Subsampling the Gibbs sampler: variance reduction

Subsampling the output of a Gibbs sampler in a non-systematic fashion can improve the efficiency of marginal estimators if the subsampling strategy is tied to the actual updates made. We illustrate this point by example, approximation, and asymptotics. The results hold both for random-scan and fixed-scan Gibbs samplers.Bayesian analysis Efficiency Estimation Markov chains Monte Carlo Stationary time series