Talk:De Finetti's theorem
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But what the heck does all that mean? This is pure math -- what's the applied math version of exchangeability? Cyan 06:38 Apr 2, 2003 (UTC)
OK, I've attempted to incoporate a sort of answer into the article. Michael Hardy 01:54 Apr 3, 2003 (UTC)
I've read that this theorem can be made to apply to finite exchangeable sequences (or the subsequences of finite exchangeable sequences...?) by removing the restriction that the the mixing function be a distribution and allowing it to assume negative values. I'm not really sure what this means in practical terms... does that information belong in this article? Cyan 08:11 Apr 3, 2003 (UTC)
I think the business about allowing it to assume negative values is from this article: http://bayes.wustl.edu/etj/articles/applications.pdf Ajb
"In particular, one may well doubt the cogency of the underlying assumptions of [the method of inverse probability], i.e. the construction of a prior probability distribution over unknown `true' probability distributions and the choice that this prior distribution should be uniform, or ask whether all this complies with the clause that `nothing else' is known, which was emphasized in the statement of the problem. All I can say is that these assumptions would be deemed appropriate precisely under this clause by most classical probability theorists. Also, it has been shown by De Finetti that this construction can be replaced by the more appealing and parsimonious assumption of `exchangeability'." Jos Uffink, The constraint rule of the maximum entropy principle,Studies in History and Philosophy of Modern Physics 27 (1996) 47-79. ...Somehow, the concept of exchangeability frees us from having to postulate an underlying "true" probability distribution? Cyan 09:56 Apr 3, 2003 (UTC)
[edit] Negative values
FWIW, negative coefficients were first proposed by Jaynes, but later analysed more deeply, as in [1]. However, allowing negative coefficients breaks the assumption that the coefficients themselves come from a distribution, and this would possibly run against de Finetti's ideas. -- Zz 15:43, 20 November 2006 (UTC)
