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For an inference problem using a Dirichlet Process prior, one can derive a "basic" Gibbs sampling scheme, where we have a conditional for any parameter $\theta_i$ given the samples $x_i$ and all the other parameters:

$$ \theta_i|\theta_{-i},x_1,...,x_n $$

Improvements can be made to this by introducing indicator variables. For the Hierarchical Dirichlet Process (HDP), in all the papers I have seen, the Gibbs samplers given are the version with indicator variables - however I am looking for the HDP "basic" Gibbs sampler equations like the DP one above, so without indicators, just with parameters and samples. Does anyone know of a reference where these are given (and ideally with a derivation)?

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