Simple perfect samplers using monotone birth-and-death processes

This paper proposes simple perfect samplers using monotone birth-and-death processes (BD-processes), which draw samples from an arbitrary finite discrete target distribution. We first construct a monotone BD-process whose stationary distribution is equal to the target distribution. We then derive upper bounds for the expected coalescence time of the copies of the monotone BD-process. We also establish upper bounds for the expected values and tail probabilities of the running times of two perfect samplers, which are Doubling CFTP and Read-once CFTP using our monotone BD-process. The latter sampler can draw samples exactly from unnormalized target distributions with little memory consumption.