A GEM (Griffiths-Engen-McCloskey) sequence specifies the (random) proportions in splitting a `resource' infinitely many ways.  Such sequences form the backbone of `stick breaking' representations of Dirichlet processes used in nonparametric Bayesian statistics.  In this talk, we consider the connections between a class of generalized `stick breaking' processes, an intermediate structure via `clumped' GEM sequences, and the occupation laws of certain time-inhomogeneous Markov chains.