But if we start with a prior over all possible six-sided dies and do Bayesian updating, we get a different answer that diverges from fairness more and more as the number of throws goes to infinity!
I’m nearly positive that the linked paper (and in particular, the above-quoted conclusion) is just wrong. Many years ago I checked the calculations carefully and found that the results come from an unavailable computer program, so it’s definitely possible that the results were just due to a bug. Meanwhile, my paper copy of PT:LOS contains a section which purports to show that Bayesian updating and maximum entropy give the same answer in the large-sample limit. I checked the math there too, and it seemed sound.
I might be able to offer more than my unsupported assertions when I get home from work.
I’ve checked carefully in PT:LOS for the section I thought I remembered, but I can’t find it. I distinctly remember the form of the theorem (it was a squeeze theorem), but I do not recall where I saw it. I think Jaynes was the author, so it might be in one of the papers listed here… or it could have been someone else entirely, or I could be misremembering. But I don’t think I’m misremembering, because I recall working through the proof and becoming satisfied that Uffink must have made a coding error.
I’m nearly positive that the linked paper (and in particular, the above-quoted conclusion) is just wrong. Many years ago I checked the calculations carefully and found that the results come from an unavailable computer program, so it’s definitely possible that the results were just due to a bug. Meanwhile, my paper copy of PT:LOS contains a section which purports to show that Bayesian updating and maximum entropy give the same answer in the large-sample limit. I checked the math there too, and it seemed sound.
I might be able to offer more than my unsupported assertions when I get home from work.
I’ve checked carefully in PT:LOS for the section I thought I remembered, but I can’t find it. I distinctly remember the form of the theorem (it was a squeeze theorem), but I do not recall where I saw it. I think Jaynes was the author, so it might be in one of the papers listed here… or it could have been someone else entirely, or I could be misremembering. But I don’t think I’m misremembering, because I recall working through the proof and becoming satisfied that Uffink must have made a coding error.