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The Dirichlet distribution refers to a family of multivariate distributions, which are the generalization of the univariate beta distribution.

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Normalization constant for uniform distribution over categorical distributions

As a quick update, I have since found the answer to my own question. Since we are concerned with finding the density of a uniform distribution, 1/c is the normalization constant for the summation acr …
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Normalization constant for uniform distribution over categorical distributions

Suppose we have a uniform distribution over all categorical distributions p for m categories, where the pdf has the form $$ f(x) = \left\{\begin{aligned} &c, && 0 \le p_i \le 1, i = 1, ..., m, \texts …
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