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I tried to learn how Gibbs sampling works on Mixture models by studying David Blei's notes:

http://www.cs.columbia.edu/~blei/fogm/2015F/notes/mixtures-and-gibbs.pdf

In the equation 28:

$p(z_i = k| z_{-i},x)\propto p(z_i=k)p(x_i|z_{-i},x_{-i},z_i=k)$

I am not sure what is the denominator on the right hand side here. Could you please help me ? Thanks a lot.

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The denominator is $$\sum_{k} p(z_i = k) p(x_i|z_{-i}, x_{-i}, z_i = k) $$

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