Bayesian Function Learning Using MCMC Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
On sequential Monte Carlo sampling methods for Bayesian filtering
Statistics and Computing
Bayes and empirical Bayes semi-blind deconvolution using eigenfunctions of a prior covariance
Automatica (Journal of IFAC)
The marginal likelihood for parameters in a discrete Gauss-Markovprocess
IEEE Transactions on Signal Processing
Parameter estimation in stochastic grey-box models
Automatica (Journal of IFAC)
System identification of nonlinear state-space models
Automatica (Journal of IFAC)
| Hi-index | 22.15 |
We consider the smoothing problem of estimating a sequence of state vectors given a nonlinear state space model with additive white Gaussian noise, and measurements of the system output. The system output may also be nonlinearly related to the system state. Often, obtaining the minimum variance state estimates conditioned on output data is not analytically intractable. To tackle this difficulty, a Markov chain Monte Carlo technique is presented. The proposal density for this method efficiently draws samples from the Laplace approximation of the posterior distribution of the state sequence given the measurement sequence. This proposal density is combined with the Metropolis-Hastings algorithm to generate realizations of the state sequence that converges to the proper posterior distribution. The minimum variance estimate and confidence intervals are approximated using these realizations. Simulations of a fed-batch bioreactor model are used to demonstrate that the proposed method can obtain significantly better estimates than the iterated Kalman-Bucy smoother.