On the simulation of Markov chain steady-state distribution using CFTP algorithm

The famous Propp and Wilson (1996, 1998) protocol called coupling from the past (CFTP) allows exact sampling from steady-state distribution of a Markov chain. When the Markov chain is stiff (i.e. existence of rarely visited states), CFTP spends a prohibitive time to reach stationarity. To reduce this time we propose to combine the variance reduction technique Importance Sampling (IS) with CFTP. Also we propose another technique, based on the power of the Markov chain kernel, to reduce the CFTP simulation time in standard case. When the period delta of the simulated Markov chain is greater than one (delta > 1), the stopping condition of CFTP is not satisfied. To break the deadlock of CFTP in this case, we propose to transform the studied chain on delta subchains that are aperiodic and for which CFTP can be applied. Some numerical examples are presented to bring the utility of the proposed simulation techniques.