On Gibbs Sampling for State Space Models

We show how to use the Gibbs sampler to carry out Bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time. Our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors. The states are generated efficiently using the Kalman filter. We illustrate our approach by several examples and empirically compare its performance to another Gibbs sampler where the states are generated one at a time. The empirical results suggest that our approach is both practical to implement and dominates the Gibbs sampler that generates the states one at a time.