Before revision:  In this paper, we introduce Ripple, an MCMC-based estimator which achieves unprecedented scalability in this task by stratifying the MCMC Markov chain state space  with a new technique that we denote {\em ordered sequential stratified Markov regenerations}.
After revision:  In this paper, we introduce Ripple, an MCMC-based estimator which achieves unprecedented scalability in this task by stratifying the MCMC Markov chain state space into ordered strata with a new technique that we denote {\em ordered sequential stratified Markov regenerations}.