Nonasymptotic bounds on the estimation error for regenerative MCMC algorithms

Details Nonasymptotic bounds on the estimation error for regenerative MCMC algorithms Nonasymptotic bounds on the estimation error for regenerative MCMC algorithms

2009-07-28

arxiv.org/abs/0907.4915v1

Statistics

Methodology

29 pages, 2 figures

Scientific paper

MCMC methods are used in Bayesian statistics not only to sample from posterior distributions but also to estimate expectations. Underlying functions are most often defined on a continuous state space and can be unbounded. We consider a regenerative setting and 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. We first derive the results in terms of the asymptotic variance and then bound the asymptotic variance for both uniformly ergodic and geometrically ergodic Markov chains.

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