Good quote.
But I would have bolded
already familiar with applied mathematics ... where inference is needed
That's where Jaynes shines. Many mathematical subjects are treated axiomatically. Jaynes instead starts from the basic problem of representing uncertainty. Churning out the implications of axioms is a very different mindset than "I have data, what can I conclude from it?"
I think this is true as well.
A previous acquaintance with probability and statistics is not necessary; indeed, a certain amount of innocence in this area may be desirable, because there will be less to unlearn.
Not too long ago, I asked LessWrong which math topics to learn. Eventually, I want to ask for what the prerequisites for each of those topics are and how I should go about learning them. This is a special case of that.
I'm rereading the sequences and Eliezer seems to love E.T. Jaynes. As part of my rationality self-study, I want to work my way through his Probability Theory: the Logic of Science. What math topics do I already need to understand to prepare myself for this? I learned calculus once upon a time, but not fantastically well, and I plan to start by reviewing that.
Also,
Despite Eliezer's praise of the "thousand-year-old vampire", it there a better book to learn probability theory?
Does anyone want to learn this (or the other math from my post above) with me? I'd love to have a partner or maybe even a work group. Location is no obstacle. [Two caveats: 1. I'm busy with stuff and may not be able to get into this for a few months 2. I hard, but I am incredibly slow at computation (such that on every math test I have ever taken, it took me at least 3 times as long as the second slowest person in the class to finish). You might find that I go to slow for you.]