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I have a basic understanding of free-energy minimization methods from doing some reading in neuroscience on prediction error minimization--primarily from Rafal Bogacz's beautiful tutorial on the free-energy framework for modelling perception and learning.

I'm interested in getting a more thorough understanding of the foundations of this and similar methods. However, I find it very difficult to find an appropriate book because as far as I can tell (a) FEM obviously has to do with other more general ideas in Bayesian inference, (b) it goes by different terms in different contexts, (c) it arises originally in physics, but is used in lots of other contexts, and (d) it's part of machine learning, deep learning, etc., but these are catchall terms for lots of methods, both closely related and not. So there are lots of books that look like they might contain what I'm looking for, but it's difficult to tell without first seriously studying the book!

I've been trying to find the right kind of book (or website, or papers) for months. I'm willing to develop whatever background is necessary to get a deeper understanding of FEM, but I admit that at the moment I'm trying to avoid learning all of Bayesian statistical inference, all of machine learning, etc.

What kind/kinds of book should I be looking for? (Particular suggestions are welcome, too.) I just want to understand the math better, so it could be OK, for example, if a book was primarily geared toward physicists or a signal compression audience.

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