In this paper we obtain a closed form expression for the convergence rate of
the Gibbs sampler applied to an AR(1) plus noise model in terms of the
parameters of the model. We also provide evidence that a ``centered''
parameterisation of a state space model is preferable for the performance of
the Gibbs sampler. These two results provide guidance when the Gaussianity
or linearity of the state space form is lost. We illustrate this by
examining the performance of a Markov Chain Monte Carlo sampler for the
Stochastic Volatility model.

KEYWORDS: Blocking; Convergence rates; Gibbs sampling; Parameterisation;
Simulation smoother; Stochastic Volatility.