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Oscar_Cunningham comments on Open thread, September 2-8, 2013 - Less Wrong Discussion

0 Post author: David_Gerard 02 September 2013 02:07PM

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Comment author: alex_zag_al 05 September 2013 09:10:07PM *  4 points [-]

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

Comment author: Oscar_Cunningham 06 September 2013 07:00:16AM *  2 points [-]

I've just looked and I have no idea either. If anyone wants to help there's a copy of the book here.

EDIT: The numbers in that copy are off by 1 from the book. "18.10" = "18-9" and so on.

Comment author: alex_zag_al 06 September 2013 03:21:02PM *  0 points [-]

Yeah, so to add some redundancy for y'all, here's the text surrounding the equations I'm having trouble with.

The 18.10 to 18.11 jump I'm having trouble with is the one in this part of the text:

But suppose that, for a given E_b, (18.8) holds independently of what E_a might be; call this 'strong irrelevance'. Then we have (what I'm calling 18.10) But if this is to hold for all (A_p|E_a), the integrands must be the same: (what I'm calling 18.11, and can't derive) .

And equation 18.15, which I can't justify, is in this part of the text:

But then, by definition (18.1) of A_p, we can see that A_p automatically cancels out E_aa in the numerator: (F|A_pE_aa)=(F|A_p). And so we have (18.13) reduced to (what I'm calling 18.15, and don't follow the justification for)