Monotonic multigamma coupling for perfect sampling
Faheem Mitha, Mark Huber · Journal of Statistical Computation and Simulation · 2011
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 ρ is variable; specifically, a function of the bounding chains. This variation is more efficient than the fixed ρ version, and can always be used when the multigamma coupler is monotonic. We apply our algorithm to two examples.