This is killing me in the use of Hamiltonian Monte Carlo, in which every parameter needs to be unbounded to eliminate overstepping boundaries in the leapfrog steps (this is much easier in something like slice sampling for Gibbs sampling). We need distributions like Beta(theta|alpha,beta) transformed with the simplex parameter theta going to a K-1-dimensional unbounded basis (basically the inverse softmax with one value pegged to 0.0) and alpha and beta log transformed.