# Dirichlet Process Clustering Prior

I'm doing dirichlet process clustering where dirichlet priors are used as:
with CRP representation as:

• First customer will always choose first table.
• Second will choose already occupied table with
• probability c/α + n - 1
• and will choose unoccupied table with
• probability α / α + n - 1 where
• α which is known as dirichlet prior and
• c is # of customers at occupied table
• n is total # of customers

Now if we use Collapsed Gibbs Sampling for initial assignments of group, α is also used as CRP probability in Collapased Gibbs Sampling. So the question is:

• Should I myself assign a value to α or is there any technique to estimate α?

Thanks!

• Are you looking at a Chinese Restaurant process ? link – EngrStudent - Reinstate Monica Mar 14 '16 at 12:58
• @EngrStudent yeah absolutely I want to Dirichlet Clustering using CRP as what I know, Dirichlet Clustering using Stick Breaking Construction or using CRP is almost same. – maliks Mar 14 '16 at 13:03
• @EngrStudent These both links shared by you are not downloadable for me here, can you please share at taufelaus@gmail.com – maliks Mar 14 '16 at 13:06
• @EngrStudent can you help me in estimating or inferring a value for α please? – maliks Mar 14 '16 at 13:07
• You can put a prior on alpha and make a draw from its conditional posterior on each sweep. – mef Mar 14 '16 at 13:41

As @mef pointed out you can put a vague gamma prior on $\alpha$, $\alpha \sim Gamma(a, b)$ and resample $\alpha$ as well as your table assignments. You can find the details in Escobar and West 95 paper, or in this note by West.