On random- and systematic-scan samplers

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We introduce a simple time-homogeneous Markov embedding of a class of time-inhomogeneous Markov chains widely used in the context of Monte Carlo sampling algorithms, such as systematic-scan Metropolis-within-Gibbs samplers. This allows us to establish that systematic-scan samplers involving two factors are always better than their random-scan counterparts, when asymptotic variance is the criterion of interest. We also show that this embedding sheds some light on the result of Maire et al. (2014) and discuss the scenario involving more than two factors.

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