Hi Eliezer,

Thanks for writing this! A few comments about this article (mostly minor, with one exception).

The famous statistician Fischer, who was also a smoker, testified before Congress that the correlation between smoking and lung cancer couldn't prove that the former caused the latter.

Fisher was specifically worried about hidden common causes. Fisher was also the one who brought the concept of a randomized experiment into statistics. Fisher was "curmudgeony," but it is not quite fair to use him as an exemplar of the "keep causality out of our statistics" camp.

Causal models (with specific probabilities attached) are sometimes known as "Bayesian networks" or "Bayes nets", since they were invented by Bayesians and make use of Bayes's Theorem.

Graphical causal models and Bayesian networks are not the same thing (this is a common misconception). A distribution that factorizes according to a DAG is a Bayesian network (this is just a property of a distribution -- nothing about causality). You can further say that a graphical model is causal if an additional set of properties holds. For example, you can (loosely) say that in a causal model all parents are "direct causes." If you want to say that formally, you would talk about the truncated factorization and do(.). Without interventions there is no interventionist causal model.

All this discipline was invented and systematized by Judea Pearl, Peter Spirtes, Thomas Verma, and a number of other people in the 1980s and you should be quite impressed by their accomplishment, because before then, inferring causality from correlation was thought to be a fundamentally unsolvable problem.

I often find myself in a weird position of having to point folks to people other than Pearl. I think it's commendable that you looked into other people in the field. The big early names in causality that you did not mention are Haavelmo (1950s) and Sewall Wright (this guy is amazing -- he figured so many things out correctly in the 1920s). Special cases of non-causal graphical models (Ising models, Hidden Markov models, etc.), along with factorizations and propagation algorithms were known long before Pearl in other communities.

P.S. Since I am in Cali.: if folks at SI are interested in new developments on the "learning causal structure from data" front, I could be bribed by the Cheeseboard to come by and give a talk.