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Quantitative Non-Geometric Convergence Bounds for Independence Samplers

Author

Listed:
  • Gareth O. Roberts

    (Lancaster University)

  • Jeffrey S. Rosenthal

    (University of Toronto)

Abstract

We provide precise, rigorous, fairly sharp quantitative upper and lower bounds on the time to convergence of independence sampler MCMC algorithms which are not geometrically ergodic. This complements previous work on the geometrically ergodic case. Our results illustrate that even simple-seeming Markov chains often converge extremely slowly, and furthermore slight changes to a parameter value can have an enormous effect on convergence times.

Suggested Citation

  • Gareth O. Roberts & Jeffrey S. Rosenthal, 2011. "Quantitative Non-Geometric Convergence Bounds for Independence Samplers," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 391-403, June.
    • Handle: RePEc:spr:metcap:v:13:y:2011:i:2:d:10.1007_s11009-009-9157-z
    DOI: 10.1007/s11009-009-9157-z
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    References listed on IDEAS

    as
    1. Fort, G. & Moulines, E., 2003. "Polynomial ergodicity of Markov transition kernels," Stochastic Processes and their Applications, Elsevier, vol. 103(1), pages 57-99, January.
    2. Marchev, Dobrin & Hobert, James P., 2004. "Geometric Ergodicity of van Dyk and Meng's Algorithm for the Multivariate Student's t Model," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 228-238, January.
    Full references (including those not matched with items on IDEAS)

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