Analytic posterior distribution and bayes factor for pearson partial correlations

This article outlines a novel Bayesian approach to the testing and estimation of Pearson partial correlations. By generalizing a Bayesian inference procedure for Pearson's correlation coefficient, we obtain analytic expressions for the Bayes factor and for the (marginal) posterior distribution of a partial correlation coefficient. Full Bayesian inference can be achieved using only the sample size, the number of controlling variables and the relevant summary statistics, that is, the sample partial correlation. The present approach is illustrated with two empirical examples.