Question: Marginalise the Gaussian mean from the Gibbs sampler to give a conditional distribution for (z_{n k}) conditioned only on the other assignments and the prior

Marginalise the Gaussian mean from the Gibbs sampler to give a conditional distribution for \(z_{n k}\) conditioned only on the other assignments and the prior parameters \(\left(\mu_{0}, \boldsymbol{\Sigma}_{0}, \alpha\right)\).

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