That’s the question I address (very partially) in a new post on my data-driven intelligence blog. The post reviews some of the recent work on causal inference done by people such as Judea Pearl. In particular the post describes the elements of a causal calculus developed by Pearl, and explains how the calculus can be applied to infer causation, even when a randomized, controlled experiment is not possible.
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One of the sexiest things about teaching math is getting a chance to enlighten on how correlation does not imply causation. Logic rocks.