On perfect simulation for some mixtures of distributions

This paper studies the implementation of the coupling from the past (CFTP) method of Propp and Wilson (1996) in the set-up of two and three component mixtures with known components and unknown weights. We show that monotonicity structures can be exhibited in both cases, but that CFTP can still be costly for three component mixtures. We conclude with a simulation experiment exhibiting an almost perfect sampling scheme where we only consider a subset of the exhaustive set of starting values.