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I have a sample of Chinese restaurant process which I want to model as Pitman–Yor process. How do I determine parameters of Pitman-Yor model from given sample?

For Dirichlet process I would just use the fact that on average K=αlogN where is K is observed number of tables and N is total number of visitors but I see no similar way for the Pitman-Yor process.

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This paper has a thorough run-down of what you're looking for. It includes a Gibbs sampler for posterior computation of a finite approximation of stick-breaking priors (the only tractable way to do it).

If you are going to use MCMC, I recommend using label-switching moves to offset the prior weight on earlier stick segments. Basically you randomly permute the stick labels at the end of every MCMC step. This will improve mixing dramatically.

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