Numerical dependency analysis (NDA): a new method for estimating the statistical dependence (not correlation) of two variables

Dependence and correlation represent distinct statistical concepts. While there are methods to measure linear and nonlinear correlation between two variables, understanding the statistical dependence between them remains a topic of great interest. In this paper, we propose a heuristic, numerical, and algorithmic approach to estimate the dependence coefficient between two variables. With this approach, first, the X–Y scatter plot is transformed into a functional scatter plot using a procedure called “functionalizing.” Next, a novel concept called “successive triangles” is employed to estimate the dependence of Y on X. The proposed method offers several advantages; it is distribution-free, so it is suitable for both Gaussian and non-Gaussian numerical variables. Moreover, it can be used for both numerical and categorical (nominal) variables. This approach can be employed in other applications such as correlation measurement and also template matching for single-dimensional patterns. The presented method has been validated by both the simulated and clinical data with promising results.