A test for independence via Bayesian nonparametric estimation of mutual information

Mutual information is a well-known tool to measure the mutual dependence between variables. In this article, a Bayesian nonparametric estimator of mutual information is established by means of the Dirichlet process and the k-nearest neighbour distance. As a result, an easy-to-implement test of independence is introduced through the relative belief ratio. Several theoretical properties of the approach are presented. The procedure is illustrated through various examples and is compared with its frequentist counterpart.