Abstract: In this paper, we present a non-monotone coupling from the past (CFTP) method for obtaining perfect samples from the equilibrium distribution of a Markov chain. This method requires no monotone structure that is difficult to define in practice. We also apply the non-monotone CFTP method to general non-monotone birth-death processes and area-interaction point processes.
Key words and phrases: Area-interaction point processes, birth-death processes, CFTP, MCMC, monotone, non-monotone, perfect simulation.