Multivariate initial sequence estimators in Markov chain Monte Carlo

Ning Dai, Galin Jones

Research output: Contribution to journalArticle

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Markov chain Monte Carlo (MCMC) is a simulation method commonly used for estimating expectations with respect to a given distribution. We consider estimating the covariance matrix of the asymptotic multivariate normal distribution of a vector of sample means. Geyer (1992) developed a Monte Carlo error estimation method for estimating a univariate mean. We propose a novel multivariate version of Geyer's method that provides an asymptotically valid estimator for the covariance matrix and results in stable Monte Carlo estimates. The finite sample properties of the proposed method are investigated via simulation experiments.

Original languageEnglish (US)
Pages (from-to)184-199
Number of pages16
JournalJournal of Multivariate Analysis
StatePublished - Jul 2017



  • Central limit theorem
  • Covariance matrix estimation
  • Gibbs sampler
  • Markov chain Monte Carlo
  • Metropolis–Hastings algorithm

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