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On reparametrization and the Gibbs sampler

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  • Román, Jorge Carlos
  • Hobert, James P.
  • Presnell, Brett

Abstract

Gibbs samplers derived under different parametrizations of the target density can have radically different rates of convergence. In this article, we specify conditions under which reparametrization leaves the convergence rate of a Gibbs chain unchanged. An example illustrates how these results can be exploited in convergence rate analyses.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:91:y:2014:i:c:p:110-116
    DOI: 10.1016/j.spl.2014.03.024
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    References listed on IDEAS

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    1. Rosenthal J.S., 2003. "Asymptotic Variance and Convergence Rates of Nearly-Periodic Markov Chain Monte Carlo Algorithms," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 169-177, January.
    2. 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.
    3. G. O. Roberts & S. K. Sahu, 1997. "Updating Schemes, Correlation Structure, Blocking and Parameterization for the Gibbs Sampler," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 291-317.
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    Cited by:

    1. 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.

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