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Manfred comments on On stopping rules - Less Wrong Discussion
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Comments (9)
Was the professor in question Jamie?
Did you read Jamie's and Larry's counterexample where they construct a case where the propensity score is known exactly but the treatment/baseline/outcome model is too complex to bother w/ likelihood methods?
https://normaldeviate.wordpress.com/2012/08/28/robins-and-wasserman-respond-to-a-nobel-prize-winner/
Couldn't we extend this to longitudinal settings and just say MSMs are better than the parametric g-formula if the models for the latter are too complex? Would this not render the strong likelihood principle false? If you don't think causal inference problems are in the "right magisterium" for the likelihood principle, just consider missing data problems instead (same issues arise, in fact their counterexample is phrased as missing data).
It's not obvious to me that they got the Bayesian analysis right in that blog post. If you can have "no observation" for Y, it seems like what we actually observe is some Y' that can take on the values {0,1,null}, and the probability distribution over our observations of the variables (X,R,Y') is p(X) * P(R|X) * P(Y'|X,R).
EDIT: Never mind, it's not a problem. Even if it was, it wouldn't have changed their case that the Bayesian update won't give you this "uniform consistency" property. Which seems like something worth looking into.
As for this "low information" bull-hockey, let us put a MML prior over theta(x) and never speak of it again.