Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2018 Feb;72(1):4-13.
doi: 10.1111/stan.12111. Epub 2017 Jul 5.

Analytic posteriors for Pearson's correlation coefficient

Alexander Ly  1 , Maarten Marsman  1 , Eric-Jan Wagenmakers  1
Affiliations

Analytic posteriors for Pearson's correlation coefficient

Alexander Ly et al. Stat Neerl. 2018 Feb.

Abstract

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.

Keywords: bivariate normal distribution; hypergeometric functions; reference priors.

PubMed Disclaimer

References

    1. Abramowitz, M. and Stegun I. A. (eds) (1992), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, Inc., New York. Reprint of the 1972 edition. MR1225604 (94b:00012).
    1. Bayarri, M. J. (1981), Bayesian inference on the correlation coefficient of a bivariate normal population, Trabajos de Estadística y de Investigación Operativa 32, 18–31, MR697200 (84i:62047).
    1. Berger, J. O. , Bernardo J. M. and Sun D (2015), Overall objective priors, Bayesian Analysis 10, 189–221.
    1. Berger, J. O. and Sun D. (2008), Objective priors for the bivariate normal model, The Annals of Statistics 36, 963–982, MR2396821 (2009b:62058).
    1. Bernardo, J. M. (2015), An overall prior for the five‐parameter normal distribution., 11th International Workshop on Objective Bayes Methodology dedicated to Susie Bayarri; Valencia.

LinkOut - more resources