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Biometrika 1998 85(1):215-227; doi:10.1093/biomet/85.1.215
© 1998 by Biometrika Trust
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Markov chain Monte Carlo for dynamic generalised linear models

DANI GAMERMAN

Instituto de Matemática, Universidade Federal do Rio de Janeiro Caixa Postal 68530, 21945-970 Rio de Janeiro, RJ, Brazil dani{at}dme.ufrj.br

This paper presents a new methodological approach for carrying out Bayesian inference about dynamic models for exponential family observations. The approach is simulationbased and involves the use of Markov chain Monte Carlo techniques. A Metropolis- Hastings algorithm is combined with the Gibbs sampler in repeated use of an adjusted version of normal dynamic linear models. Different alternative schemes based on sampling from the system disturbances and state parameters separately and in a block are derived and compared. The approach is fully Bayesian in obtaining posterior samples with state parameters and unknown hyperparameters. Illustrations with real datasets with sparse counts and missing values are presented. Extensions to accommodate more general evolution forms and distributions for observations and disturbances are outlined.

Key Words: Adjusted time series • Bayesian • Metropolis-Hastings algorithims • Reparameterisation • Sampling schemes • System disturbances


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