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 will give it a shot (I recall reading a well-written explanation elsewhere on LW, and I don't expect to be as clear as what I read there).
In any estimation or prediction setting we are interested in making accurate probabilistic claims about the behaviour of our system of study. In particular we would like to give a description of how the system will behave in the future (for example: 'this drug cures patients 30% of the time'). This is captured by the posterior probability distribution.
Now if we have any algorithm whatsover that makes statements about o...
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?