I agree with the Kruschke recommendation. I bought a copy of Doing Bayesian Data Analysis a couple of weeks ago and am working my way through it now. It is quite good. You'll need an understanding of undergraduate-level calculus and some background in basic probability to understand it, I think.
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.]