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Cyan comments on Against improper priors - Less Wrong Discussion

2 Post author: DanielLC 26 July 2011 11:50PM

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Comment author: Cyan 27 July 2011 04:26:11AM *  6 points [-]

you can always make a proper prior that's better in every way to a given improper prior

[emphasis mine]

"In every way" is too strong. Some improper priors are derived from the optimization of some criterion, so they are the best in a certain specific way. Also, some improper priors give posterior means that, when treated as estimators, have minimax-optimal frequentist risk. I think you mean something more like "better in every way that ought to matter to someone concerned with rationality".

Comment author: DanielLC 27 July 2011 04:56:43AM 0 points [-]

Perhaps "better in every case" would work? That is, less surprising no matter what happens?

Comment author: Cyan 27 July 2011 05:58:23AM 1 point [-]

Since I don't think it makes sense to speak of the "surprise" associated with an improper distribution, I think the claim you want to make doesn't cut to the heart of the matter. There are lots of reasons to object to improper priors, but this isn't well-formed enough to be one of them.