For me the sections on Bertand’s paradox are very clear in that he claims only Emile Borel saw the light in proposing a definitive solution (which happens to coincide with Jaynes’) and all other (from Bertrand to Poincaré, to von Mises) were mathematical nit-pickers… The very final sentence of the section where he mentions an experimental verification of Borel’s law is quite supportive of this interpretation.

And you are more than welcome to run this seminar next time you visit!!!

]]>**W**hen I read this (and similar examples) in Jaynes’s book, I interpreted his philosophy somewhat differently. I agree that if you read Jaynes literally, it appears that he claims there is a correct distribution, similarly to the way he appears to claim elsewhere that maximum entropy gives the correct unique specification of a probability distribution given some specified moments.

But I give a slightly different interpretation. To me, what Jaynes is saying is that given what appears to be partial information, it makes sense to make some strong assumptions based on some theoretical framework, and then go with those assumptions until they’re violated. Once you have some data it should be easy enough to find problems with any particular model you assume. Then when there’s a problem, Jaynes says to go back and see what you did wrong earlier and to specify what additional information you have. To me, this is very consistent with the 3 steps of BDA (model building, inference, model checking); in fact my reading of Jaynes was a major inspiration behind our framing Bayesian data analysis in that way. Even though I expect that Jaynes himself would’ve been horrified by my pragmatic-style Bayesian philosophy, I think that it is in the spirit of the best of his work.

If you can wait a couple years, perhaps we can do that seminar together during my next année sabbatique!

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