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I agree that the first few chapters of Jaynes are illuminating, haven't tried to read further. Bayesian Data Analysis by Gelman feels much more practical at least for what I personally need (a reference book for statistical techniques).
The general pre-requisites are actually spelled out in the introduction of Jayne's Probability Theory. Emphasis mine.
The following material is addressed to readers who are already familiar with applied mathematics at the advanced undergraduate level or preferably higher; and with some field, such as physics, chemistry, biology, geology, medicine, economics, sociology, engineering, operations research, etc., where inference is needed. 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.
familiar with applied mathematics at the advanced undergraduate level or preferably higher
In working through the text, I have found that my undergraduate engineering degree and mathematics minor would not have been sufficient to understand the details of Jaynes' arguments, following the derivations and solving the problems. I took some graduate courses in math and statistics, and more importantly I've picked up a smattering of many fields of math after my formal education, and these plus Google have sufficed.
Be advised that there are errors (typographic...
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.]