Talk:Chinese restaurant process

It is not "immediate" that the probability assigned to a particular partition is ...

"It is then immediate that the probability assigned to any particular partition (ignoring the order in which customers sit around any particular table) is"

I am a mathematics graduate and it is not obvious to me why the given formula holds. I think that a derivation of the simple, non-generalized case belongs here. I hate it when people say that something "follows immediately" when, in fact, it requires half a hour's thought and a half-page derivation. — Preceding unsigned comment added by 78.105.228.69 (talk) 00:58, 31 December 2011 (UTC)

article needs discussion of meaning of this distribution

doesnt it :) Anlace 21:41, 27 June 2006 (UTC)

What is the application of this formula?

How, or in what circumstances, is it useful? --80.41.36.60 13:54, 25 July 2006 (UTC)

That it is relevant to the Ewens sampling formula is stated explicitly in the article. Therefore I was surprised by the question above. But now I've made it more explicit by adding a link to population genetics. Michael Hardy 15:01, 25 July 2006 (UTC)

notation

is the notation inconsistent? for example: n_k is the number of elements in the n-th block... but... |b| is also the number of elements in a block. —Preceding unsigned comment added by 143.215.146.218 (talk • contribs)

Does the generalization actually work?

Forgive me, I don't know much about the notations used here. But even using the convention $(a)_{0,c}=1$, which I myself thought appropriate of adding, taking the case α = 0, corresponding to Ewens' distribution, we should have:

$n=1$

$\Pr(B_{1}=B)={\dfrac {(\theta )_{|B|,0}}{(\theta +1)_{0,1}}}\prod _{b\in B}(1)_{|b|-1,1}={\dfrac {(\theta )_{1,0}}{(\theta +1)_{0,1}}}\cdot (1)_{0,1}={\dfrac {\prod _{i=0}^{0}\theta }{1}}\cdot 1=\theta \neq 1$

or with $n=2$, assuming only one occupied table with both people

${\begin{aligned}\Pr(B_{2}=B)&={\dfrac {(\theta )_{|B|,0}}{(\theta +1)_{1,1}}}\prod _{b\in B}(1)_{|b|-1,1}={\dfrac {\theta }{\prod _{i=0}^{1}(\theta +1+i)}}\cdot (1)_{1,1}=\\&={\dfrac {\theta }{(\theta +1)(\theta +2)}}\prod _{i=0}^{0}(1+i)=\\&={\dfrac {\theta }{(\theta +1)(\theta +2)}}=\\&\neq {\dfrac {1}{\theta +2}},\end{aligned}}$

which I get by directly computing the probability ${\dfrac {|b|}{n+\theta }}$ that the second person sit at the same table as the first.
Anyone knows better?

212.126.224.100 (talk) 19:05, 27 July 2010 (UTC)

I see this comment has been here for several weeks. I just saw it. I'll look at it later this afternoon. Michael Hardy (talk) 15:08, 17 August 2010 (UTC)

....I still haven't gotten to this. I suspect no one who's actually an expert on the Ewen's formula and the Chinese restaurant process has worked on this article. Michael Hardy (talk) 16:57, 27 August 2010 (UTC)

guess not. 212.126.224.100 (talk) 14:41, 31 August 2010 (UTC)

The formulate is indeed wrong. Instead of |B| it should read |B|-1 in the above quoted section. Since this is properly the most important thing to get right I hope it is okay that I correct the text, see for instance formula 16 of pitmanns paper: http://www.springerlink.com/content/k175tg8150441520/fulltext.pdf (quoted within main body of the text). — Preceding unsigned comment added by 130.225.93.116 (talk) 12:13, 24 September 2012 (UTC)

The intro to this article is currently too technical for most readers

The intro to this article currently fails to comply with the Wikipedia policy [[Wikipedia:Make technical articles understandable"}}. The intro fails to properly explain what the "Chinese restaurant process" is in basic terms that most readers can understand. The first sentence should describe the in a very general sense what the Chinese restaurant process is, then go into the specifics about the formula. The intro should also include a sentence explaining why it's called the Chinese restaurant process. --67.101.213.239 (talk) 14:55, 27 April 2013 (UTC)

The above criticism is still valid. The article should explain why anyone might be interested in studying this process. If there is any heuristic or intuitive way to understand the process, it should be mentioned as a non-rigorous way of gaining some insight into its significance. Reify-tech (talk) 01:28, 3 August 2014 (UTC)

I found that the second explanation, in "definition", was easier to understand than the first explanation in the introduction, so I essentially swapped them around. Hope this helps. Grabigail (talk) 15:27, 26 September 2014 (UTC)