LESSWRONGLW

EDIT: I've removed this draft & posted a longer version incorporating some of the feedback here at http://lesswrong.com/lw/khd/confound_it_correlation_is_usually_not_causation/

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[anonymous]6y0

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9Nominull6yThis post is a good example of why LW is dying. Specifically, that it was posted as a comment to a garbage-collector thread in the second-class area. Something is horribly wrong with the selection mechanism for what gets on the front page.
16IlyaShpitser6yHi, gwern it's awesome you are grappling with these issues. Here are some jambling responses. -------------------------------------------------------------------------------- You might enjoy Sander Greenland's essay here: http://bayes.cs.ucla.edu/TRIBUTE/festschrift-complete.pdf [http://bayes.cs.ucla.edu/TRIBUTE/festschrift-complete.pdf] Sander can be pretty bleak! -------------------------------------------------------------------------------- I am not sure exactly what you mean, but I can think of a formalization where this is not hard to show. We say A "structurally causes" B in a DAG G if and only if there is a directed path from A to B in G. We say A is "structurally dependent" with B in a DAG G if and only if there is a marginal d-connecting path from A to B in G. A marginal d-connecting path between two nodes is a path with no consecutive edges of the form -> <- * (that is, no colliders on the path). In other words all directed paths are marginal d-connecting but the opposite isn't true. The justification for this definition is that if A "structurally causes" B in a DAG G, then if we were to intervene on A, we would observe B change (but not vice versa) in "most" distributions that arise from causal structures consistent with G. Similarly, if A and B are "structurally dependent" in a DAG G, then in "most" distributions consistent with G, A and B would be marginally dependent (e.g. what you probably mean when you say 'correlations are there'). I qualify with "most" because we cannot simultaneously represent dependences and independences by a graph, so we have to choose. People have chosen to represent independences. That is, if in a DAG G some arrow is missing, then in any distribution (causal structure) consistent with G, there is some sort of independence (missing effect). But if the arrow is not missing we cannot say anything. Maybe there is dependence, maybe there is independence. An arrow may be present in G, and there may still be independenc

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