A Note on Markov Chain Monte Carlo Sweep Strategies

Markov chain Monte Carlo (MCMC) routines have become a fundamental means for generating random variates from distributions otherwise difficult to sample. The Hastings sampler, which includes the Gibbs and Metropolis samplers as special cases, is the most popular MCMC method. A number of implementations are available for running these MCMC routines varying in the order through which the components or blocks of the random vector of interest X are cycled or visited. The two most common implementations are the deterministic sweep strategy, whereby the components or blocks of X are updated successively and in a fixed order, and the random sweep strategy, whereby the coordinates or blocks of X are updated in a randomly determined order. In this note, we present a general representation for MCMC updating schemes showing that the deterministic scan is a special case of the random scan.