I know there are linear correlation measures such as Pearson that might not capture all cases of statistical dependence or nonlinear correlations. I know there are also nonlinear correlations, which can be measured by distance correlation or mutual information.
Then there's the idea of dependence and association " association is synonymous with dependence and is different from correlation (Fig. 1a). Association is a very general relationship: one variable provides information about another."
I know the distance correlation and mutual information are other ways to measure dependence. If we say 2 variables have a dependence/association, does that mean its either a linear correlation or nonlinear correlation? Or is it possible for it to exist without these?
In the following article, they discuss a case where " x and y are uncorrelated but their magnitudes are not. That is, there are functions of x and functions of y that are correlated." This would this be a nonlinear correlation?
