I just unflagged this comment. While it's actually somewhat wrong, it makes an important point.
Statistics can be used to discover a causal relationship. It can't give you an absolute answer, but it can give you a statistical likelihood of the causality. That's a pretty important step forward.
Likehood or probability makes sense only in models where one knows with maximum certainty that he have captured all/every relevant variables, its weights and has all kinds of possible events in a distribution. Otherwise the whole model is mere a story. An illusion. Failure to capture reality adequately is where so-called "black swans" are coming from.
This is meaning behind the "correlation is not causation" meme. There is nothing wrong with Bayesian reasoning, except when it is applyed to an inadequate dataset, which is almost always the case.
Would you like to elaborate about "somewhat wrong", with quotations from Principles of Mathematics, for example?
Would you like to elaborate about "somewhat wrong", with quotations from Principles of Mathematics, for example?
It's "somewhat wrong" because in some cases it is possible to derive causation using statistical methods.
Have you read the linked book? It should answer your questions. If not I'll point you to Michael Nielsen's post[1], where he explain[s] how the causal calculus can sometimes (but not always!) be used to infer causation from a set of data, even when a randomized controlled experiment is not possible. Also in the post, I’ll describe some of the limits of the causal calculus
It's a pretty long post, but the gist of it is that in some circumstances it's possible to build a world model of an imaginary controlled, randomized experiment and then see if non-controlled, real world data matches those expectations.
What that gives you is a distribution of the probabilities of causality.
The probability calculus has nothing to do with correctness of probabilities supplied the very same way the propositional calculus had nothing to do with validity of given propositions. Or any calculus in that matter.
Inference is application of valid heuristics. Mere statistics is not sufficient.
Statistics can be used to discover a causal relationship. It can't give you an absolute answer, but it can give you a statistical likelihood of the causality. That's a pretty important step forward.
That's what this is about.