Simplex Distributions
The simplex probabilities have support on the unit \(K\)-simplex for a
specified \(K\). A \(K\)-dimensional vector \(\theta\) is a unit
\(K\)-simplex if \(\theta_k \geq 0\) for \(k \in \{1,\ldots,K\}\) and
\(\sum_{k = 1}^K \theta_k = 1\).