Monotonic multigamma coupling for perfect sampling
We consider a monotonic version of the multigamma coupler introduced by Murdoch and Green in 'Exact Sampling from a Continuous State Space' (Scandinavian Journal of Statistics, 1998) in the context of bounded multivariate distributions. Monotonicity greatly increases the efficiency of the coupler. We prove the validity of the multigamma coupler when the coalescence probability rho is variable; specifically, a function of the bounding chains. This variation is more efficient than the fixed rho version, and can always be used when the multigamma coupler is monotonic. We apply our algorithm to two examples.
monotonicity perfect sampling multigamma coupler markov chain coupling from the past read once coupling from the past