the claim that any prediction can be interpreted in this minimal and consistent framework without exceptions whatsoever is a rather strong claim
The Bayes Rule by itself is not a framework. It's just a particular statistical operation, useful no doubt, but hardly arising to the level of framework.
The claim that you can interpret any prediction as forecasting a particular probability distribution has nothing to do with Bayes. For example, let's say that an analyst predicts the average growth in the GDP of China for the next five years to be 5%. If we dig and poke we can re-express this as a forecast of something like a normal distribution centered at 5% and with some width which corresponds to the expected error -- so there is your forecast probability distribution. But is there a particular prior here? Any specific pieces of evidence on which the analyst updated the prior? Um, not really.
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?