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Simple question about Gibbs Sampling with a single Dirichlet-Multinomial

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I assume the most simple model:

theta | alpha ~ Dir(alpha + N)

X_i | Discrete(theta), i = 1, 2, 3

What would be the update equation, p(x_i, x_-i)? Is it the predictive distribution of a Dirichlet-Multinomial?

submitted by wordsoup
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