On Estimating Non-standard Discrete Distributions Using Adaptive MCMC Methods

In this paper, we compare empirically the performance of some adaptive MCMC methods, that is, Adaptive Metropolis (AM) algorithm, Single Component Adaptive Metropolis (SCAM) algorithm and Delayed Rejection Adaptive Metropolis (DRAM) algorithm. The context is the simulation of non-standard discrete distributions. The performance criterion used is the precision of the frequency estimator. An application to a Bayesian hypothesis testing problem shows the superiority of the DRAM algorithm over the other considered sampling schemes.