Variance reduction for Markov chains with application to MCMC

@article{Belomestny2020VarianceRF,
  title={Variance reduction for Markov chains with application to MCMC},
  author={Denis Belomestny and Leonid Iosipoi and {\'E}ric Moulines and Alexey Naumov and Sergey Samsonov},
  journal={Statistics and Computing},
  year={2020},
  volume={30},
  pages={973-997}
}
In this paper, we propose a novel variance reduction approach for additive functionals of Markov chains based on minimization of an estimate for the asymptotic variance of these functionals over suitable classes of control variates. A distinctive feature of the proposed approach is its ability to significantly reduce the overall finite sample variance. This feature is theoretically demonstrated by means of a deep non-asymptotic analysis of a variance reduced functional as well as by a thorough… 
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