New Causality Statistical Test Is Very Limited
A lot of hay has been made over the past week regarding the paper Distinguishing cause from effect using observational data: methods and benchmarks. E.g. a medium.com blog croons:
Cause And Effect: The Revolutionary New Statistical Test That Can Tease Them Apart
Statisticians have always thought it impossible to tell cause and effect apart using observational data. Not any more."
However, early on in the Mooij et al paper they explicitly state, prominently in their introduction:
We simplify the causal discovery problem by assuming no confounding, selection bias and feedback
Thus their technique would not be applicable to the situation illustrated at the top of this blog post, where one has data on "hair wet" and "street wet" and one is trying to establish causality. As one Slashdot commenter put it, I can't think of any cases where I know there are no confounding factors but don't know which is the cause and which is the effect.
For the only real way to identify causality for real-life cases, see my classic blog entry Causality.