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Multivariate initial sequence estimators in Markov chain Monte Carlo

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  • Dai, Ning
  • Jones, Galin L.

Abstract

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.

Suggested Citation

  • Dai, Ning & Jones, Galin L., 2017. "Multivariate initial sequence estimators in Markov chain Monte Carlo," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 184-199.
    • Handle: RePEc:eee:jmvana:v:159:y:2017:i:c:p:184-199
    DOI: 10.1016/j.jmva.2017.05.009
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    References listed on IDEAS

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    1. Jones, Galin L. & Haran, Murali & Caffo, Brian S. & Neath, Ronald, 2006. "Fixed-Width Output Analysis for Markov Chain Monte Carlo," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1537-1547, December.
    2. Johnson, Alicia A. & Jones, Galin L., 2015. "Geometric ergodicity of random scan Gibbs samplers for hierarchical one-way random effects models," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 325-342.
    3. Alexei J Drummond & Simon Y W Ho & Matthew J Phillips & Andrew Rambaut, 2006. "Relaxed Phylogenetics and Dating with Confidence," PLOS Biology, Public Library of Science, vol. 4(5), pages 1-1, March.
    4. Kosorok, Michael R., 2000. "Monte Carlo error estimation for multivariate Markov chains," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 85-93, January.
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    Cited by:

    1. Dai, Ning & Jones, Galin L. & Fiecas, Mark, 2020. "Bayesian longitudinal spectral estimation with application to resting-state fMRI data analysis," Econometrics and Statistics, Elsevier, vol. 15(C), pages 104-116.
    2. Sanha Noh, 2020. "Posterior Inference on Parameters in a Nonlinear DSGE Model via Gaussian-Based Filters," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 795-841, December.

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