Error bounds of MCMC for functions with unbounded stationary variance

Daniel Rudolf*, Nikolaus Schweizer

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)


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 is an element of (1, 2) so that the functions have finite L-p-norm. For uniformly ergodic Markov chains we obtain error bounds with the optimal order of convergence n(1/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. (C) 2015 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)6-12
JournalStatistics & probability letters
Publication statusPublished - Apr 2015
Externally publishedYes


  • Markov chain Monte Carlo
  • Absolute mean error
  • Uniform ergodicity
  • Spectral gap


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