I'm afraid I don't understand. (Theoretical) Bayesian statistics is the study of probability flows under minimal assumptions - any quantity that behaves like we want a probability to behave can be described by Bayesian statistics. Therefore learning this general framework is useful when later looking at applications and most notably approximations. For what reasons do you suggest studying the approximation algorithms before studying the underlying framework?
Also you mention 'Bayesian procedures', I would like to clarify that I wasn't referring to any particular Bayesian algorithm but to the complete study of (uncomputable) ideal Bayesian statistics.
(Theoretical) Bayesian statistics is the study of probability flows under minimal assumptions - any quantity that behaves like we want a probability to behave can be described by Bayesian statistics.
But nobody, least of all Bayesian statistical practitioners, does this. They encounter data, get familiar with it, pick/invent a model, pick/invent a prior, run (possibly approximate) inference of the model against the data, verify if inference is doing something reasonable, and jump back to an earlier step and change something if it doesn't. After however l...
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?