If correlation doesn’t imply causation, then what does? (2012)

You should be able to have cyclic graphs, though. W could cause X which causes Y which causes Z which causes more X.

But, epidemiology is not all of science, it's just one way to do science. So this statement is wrong, or, at least, not complete:

> The standard scientific answer to this question is that (with some caveats) we can infer causality from a well designed randomized controlled experiment.

The more general scientific answer is that we need an hypothesis that can be tested and disproven by observation. Such observations can come from a randomized controlled trial, but a surprising amount of important scientific observations do not. For example, a major confirming test of relativity was to measure the apparent displacement of stars due to gravitational lensing during an eclipse. Obviously there is no way to create a random double blind study of this. (Unless one were to stare too long without eye protection! [rimshot])

But wait, I could hypothesize that saying "blutarski" when flipping a coin will make it land heads up, and if I only do the observation once, my stupid hypothesis might get confirmed. Right?

In this case, yes, a lengthy trial would help provide much better observations. But the more general answer is that a reasonable hypothesis must propose a physical system that could plausibly cause the predicted result. There is no known physical system that connects "blutarski" with coins, or Facebook traffic with Greek bonds. But there is a plausible physical mechanism by which smoke inhalation could lead to lung cancer.

This is what scientists are talking about when they say things like "there's more to science than curve-fitting." But most people do not understand the difference, and that's why we see things like global climate circulation models get mixed up with historical climate reconstruction, or paleontology get mixed up with evolutionary biology.

It's the flip-side of extraordinary claims require extraordinary evidence.

Facebook driving Greek debt is implausible and two vaguely shaped curves aren't enough. A formula that predicts to many decimal places over a fair period, prospectively, would be really weird but hard to ignore.

Spanish debt, gold prices or something related on the other hand, would require proportionately less evidence for causation.

This disturbs people because it implies you can get stuck in a pathological view of the world and statistics and evidence won't get you out. Sorry about that.

Edit: And this is pretty the Bayesian Approach. It's just that Bayesian Statistics and Pearl arguments, are themselves just models of the world. You can have others but, even more, you need more of an arguments than "stuff that seems implausible needs more evidence" and all of the more elaborate stuff is going to be specific to a given situation and thus might be applicable to a different one.