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alex_zag_al comments on Open Thread, September 30 - October 6, 2013 - Less Wrong Discussion
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ah, thank you! It makes me so happy to finally see why that first term disappears.
But now I don't see why you subtract the second-order terms.
I mean, I do see that since you're at a maximum, the value of the function has to decrease as you move away from it.
But, in the single-parameter case, Jaynes's formula becomes
But that second derivative there is negative. And since we're subtracting it, the function is growing as we move away from the minimum!
Yes, that formula doesn't make sense (you forgot the 1/2, by the way). I believe 8.52/8.53 should not have a minus there and 8.54 should have a minus that it's missing. Also 8.52 should have expected values or big-O probability notation. This is a frequentist calculation so I'd suggest a more standard reference like Ferguson