Skip to main content
SpringerLink
Log in

Bounding convergence rates for Markov chains: An example of the use of computer algebra

  • Published:
Statistics and Computing Aims and scope Submit manuscript

Abstract

Kolassa and Tanner (J. Am. Stat. Assoc. (1994) 89, 697–702) present the Gibbs-Skovgaard algorithm for approximate conditional inference. Kolassa (Ann Statist. (1999), 27, 129–142) gives conditions under which their Markov chain is known to converge. This paper calculates explicity bounds on convergence rates in terms calculable directly from chain transition operators. These results are useful in cases like those considered by Kolassa (1999).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Kolassa J.E. and Tanner M.A. 1994. Approximate conditional inference in exponential families via the Gibbs sampler. Journal of the American Statistical Association 89: 697-702.

    Google Scholar 

  • Kolassa J.E. 1999. Convergence and accuracy of Gibbs sampling for conditional distributions in generalized linear models. Ann. Statist., 27: 129-142.

    Google Scholar 

  • Kolassa J.E. 2000. Explicit bounds for geometric convergence of Markov chains. Journal of Applied Probability, In press.

  • Meyn S.P. and Tweedie R.L. 1994. Computable bounds for geometric convergence rates of Markov chains. Advances in Applied Probability 4: 981-1011.

    Google Scholar 

  • Nummelin E. 1984. General Irreducible Markov Chains and Non-Negative Operators. Cambridge University Press, New York.

    Google Scholar 

  • Rosenthal J.S. 1995a. Rates of convergence for Gibbs sampling for variance components models. Annals of Statistics 23: 740-761.

    Google Scholar 

  • Rosenthal J.S. 1995b. Minorization conditions and convergence rates for Markov chain Monte Carlo. Journal of the American Statistical Association 90: 558-566.

    Google Scholar 

  • Roberts G.O. and Polson N.G. 1994. On the geometric convergence of the Gibbs sampler. Journal of the Royal Statistical Society Series B 56: 377-384.

    Google Scholar 

  • Schervish M.J. and Carlin B.P. 1992. On the convergence of successive substitution sampling.Journal of Computational and Graphical Statistics 1: 111-127.

    Google Scholar 

  • Tanner M.A. 1996. Tools for Statistical Inference. Springer-Verlag, Heidelberg.

    Google Scholar 

  • Tierney L. 1994. Markov Chains for exploring posterior distributions. Annals of Statistics 22: 1701-1762.

    Google Scholar 

  • Wolfram Research. 1996. Mathematica 3.0. Wolfram Research, Champaign, IL.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Rutgers University, 501 Hill Center, Busch Campus, Piscataway, NJ, 08855

    John E. Kolassa

Authors
  1. John E. Kolassa
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kolassa, J.E. Bounding convergence rates for Markov chains: An example of the use of computer algebra. Statistics and Computing 11, 83–87 (2001). https://doi.org/10.1023/A:1026566101230

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1026566101230

Search

Navigation