The Dirichlet-Multinomial and Dirichlet-Categorical models for Bayesian inference

There are some pedagogical concerns to be noted. First, the pdf f(x) is technically defined only in (K−1)-dimensional space and not K; this is because SK has zero measure in K dimensions. Second, the support is actually the open simplex, meaning all xi > 0 (which implies no xi = 1). The Dirichlet distribution is a generalization of the Beta distribution, which is the conjugate prior for coin flipping.