Nonasymptotic Bounds on the Mean Square Error for MCMC Estimates via Renewal Techniques

  • Krzysztof Łatuszyński
  • Błażej Miasojedow
  • Wojciech Niemiro
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 23)


The Nummellin’s split chain construction allows to decompose a Markov chain Monte Carlo (MCMC) trajectory into i.i.d. “excursions”. Regenerative MCMC algorithms based on this technique use a random number of samples. They have been proposed as a promising alternative to usual fixed length simulation (Hobert et al., Biometrika 89:731–743, 2002; Mykland et al., J. Am. Statist. Assoc. 90:233–241, 1995; Rosenthal, J. Amer. Statist. Association 90:558–566, 1995). 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 construct 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Krzysztof Łatuszyński
    • 1
  • Błażej Miasojedow
    • 2
  • Wojciech Niemiro
    • 3
  1. 1.Department of StatisticsUniversity of WarwickCoventryUK
  2. 2.Institute of Applied Mathematics and MechanicsUniversity of WarsawWarszawaPoland
  3. 3.Faculty of Mathematics and Computer ScienceNicolaus Copernicus UniversityToruńPoland

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