Conditional Prior Proposals in Dynamic Models

Dynamic models extend state space models to non-normal observations. This paper suggests a speci®c hybrid Metropolis±Hastings algorithm as a simple device for Bayesian inference via Markov chain Monte Carlo in dynamic models. Hastings proposals from the (conditional) prior distribution of the unknown, time-varying parameters are used to update the corresponding full conditional distributions. It is shown through simulated examples that the methodology has optimal performance in situations where the prior is relatively strong compared to the likelihood. Typical examples include smoothing priors for categorical data. A speci®c blocking strategy is proposed to ensure good mixing and convergence properties of the simulated Markov chain. It is also shown that the methodology is easily extended to robust transition models using mixtures of normals. The applicability is illustrated with an analysis of a binomial and a binary time series, known in the literature.