Bayesian Inference for Kendall's Rank Correlation Coefficient

This article outlines a Bayesian methodology to estimate and test the Kendall rank correlation coefficient τ. The nonparametric nature of rank data implies the absence of a generative model and the lack of an explicit likelihood function. These challenges can be overcome by modeling test statistics rather than data (Johnson, 2005). We also introduce a method for obtaining a default prior distribution. The combined result is an inferential methodology that yields a posterior distribution for Kendall's τ.