Analytic posteriors for Pearson's correlation coefficient

Pearson's correlation is one of the most common measures of linear dependence. Recently, Bernardo (11th International Workshop on Objective Bayes Methodology, 2015) introduced a flexible class of priors to study this measure in a Bayesian setting. For this large class of priors, we show that th...

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Bibliographic Details
Published in:Statistica Neerlandica 2018-02, Vol.72 (1), p.4-13
Main Authors: Ly, Alexander, Marsman, Maarten, Wagenmakers, Eric‐Jan
Format: Article
Language:English
Subjects:
Bayesian analysis
bivariate normal distribution
Correlation analysis
Correlation coefficients
hypergeometric functions
Open source software
Original
reference priors
Source code
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Summary:Pearson's correlation is one of the most common measures of linear dependence. Recently, Bernardo (11th International Workshop on Objective Bayes Methodology, 2015) introduced a flexible class of priors to study this measure in a Bayesian setting. For this large class of priors, we show that the (marginal) posterior for Pearson's correlation coefficient and all of the posterior moments are analytic. Our results are available in the open‐source software package JASP.
ISSN:0039-0402
1467-9574
DOI:10.1111/stan.12111