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Related Experiment Videos

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
PubMed
Summary
This summary is machine-generated.

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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.
Keywords:
bivariate normal distributionhypergeometric functionsreference priors

Related Experiment Videos

  • 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.