Monte Carlo integration with Markov chain

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6 Scopus citations


There are two conceptually distinct tasks in Markov chain Monte Carlo (MCMC): a sampler is designed for simulating a Markov chain and then an estimator is constructed on the Markov chain for computing integrals and expectations. In this article, we aim to address the second task by extending the likelihood approach of Kong et al. for Monte Carlo integration. We consider a general Markov chain scheme and use partial likelihood for estimation. Basically, the Markov chain scheme is treated as a random design and a stratified estimator is defined for the baseline measure. Further, we propose useful techniques including subsampling, regulation, and amplification for achieving overall computational efficiency. Finally, we introduce approximate variance estimators for the point estimators. The method can yield substantially improved accuracy compared with Chib's estimator and the crude Monte Carlo estimator, as illustrated with three examples.

Original languageEnglish (US)
Pages (from-to)1967-1980
Number of pages14
JournalJournal of Statistical Planning and Inference
Issue number7
StatePublished - Jul 1 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


  • Gibbs sampling
  • Importance sampling
  • Markov chain Monte Carlo
  • Partial likelihood
  • Stratification
  • Variance estimation


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