On the geometric ergodicity of hybrid samplers

In this paper, we consider the random-scan symmetric random walk Metropolis algorithm (RSM) onℝd. This algorithm performs a Metropolis step on just one coordinate at a time (as opposed to the full-dimensional symmetric random walk Metropolis algorithm, which proposes a transition on all coordinates at once). We present various sufficient conditions implyingV-uniform ergodicity of the RSM when the target density decreases either subexponentially or exponentially in the tails.