Analytic Posteriors for Pearson's Correlation Coefficient

TL;DR

This paper derives analytic expressions for the posterior distribution and moments of Pearson's correlation coefficient in a Bayesian framework, facilitating easier inference and implementation.

Contribution

It introduces a broad class of priors for Pearson's correlation and proves that the posterior and moments are analytic, enhancing Bayesian analysis tools.

Findings

Posterior for Pearson's correlation is analytic under the proposed priors.

All posterior moments can be computed analytically.

Results are implemented in the open-source JASP software.

Abstract

Pearson's correlation is one of the most common measures of linear dependence. Recently, Bernardo (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.