Dirichlet Simplex Exploration: Or, My Prayer Answered 

 Andrew Fernandes, a fellow Canadian expat and PhD student at NC State, responded to my earlier request for  advice on exploring a Dirichlet-type simplex . 

 Among other places, the idea is presented in the Wikipedia entry for  Simplex . He suggests perturbing the cumulative sums, then putting the perturbed sums back in order to draw a time-reversible proposal. This has the advantage of not sending too many parameters below zero - a maximum of one - as opposed to an equal perturbation of each parameter, and not pinning a high-valued parameter in place with a standard Dirichlet proposal.