No idea more obscure and uncertain

We don’t celebrate Halloween in a big way here in Australia but I’m sure going trick or treating as Standard Deviation would be fun, if a little dangerous.

I’m with Matt here (and indeed have just co-written a paper trying to bring recent scholarship on mechanisms and causation to the benighted wilderness of international relations scholarship).

Semi-on-topic, can anyone recommend a good book or two about the misuse of epidemiological methods? Even in non-ideological, non-pop debates I sometimes see dubious conclusions being made.

What I tell my statistics students is “correlation might be evidence of causation, but it isn’t necessarily so.” I then describe various reasons why, with confounding variables being the most likely culprit. They seem to get the idea.

The problem with the maxim, “correlation is not causation,” is that if it were true, there’d be no reason to look for correlations at all.

Not to mention the fact that there’s some serious debate as to whether Hume really thought that “causation is just correlation” or not. See:

for a pretty good (and to my mind mostly convincing) argument that he did not.

You weren’t being serious! And here I was thinking that someone doing some cool and witty philosophy.

I really don’t know what Matt means by mechanism above. For my money Feynman had it bang on: it is about correlations all right, as long as some of those correlations lie in the future: it’s about making interesting (i.e., surprising) predictions.

I have written a bit more on this here.

According to a rigorous meta-analysis, correlation is correlated with causation. Therefore, correlation implies causation. QED.

One problem with demanding mechanisms is that it’s potentially an infinite regress. Undergrad students of fundamental physics often get frustrated because they’re not shown any mechanism beneath the basic rules of electromagnetism, gravity, etc.–that is, the things we use to construct other explanatory mechanisms. Gravity happens because matter and energy curve space-time; but why? Who knows? A kid asking “why” repeatedly can usually drive you to the limit of human knowledge in four or five steps.

People may end up discovering other levels of mechanism in the future (strings? quantum gravity? etc.) but at any given time, at some point, observed correlation and successful prediction are all you’ve got.

seth gordon: I liked Tufte’s comment about correlation being a strong “hint” of causation that was quoted in the article you referenced. It seems to capture the flavor of the whole exercise in one “pithy” (I know, O’Reilly, etc.) statement about as well as anything else that’s been written.

Hume was smart, but this is one of the rare occasions he was seriously wrong.

A rooster’s crowing is certainly correlated with sunrise, but it’s quite evidently absurd to say that the rooster causes the sun to rise. Interventionist accounts of causality (e.g., Menzies & Price’s, or Judea Pearl’s) accord reasonably well with intuitions about causation, and the mathematics of interventions is certainly not the same as the math of correlation.

It’s certainly often true that the data you need to establish causation are unavailable, especially in the social sciences, but really that’s more a problem for social scientists to solve than for statisticians.

Neel @ 23,

As was remarked above, Hume’s point was not that correlation just is causation, but that correlation is the only thing the data are capable of establishing, ever. Interventionist accounts of causation offer little more than a formalization of Hume’s positive point: that we can use the scientific method to identify false causes by wiggling some variables while holding others steady. But even if we have established that wiggling X invariably leads to changes in Y, we still have nothing more than a very reliable correlation. Social scientists aren’t going to solve that problem any time soon.

This post makes me want to throw Judea Pearl or Clark Glymour at you. http://ftp.cs.ucla.edu/pub/stat_ser/r284-reprint.pdf is probably a good place to start. Then maybe http://singapore.cs.ucla.edu/LECTURE/lecture_sec1.htm

“in practice one finds that for every mechanism, there is an equally plausible and opposite mechanism, and then it’s either back to the messy data, like a good empiricist; or reject the data as useless and hew to the theory”

The formation of opposing mechanisms isn’t a bad thing, it helps direct future experiments! For science to work correctly there needs to be continual interplay between theory and experiment.
In the case of the competing mechanisms for sunrise (rooster’s crow vs. spinning earth) one could kill the rooster and see if the sun still rises, but one wouldn’t necessarily know to try if one didn’t have the competing theories. Popper says all this much better than I do.

What was it that killed him?

It was the sun, just like with the rooster’s crow. Without the sun nothing would’ve happened. For sure.

scentofviolets: Does the possible existence of your demons(outer, not inner) mean that it really IS possible that it’s “turtles all the way down?”

Actually, as I understand it, the work of Glymour, Spirtes, and all their collaborators at CMU and elsewhere seems to show that really you can infer causation just from correlation (at least, if causal bayes nets gives the right model of causation). While you can’t infer causation from correlation between merely two variables, even once you get three you can reliably tell the difference between a collision (A->B<-C), a common cause (A<-B->C), and a chain, though you can’t tell apart the two types of chain. Maybe I’m wrong about three variables being sufficient for this, and you really need correlations between five or more, but at some point you can start reading the actual directions of particular arrows off the correlations alone.

Of course, you can’t eliminate the possibility that you’ve ignored some extra variables that play very important roles in your model, or the possibility that you’ve just got very non-representative data. But that’s just what makes science hard. Controlled experiments are nice for giving you variables where you specifically know there are no incoming arrows, but even in observational (is that the same as epidemiological?) studies, you can sometimes get enough correlations to be sure that some of them are causal.

Of course, I’d still prefer a model of causation that involves mechanisms, but I think you can predict the existence of mechanisms even when you don’t know anything about them. (For instance, see the amazing successes of Darwin and Mendel prior to Watson, Crick, and Franklin.)

Virgil, yes, it is possible it it Turtles All The Way Down. Worlds ‘really’ could move in epicycles. You ‘really’ could be in the grip of an infinitely powerful deceiver. And so on and so forth. But . . .

Kenny, yes, _given_ a known set of variables, _then_ you could argue just as you have. But it is almost impossible to definitively say that you’ve ruled out all other forms of interference. Which is why the logical arrow, the correlation =>causation contrapositive is much more better, to quote a snippet of Cap’n Jack, and we speak of the essential trait of any good theory, that of falsifiability.

…you can sometimes get enough correlations to be sure that some of them are causal.

Thirty-five posts into the thread, and some of us still fail to grasp Hume’s very simple point.

OF COURSE you can infer causation from correlation on Bayesian network models of causation, because they simply define causation in terms of statistical correlation. Refuting Hume with interventionism is like refuting Berkeley by kicking rocks.

otoh, lack of correlation definitely implies lack of causation: That must be qualified, because we often balance competing causes to achieve an overall correlation near 0.

For example, it turns out (from a very large study) that applying sunscreen has no effect on skin cancer. A likely explanation is that we adjust for constant exposure — staying in the sun about as long as we can without burning.

Mind you, it’s a good heuristic. In fact, most causal discovery algorithms assume it. But it doesn’t always work.

I’m not sure what you’re getting at Chris. Discovering a correlation is an invitation to further study. One shouldn’t leap to conclusions. The problem is that no matter how fine grained our mechanism is there will always be a leap involved. So we are left with observing that B follows A and concluding that A causes B. We call that deduction but there is a gap in our understanding. There always will be.