyses.
Purpose of the Study:
- To investigate the properties of Pearson's correlation coefficient within a Bayesian framework.
- To introduce and analyze a flexible class of priors for Bayesian correlation.
- To determine the analytical properties of posterior distributions for correlation coefficients.
Main Methods:
- Utilized a novel, flexible class of prior distributions for Pearson's correlation.
- Derived analytical results for the marginal posterior distribution.
- Investigated the posterior moments of the correlation coefficient.
Main Results:
- The marginal posterior distribution for Pearson's correlation coefficient is analytic.
- All posterior moments of Pearson's correlation are also analytic.
- These findings are applicable to a broad class of priors.
Conclusions:
- A flexible class of priors enables analytic posterior distributions for Pearson's correlation.
- The analyticity of posterior distributions and moments simplifies Bayesian analysis.
- Results are implemented in the JASP open-source software package.
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