The dirichlet distribution takes this form:
I'm trying to understand how we end up with a vector from this formula rather than a scalar. The only way I see how is that each x itself is a vector sampled from the simplex.
In particular, I'm trying to understand in the context of Latent Dirichlet Allocation. K would represent the number of topics we have (points on the simplex). So if we have 3 topics, do we sample three points in the simplex, multiply them, and then normalize them with the beta function?