Analytic convergence rates and parameterisation issues for the Gibbs sampler applied to state space models. - Pitt, M; Shephard, N (Nuffield College (University of Oxford), 1996)
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.