An Improved Non-parametric Bayesian Independence Test for Probabilistic Learning of the Dependence Structure Among Continuous Random Variables

Probabilistic analysis of real-world complex systems such as civil infrastructures requires an effective identification of dependence among the input random variables. The correct modelling of such dependence is crucial for the accuracy and efficiency of a probabilistic assessment and decision-support. In particular, deciding if a pair of random variables is independent is an important step, and several methodologies have been developed for this task. The non-parametric Bayesian independence test is noteworthy among these, since it can deal with data sets whose distributions are unknown and it provides posterior probabilities of independence, which can be helpful in decision making. This paper first summarizes the general procedure of the nonparametric Bayesian independence test, and then examines the application of various types of non-informative priors — uniform, Jeffreys’ and reference priors — from both the theoretical and numerical viewpoint. In the end, the reference prior is recommended as the most suitable prior distribution for the purpose of Bayesian independence test. Furthermore, efficient and accurate discretization algorithms are proposed to facilitate a non-parametric Bayesian independence test of continuous random variables. Five numerical examples are studied to test the validity of the priors, and demonstrate the accuracy and efficiency of the proposed test algorithms. The supporting source codes and data used in the numerical examples are available for download at https://github.com/jieunbyun/GitHub-BIT-code.