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IlyaShpitser comments on Explicit and tacit rationality - Less Wrong
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This is a causal question, not a statistical question. You answer by implementing the relevant intervention, usually by randomization, or maybe you find a natural experiment, or maybe [lots of other ways people thought of].
You can't in general use observational data (e.g. what you call "evidence") to figure out causal relationships. You need causal assumptions somewhere.
What do you think of this challenge, to detect causality from nothing but a set of pairs of values of unnamed variables?
You can do it with enough causal assumptions (e.g. not "from nothing"). There is a series of magical papers, e.g. this:
http://www.cs.helsinki.fi/u/phoyer/papers/pdf/hoyer2008nips.pdf
which show you can use additive noise assumptions to orient edges.
I have a series of papers:
http://www.auai.org/uai2012/papers/248.pdf
http://arxiv.org/abs/1207.5058
which show you don't even need conditional independences to orient edges. For example if the true dag is this:
1 -> 2 -> 3 -> 4, 1 <- u1 -> 3, 1 <- u2 -> 4,
and we observe p(1, 2, 3, 4) (no conditional independences in this marginal), I can recover the graph exactly with enough data. (The graph would be causal if we assume the underlying true graph is, otherwise it's just a statistical model).
People's intuitions about what's possible in causal discovery aren't very good.
It would be good if statisticians and machine learning / comp. sci. people came together to hash out their differences regarding causal inference.
Gelman seems skeptical.
I saw that, but I didn't see much substance to his remarks, nor in the comments.
Here is a paper surveying methods of methods of causal analysis for such non-interventional data, and summarising the causal assumptions that they make:
"New methods for separating causes from effects in genomics data"
Alexander Statnikov, Mikael Henaff, Nikita I Lytkin, Constantin F Aliferis