Abstract: We provide a complete proof of the convergence of a recently developed sampling algorithm called the equi-energy (EE) sampler ([#!Kou!#]) in the case that the state space is countable. In a countable state space, each sampling chain in the EE sampler is strongly ergodic a.s. with the desired steady-state distribution. Furthermore, all chains satisfy the individual ergodic property. We apply the EE sampler to the Ising model to test its efficiency, comparing it with the Metropolis algorithm and the parallel tempering algorithm. We observe that the dynamic exponent of the EE sampler is significantly smaller than those of parallel tempering and the Metropolis algorithm, demonstrating its high efficiency.
Key words and phrases: Dynamic exponent, ergodic property, Monte Carlo methods, phase transition, steady-state distribution, temperature, transition kernel.