As I've mentioned several times above Bayesian statistics are not just a set of estimators to be used on problems, they are the minimal framework of probability that satisfy Cox' law. This means that any algorithm that isn't even approximately Bayesian will spit out something other than (an approximation of) the posterior probability. In other words, in order to even get any sort of answer that can reasonably be used for further computation there has to be a Bayesian explanation, otherwise what your algorithm is doing just doesn't have anything to do with statistics. This does not mean that the only useful algorithms are those crafted by trying to compute the likelihood ratio, nor does it mean that there is always a simple algorithm that would be classified as a 'Bayesian algorithm'. It merely means that to do probability you have to do Bayes, and then maybe some more.
Bayesian statistics are ... the minimal framework of probability that satisfy Cox' law.
Can you elaborate on this? I don't think that's how most people understand Bayesian statistics.
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?