Right now, we use hyperspherical coordinates. It would be better to just normalize as explained at https://en.wikipedia.org/wiki/N-sphere#Uniformly_at_random_from_the_.28n.C2.A0.E2.88.92.C2.A01.29-sphere See also See https://groups.google.com/d/msg/stan-dev/0cXoSwAs3tw/dPT-fAVojdIJ