A comparison of two Markov Chain Monte Carlo methods for sampling from unnormalized discrete distributions
Carlos Townes Gillett · Texas ScholarWorks (Texas Digital Library) · 2015
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 iv scaled Metropolis-Hastings algorithm.We conclude that this alternative algorithm represents a valuable addition to extant Markov Chain Monte Carlo Methods.v 1000 Iterations of Poisson with Mean 10 and Optimally Scaled Metropolis-Hastings . . . . . . . . . . . . . . . . .32 vii 10 Transition Density from Current State θ = 5 for Poisson with Mean 10 and Spread Parameter k = 100 . . . . . .34 11 Transition Density from Current State θ = 10 for Poisson with Mean 10 and Spread Parameter k = 100 . . . . . .35 12 Transition Density from Current State θ = 20 for Poisson with Mean 10 and Spread Parameter k = 100 . . . . . .36 viii