You're welcome for the link, and it's more than repaid by your causal inference restatement of the Robins-Ritov problem.
Of course arguably this entire setting is one Bayesians don't worry about (but maybe they should? These settings do come up).
Yeah, I think this is the heart of the confusion. When you encounter a problem, you can turn the Bayesian crank and it will always do the Right thing, but it won't always do the right thing. What I find disconcerting (as a Bayesian drifting towards frequentism) is that it's not obvious how to assess the adequacy of a Bayesian analysis from within the Bayesian framework. In principle, you can do this mindlessly by marginalizing over all the model classes that might apply, maybe? But in practice, a single model class usually gets picked by non-Bayesian criteria like "does the posterior depend on the data in the right way?" or "does the posterior capture the 'true model' from simulated data?". Or a Bayesian may (rightly or wrongly) decide that a Bayesian analysis is not appropriate in that setting.
I have started to put together a sort of curriculum for learning the subjects that lend themselves to rationality. It includes things like experimental methodology and cognitive psychology (obviously), along with "support disciplines" like computer science and economics. I think (though maybe I'm wrong) that mathematics is one of the most important things to understand.
Eliezer said in the simple math of everything:
I want to have access to outlook-changing insights. So, what math do I need to know? What are the generally applicable mathematical principles that are most worth learning? The above quote seems to indicate at least calculus, and everyone is a fan of Bayesian statistics (which I know little about).
Secondarily, what are some of the most important of that "drop-dead basic fundamental embarrassingly simple mathematics" from different fields? What fields are mathematically based, other than physics and evolutionary biology, and economics?
What is the most important math for an educated person to be familiar with?
As someone who took an honors calculus class in high school, liked it, and did alright in the class, but who has probably forgotten most of it by now and needs to relearn it, how should I go about learning that math?