Nonasymptotic bounds on the mean square error for MCMC estimates via renewal techniques

Details Nonasymptotic bounds on the mean square error for MCMC estimates via renewal techniques Nonasymptotic bounds on the mean square error for MCMC estimates via renewal techniques

2011-01-31

arxiv.org/abs/1101.5837v2

for MCQMC 2010 Conference Proceeding

Statistics

Computation

Scientific paper

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.

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