© 1994 by Biometrika Trust
Articles |
On Gibbs sampling for state space models
Australian Graduate School of Management, University of New South Wales PO Box 1, Kensington, N.S.W., Australia, 2033
Received for publication 1 June 1992.
Revision received 1 July 1993.
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Abstract |
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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.
Key Words: Diffuse parameter • Kalman filter • Markov chain Monte Carlo • Mixture of normals • Spline smoothing • Switching regression • Trend plus seasonal model
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