I've been reading the 'book of why' by Judea Pearl and come to understand that Bayesian Networks can be used to establish causality given a directed acyclic graph (DAG) and that the methods are non-parametric. Throughout the book, the author drags Pearson and Fisher through the mud; it can be hard to tell what is an emotional reaction to resistance from the stats community vs genuine criticisms/improvements to traditional stats approaches to causal inference.
My question is: How are traditional approaches from stats different?