MPS-RR 2002-1

February 2002

# Geometric ergodicity of Metropolis-Hastings algorithms for conditional simulation in generalised linear mixed models

by:

### O.F. Christensen, R.P. Waagepetersen

Conditional simulation is useful in connection with inference and prediction
for a generalised 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.

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This paper has now been published in *Methodology and Computing in Applied Probability 3, 309 -
327 (2001)*