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Paper No. 09-23

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K Latuszynski, B Miasojedow and W Niemiro

Nonasymptotic bounds on the estimation error for regenerative MCMC algorithms under a drift condition

Abstract: MCMC methods are used in Bayesian statistics not only to sample from posterior distributions but also to estimate expectations. Underlying functions are most often dened on a continuous state space and can be unbounded. We consider Monte Carlo estimators based on i.i.d. blocks of a Markov chain trajectory. The main result is an inequality for the mean square error. We also consider confidence bounds. The basic assumption is a version of geometric drift condition.