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Geometric Ergodicity of Metropolis-Hastings Algorithms for Conditional Simulation in Generalized Linear Mixed Models

Author

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  • O. F. Christensen

    (Aalborg University)

  • J. Møller

    (Aalborg University)

  • R. P. Waagepetersen

    (Aalborg University)

Abstract

Conditional simulation is useful in connection with inference and prediction for a generalized linear mixed model. We consider random walk Metropolis and Langevin-Hastings algorithms for simulating the random effects given the observed data, when the joint distribution of the unobserved random effects is multivariate Gaussian. In particular we study the desirable property of geometric ergodicity, which ensures the validity of central limit theorems for Monte Carlo estimates.

Suggested Citation

  • O. F. Christensen & J. Møller & R. P. Waagepetersen, 2001. "Geometric Ergodicity of Metropolis-Hastings Algorithms for Conditional Simulation in Generalized Linear Mixed Models," Methodology and Computing in Applied Probability, Springer, vol. 3(3), pages 309-327, September.
    • Handle: RePEc:spr:metcap:v:3:y:2001:i:3:d:10.1023_a:1013779208892
    DOI: 10.1023/A:1013779208892
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    References listed on IDEAS

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    1. O. Stramer & R. L. Tweedie, 1999. "Langevin-Type Models II: Self-Targeting Candidates for MCMC Algorithms," Methodology and Computing in Applied Probability, Springer, vol. 1(3), pages 307-328, October.
    2. Jarner, Søren Fiig & Hansen, Ernst, 2000. "Geometric ergodicity of Metropolis algorithms," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 341-361, February.
    3. Gareth O. Roberts & Jeffrey S. Rosenthal, 1998. "Optimal scaling of discrete approximations to Langevin diffusions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 255-268.
    4. Breyer, L. A. & Roberts, G. O., 2000. "From metropolis to diffusions: Gibbs states and optimal scaling," Stochastic Processes and their Applications, Elsevier, vol. 90(2), pages 181-206, December.
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