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Abstract
The Nummellin's split chain construction allows to decompose a Markov chain Monte
Carlo (MCMC) trajectory into i.i.d. "excursions". RegenerativeMCMC algorithms based
on this technique use a random number of samples. They have been proposed as a promising
alternative to usual fixed length simulation [25, 33, 14]. In this note we derive
nonasymptotic bounds on the mean square error (MSE) of regenerative MCMC estimates
via techniques of renewal theory and sequential statistics. These results are applied
to costruct confidence intervals. We then focus on two cases of particular interest:
chains satisfying the Doeblin condition and a geometric drift condition. Available
explicit nonasymptotic results are compared for different schemes of MCMC simulation.