The terminology categorical distribution is not used everywhere. Bishop does not use that name, but he does have different formulas in his book (Pattern Recognition and Machine Learning) for the multinomial and categorical distribution. (Minka simply calls both multinomial.) Since wikipedia already has an article called categorical distribution, I thought it would help to use this terminology here and elsewhere in Wikipedia. CalvynkW (talk) 12:03, 14 April 2011 (UTC)
Hi does anyone have the original Pòlya reference on this topic? From some search it appear to have been done in the twenties. — Preceding unsigned comment added by 18.104.22.168 (talk) 17:20, 15 December 2011 (UTC)
Despite the comment above, the distinction wasn't clearly made between the two forms of the DCM. I have almost totally rewritten and greatly expanded the page, and it should hopefully now make the distinction clear enough. The page now mostly focuses on the simpler form (without the multinomial constant). Benwing (talk) 21:35, 17 March 2012 (UTC)
The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.
The result of the move request was: Move already madeMike Cline (talk) 12:48, 24 March 2012 (UTC)
The term "Polya distribution" has been used for a large number of different distributions with divergent characteristics (e.g. a special case of the negative binomial; a generalization of the negative binomial; another parameterization of a negative binomial; a distribution that generalizes the binomial and hypergeometric; and sometimes for the DCM dist itself). So the term "multivariate Polya" might equally well refer to multivariate extensions of various different distributions.
On top of this, the term "Polya distribution" does NOT seem to be used for the beta-binomial distribution. Logically, if the DCM is described as "Multivariate X distribution" for some X, that X ought to refer to the beta-binomial dist.
The second item above suggests that "Dirichlet-multinomial distribution" might be an alternative, and indeed that term does exist, but seems less common than DCM dist. Benwing (talk) 11:50, 17 March 2012 (UTC)
Personally, I think "Polya distribution" should stay, since "dirichlet compound multinomial" is a very cumbersome name. It makes sense to me to call a beta-binomial a Polya distribution, since it is equivalent to drawing from a Polya urn. If you do change it though, "dirichlet-multinomial" is less cumbersome than "dirichlet compound multinomial" and is more directly analogous to "beta-binomial". These are also the two names for it used in Tom Minka's paper, referenced above. Disclaimer: I didn't contribute to this article.Satyr9 (talk) 21:46, 21 March 2012 (UTC)
I went ahead and changed it to "Dirichlet-multinomial": Various statisticians told me that "Dirichlet-multinomial" was the most common, and it fits the analogy best. "Polya distribution" has horrible problems with ambiguity, unfortunately, which is one main reason I don't want to use it. Benwing (talk) 09:02, 24 March 2012 (UTC)
The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.