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They've been debating this for many years, and Gelman is a coauthor and student of Rubin, who has been debating with Pearl for decades. Gelman is saying he doesn't want to debate the same issues yet again.

The primary message of Pearl is "all other methods are trash and all empirical work done using those methods is trash." My interpretation of the post is that Gelman is arguing other methods are not trash.

I probably agree more with Pearl than Gelman on the details, but Pearl's approach is just not appropriate for an academic setting.

What they are really fighting about is who gets to reference colloquial notions of causality when discussing their work. I don't think it's fair to say that Pearl treats the rest of stats as trash, but he is saying that they are misleading folks by describing their inference as evidence of cause and effect - which is about as bad for most academics and especially for the Rubin crew who have often policed integrity of other inference regimes (like less rigorous ML).

Debating who gets to use which words is a great way to make sure your debate only matters to other academics. I'd love to see the causality camp make their point by unlocking some great new applied results instead!

Refusing to provide a demonstration of the statistical technique on a toy example constructed for pedagogic purpose, hardly constitutes as a "debate". I would file that under: using a lot of words to avoid answering a direct and fundamental question

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