Subsampling the Gibbs Sampler
Steven N. MacEachern, L. Mark Berliner · The American Statistician · 1994
This article provides a justification of the ban against sub-sampling the output of a stationary Markov chain that is suitable for presentation in undergraduate and beginning graduate-level courses. The justification does not rely on reversibility of the chain as does Geyer's (1992) argument and so applies to the usual implementation of the Gibbs sampler.