Has anyone here read up through ch18 of Jaynes' PT:LoS? I just spent two hours trying to derive 18.11 from 18.10. That step is completely opaque to me, can anybody who's read it help?
You can explain in a comment, or we can have a conversation. I've got gchat and other stuff. If you message me or comment we can work it out. I probably won't take long to reply, I don't think I'll be leaving my computer for long today.
EDIT: I'm also having trouble with 18.15. Jaynes claims that P(F|A_p E_aa) = P(F|A_p) but justifies it with 18.1... I just don't see how that follows from 18.1.
EDIT 2: It hasn't answered my question but there's online errata for this book: http://ksvanhorn.com/bayes/jaynes/ Chapter 18 has a very unfinished feel, and I think this is going to help other confusions I get into about it
A not-quite-rigorous explanation of the thing in 18.15:
E_aa is, by construction, only relevant to A. A_p was defined (in 18.1) to screen off all previous knowledge about A. So in fact, if we are given evidence E_aa but then given evidence A_p, then E_aa becomes completely irrelevant: it's no longer telling us anything about A, but it never told us anything about anything else. Therefore P(F|A_p E_aa) can be simplified to P(F|A_p).
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.