Bayesian estimation of state-space models using the Metropolis¯Hastings algorithm within Gibbs sampling

In this paper, an attempt is made to show a general solution to nonlinear and/or non-Gaussian state-space modeling in a Bayesian framework, which corresponds to an extension of Carlin et al. (J. Amer. Statist. Assoc. 87(418) (1992) 493¯500) and Carter and Kohn (Biometrika 81(3) (1994) 541¯553; Biometrika 83(3) (1996) 589¯601). Using the Gibbs sampler and the Metropolis¯Hastings algorithm, an asymptotically exact estimate of the smoothing mean is obtained from any nonlinear and/or non-Gaussian model. Moreover, taking several candidates of the proposal density function, we examine precision of the proposed Bayes estimator.