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Paper No. 09-35

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K Latuszynski and W Niemiro

Rigorous confidence bounds for MCMC under a geometric drift condition

Abstract: We assume a drift condition towards a small set and bound the mean square error of estimators obtained by taking averages along a single trajectory of a Markov chain Monte Carlo algorithm. We use these bounds to construct fixed-width nonasymptotic confidence intervals.

Keywords: MCMC estimation, confidence intervals, mean square error, Markov chain, convergence rate, V-uniform ergodicity, drift condition, simulation cost.