A comparison of two Markov Chain Monte Carlo methods for sampling from unnormalized discrete distributions

This report compares the convergence behavior of the Metropolis-Hastings and an alternative Markov Chain Monte Carlo sampling algorithm targeting unnormalized, discrete distributions with countably infinite sample spaces. The two methods are compared through a simulation study in which each is used to generate samples from a known distribution. We find that the alternative sampler generates increasingly independent samples as the scale parameter is increased, in contrast to the Metropolis-Hastings. These results suggest that, regardless of the target distribution, our alternative algorithm can generate Markov chains with less autocorrelation than even an optimally scaled Metropolis-Hastings algorithm. We conclude that this alternative algorithm represents a valuable addition to extant Markov Chain Monte Carlo Methods.