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I am trying to understand Dirichlet Process Mixture models. One of the videos I have been watching is by Tamara Broderick. I think it is a very good introductory video to Dirichlet Process mixture models. Another resource I am looking at is by radford Neal which talks about MCMC sampling for the posterior distribution of Dirichlet Porcess Mixture Models. Both videos also talk about sampling from the posterior distribution of a DP mixture, however I am not sure why the posterior distributions Neal and Tamara refers to are different.

In particular, Tamara Broderick does not talk about updating the cluster parameters $\mu_k$ but rather only the cluster assignments $z_i$. radford Neal on the other hand talks about sampling a new cluster mean $\mu_k$ from the posterior at every step of gibbs sampling. (Algorithm 2)

I have a few questions regarding.

  1. What is the posterior distribution of a DP mixture model ?
  2. What is the difference between Tamara Broderick and radford Neal method ?
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Regarding your second question, Tamera Broderick addresses the case when the cluster parameters can be analytically marginalized (she mentions this briefly at https://youtu.be/mC-jZcEb7ME?t=1042) whereas Radford Neal's paper is about methods that explicitly sample the cluster parameters.

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  • $\begingroup$ Might you know what the full posterior distribution for the Dirichlet process mixture model is with respect to eq (2.3) of radford neal's paper ? $\endgroup$
    – calveeen
    Commented Oct 16, 2020 at 14:21

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