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Error bounds of MCMC for functions with unbounded stationary variance

Author

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  • Rudolf, Daniel
  • Schweizer, Nikolaus

Abstract

We prove explicit error bounds for Markov chain Monte Carlo (MCMC) methods to compute expectations of functions with unbounded stationary variance. We assume that there is a p∈(1,2) so that the functions have finite Lp-norm. For uniformly ergodic Markov chains we obtain error bounds with the optimal order of convergence n1/p−1 and if there exists a spectral gap we almost get the optimal order. Further, a burn-in period is taken into account and a recipe for choosing the burn-in is provided.

Suggested Citation

  • Rudolf, Daniel & Schweizer, Nikolaus, 2015. "Error bounds of MCMC for functions with unbounded stationary variance," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 6-12.
    • Handle: RePEc:eee:stapro:v:99:y:2015:i:c:p:6-12
    DOI: 10.1016/j.spl.2014.07.035
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    References listed on IDEAS

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    1. Asmussen, Søren & Glynn, Peter W., 2011. "A new proof of convergence of MCMC via the ergodic theorem," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1482-1485, October.
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