Counterfactuals! There is currently a mishegas at Andrew Gelman's place about Pearl and Mackenzie's Book of Why, which has a reference to this and has led me to the conclusion that I really need to find time to work my way through this entire book: Cosma Shalizi: Advanced Data Analysis from an Elementary Point of View: "The distributions we observe in the world are the outcome of complicated stochastic processes. The mechanisms which set the value of one variable inter-lock with those which set other variables. When we make a probabilistic prediction by conditioning—whether we predict E[Y|X=x] or Pr (Y|X=x) or something more complicated—we are just filtering the output of those mechanisms, picking out the cases where they happen to have set X to the value x, and looking at what goes along with that. When we make a causal prediction, we want to know what would happen if the usual mechanisms controlling X were suspended and it was set to x. How would this change propagate to the other variables? What distribution would result for Y? This is often, perhaps even usually, what people really want to know from a data analysis, and they settle for statistical prediction either because they think it is causal prediction, or for lack of a better alternative...
#noted #reasoning
