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Markov Chains and De‐initializing Processes

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  • Gareth O. Roberts
  • Jeffrey S. Rosenthal

Abstract

We define a notion of de‐initializing Markov chains. We prove that to analyse convergence of Markov chains to stationarity, it suffices to analyse convergence of a de‐initializing chain. Applications are given to Markov chain Monte Carlo algorithms and to convergence diagnostics.

Suggested Citation

  • Gareth O. Roberts & Jeffrey S. Rosenthal, 2001. "Markov Chains and De‐initializing Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 489-504, September.
    • Handle: RePEc:bla:scjsta:v:28:y:2001:i:3:p:489-504
    DOI: 10.1111/1467-9469.00250
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    Cited by:

    1. James P. Hobert & Christian P. Robert & Vivekanada Roy, 2010. "Improving the Convergence Properties of the Data Augmentation Algorithm with an Application to Bayesian Mixture Modelling," Working Papers 2010-29, Center for Research in Economics and Statistics.
    2. Román, Jorge Carlos & Hobert, James P. & Presnell, Brett, 2014. "On reparametrization and the Gibbs sampler," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 110-116.
    3. Jin, Zhumengmeng & Hobert, James P., 2022. "On the convergence rate of the “out-of-order” block Gibbs sampler," Statistics & Probability Letters, Elsevier, vol. 188(C).
    4. Jin, Zhumengmeng & Hobert, James P., 2022. "Dimension free convergence rates for Gibbs samplers for Bayesian linear mixed models," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 25-67.
    5. Wang, Xin & Roy, Vivekananda, 2018. "Analysis of the Pólya-Gamma block Gibbs sampler for Bayesian logistic linear mixed models," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 251-256.
    6. Bryant Davis & James P. Hobert, 2021. "On the Convergence Complexity of Gibbs Samplers for a Family of Simple Bayesian Random Effects Models," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1323-1351, December.
    7. Kshitij Khare & Malay Ghosh, 2022. "MCMC Convergence for Global-Local Shrinkage Priors," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 211-234, September.

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