Larry Wasserman posted the following comments on his “normal-deviate” blog:
I am back from the JSM (http://www.amstat.org/meetings/jsm/2013/). For those who don’t know, the JSM is the largest statistical meeting in the world. This year there were nearly 6,000 people.
On Tuesday, I went to Judea Pearl’s medallion lecture, with discussions by Jamie Robins and Eric Tchetgen Tchetgen. Judea gave an unusual talk, mixing philosophy, metaphors (eagles and snakes can’t build microscopes) and math. Judea likes to argue that graphical models/structural equation models are the best way to view causation. Jamie and Eric argued that graphs can hide certain assumptions and that counterfactuals need to be used in addition to graphs.
I posted the following reply:
Your note about my Medallion Lecture (at JSM 2013) may create the impression that I am against the use of counterfactuals.
This is not the case.
1. I repeatedly say that counterfactuals are the building blocks of rational behavior and scientific thoughts.
2. I showed that ALL counterfactuals can be encoded parsimoniously in one structural equation model, and can be read easily from any such model.
3. I showed how the graphical-counterfactual symbiosis can work to unleash the merits of both. And I emphasized that mediation analysis would still be in its infancy if it were not for the algebra of counterfactuals (as it emerges from structural semantics.)
4. I am aware of voiced concerns about graphs hiding assumptions, but I prefer to express these concerns in terms of “hiding opportunities”, rather than “hiding assumptions” because the latter is unnecessarily alarming.
A good analogy would be Dawid’s notation X||Y for independence among variables, which states that every event of the form X = x_i is independent of every event of the form Y=y_j. There may therefore be hundreds of assumptions conveyed by the innocent and common statement X||Y.
Is this a case of hiding assumptions?
I do not believe so.
Now imagine that we are not willing to defend the assumption “X = x_k is independent of Y=y_m” for some specific k and m. The notation forces us to write “variable X is not independent of variable Y” thus hiding all the (i,j) pairs for which the independence is defensible. This is a loss of opportunity, not a hiding of assumptions, because refraining from assuming independence is a more conservative strategy; it prevents unwarranted conclusions from being drawn.
Thanks for commenting on my lecture.