On Markov Chain Monte Carlo Methods for Nonlinear and Non-gaussian State-space Models
نویسندگان
چکیده
In this paper, a nonlinear and/or non-Gaussian smoother utilizing Markov chain Monte Carlo Methods is proposed, where the measurement and transition equations are specified in any general formulation and the error terms in the state-space model are not necessarily normal. The random draws are directly generated from the smoothing densities. For random number generation, the Metropolis-Hastings algorithm and the Gibbs sampling technique are utilized. The proposed procedure is very simple and easy for programming, compared with the existing nonlinear and non-Gaussian smoothing techniques. Moreover, taking several candidates of the proposal density function, we examine precision of the proposed estimator.
منابع مشابه
Nonlinear and Non-Gaussian State-Space Modeling with Monte Carlo Techniques: A Survey and Comparative Study
Since Kitagawa (1987) and Kramer and Sorenson (1988) proposed the filter and smoother using numerical integration, nonlinear and/or non-Gaussian state estimation problems have been developed. Numerical integration becomes extremely computer-intensive in the higher dimensional cases of the state vector. Therefore, to improve the above problem, the sampling techniques such as Monte Carlo integrat...
متن کاملParticle Markov Chain Monte Carlo
Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods have emerged as the two main tools to sample from high-dimensional probability distributions. Although asymptotic convergence of MCMC algorithms is ensured under weak assumptions, the performance of these latters is unreliable when the proposal distributions used to explore the space are poorly chosen and/or if highly corr...
متن کاملIdentification of Gaussian Process State-Space Models with Particle Stochastic Approximation EM
Gaussian process state-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters governing the properties of this nonparametric representation. The Bayesian formalism enables systematic reasoning about the uncertainty in the system dynamics. We ...
متن کاملParticle filters and Markov chains for learning of dynamical systems
Sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) methods provide computational tools for systematic inference and learning in complex dynamical systems, such as nonlinear and non-Gaussian state-space models. This thesis builds upon several methodological advances within these classes of Monte Carlo methods. Particular emphasis is placed on the combination of SMC and MCMC in so c...
متن کاملApproximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations
Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider app...
متن کامل