Talk:Generalized Dirichlet distribution

message: The article would become a lot more interesting and informative if the difference with the usual Dirichlet distribution could be clarified. Tomixdf 10:20, 25 August 2007 (UTC)
replies: text: Hello Tomixdf.  The condition for the GDD to reduce to the DD is stated just after the first displayed equation.  I will emphasise it.  Do you have any idea what Wong's "two wooden box" experiment means?  I sure don't.  Best wishes, Robinh 21:43, 25 August 2007 (UTC)
replies: text:  No, I have no idea what the "two wooden box experiment" is about :-). I'll look into the GDD though, it looks quite interesting. What I actually meant was: in which situations would a GDD perform better than an ordinary DD? A simple, real world example would be nice, IMO. Some plots of samples drawn from GDDs with different parameters would be great, for example. Tomixdf 23:24, 25 August 2007 (UTC)
replies: text: Hello again Tomixdf.  Unfortunately, the best real world example of GDD being better than the DD is Wong's two wooden box experiment.  Which I do not understand (not for lack of trying).  I have Wong 1998 right in front of me, open at the right page, which I have been staring at for hours and hours.  And I still don't understand it properly.  Connor and Mosiman discuss two nice little examples (one of percentages  of bone constituents and one of areas of turtle scutes) but these are better discussed on the Neutral vector page, IMO.  Let me know if you think this is inappropriate!   I'll stick them in when I get a minute.  Best wishes, Robinh 21:37, 26 August 2007 (UTC)
replies: text: I'm also a bit puzzled by Wong's boxes :-D. But there is some pseudocode to generate samples from GDD, so it should be easy to make some plots showing the different shapes of DD and GDD for different parameter sets. I'll try to look into it one of these days. Tomixdf 18:18, 29 August 2007 (UTC)

text: Hello.  Thanks for your comments.  Problems sorted.  To me, 'ball' and 'marble' are near-synonyms.  I used these words because Wong used them.  You are quite right about the order of the boxes: the GD distribution is neutral, but not completely neutral.  Best wishes, Robinh (talk) 07:27, 30 September 2008 (UTC)

message: One of the most useful facts to know about a distribution is how it arises in practice, i.e. what sort of real world situations are well modelled by the distribution.
The ordinary Dirichlet distribution arises in situations such as rolling a (possibly biased) die. Following a Bayesian approach, you start with a Dirichlet prior, say \alpha = (1, 1, 1, 1, 1, 1) if you think the die is fair (one prior count for each face), then roll the die numerous times, updating the face counts. The resulting Dirichlet reflects one's posterior belief about the die taking into account the experimental evidence. This example is helpful if it follows an introductory example of coin-tossing using the beta distribution. The Dirichlet is understood as being like a beta but with more options. The marginal distribution for one die face is intuitively seen to be beta, because the face corresponds to "heads" and all the other faces, lumped together, correspond to "tails".
However, what sort of situation gives rise to the GDD? The urn thought-experiment seems contrived and unlike any situation I can think of. Why are the boxes opaque? What's the role of the marbles? Why does the order of the boxes matter?
Presumably the GDD was devised out of necessity, not as a pure maths exercise, so it would be very helpful to have some real world examples of where it applies. (I've always found urns and balls particularly unhelpful; it's not something one does every day.)
--88.109.216.145 (talk) 12:42, 5 November 2009 (UTC)
thread_title:  How does the GDD arise?