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

Authors:
John Geweke;Hisashi Tanizaki
Affiliations:
Department of Economics, University of Iowa, Iowa City, IA 52242-1000, USA;Graduate School of Economics, Kobe University, Rokkodai, Nadaku, Kobe 657-8501, Japan
Venue:
Computational Statistics & Data Analysis
Year:
2001

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Abstract

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.