A Monte Carlo Approach to Nonnormal and Nonlinear State-Space Modeling

Carlin, Bradley P.; Polson, Nicholas G.; Stoffer, David S.

doi:10.1080/01621459.1992.10475231

Cited by 376 publications

(216 citation statements)

References 22 publications

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“…The Kalman filter is popular in areas as diverse as medicine (Jones 1984), economics (Shumway and Stoffer 1982) and geosciences (Evensen 2003). Variants were devised for, e.g., nonlinear problems (Jazwinski 1970), missing observations (Shumway and Stoffer 1982), censored observations (Johns and Shumway 2005), irregular observation times (Jones 1984), nonlinear updates (Harvey 1989), and non-Gaussian distributions (Carlin et al 1992;Kitagawa 1987;Meinhold and Singpurwalla 1989).…”

Section: Introductionmentioning

confidence: 99%

A two-stage ensemble Kalman filter for smooth data assimilation

Johns

Mandel

2007

Environ Ecol Stat

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The ensemble Kalman Filter (EnKF) applied to a simple fire propagation model by a nonlinear convection-diffusion-reaction partial differential equation breaks down because the EnKF creates nonphysical ensemble members with large gradients. A modification of the EnKF is proposed by adding a regularization term that penalizes large gradients. The method is implemented by applying the EnKF formulas twice, with the regularization term as another observation. The regularization step is also interpreted as a shrinkage of the prior distribution. Numerical results are given to illustrate success of the new method.

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Section: Introductionmentioning

confidence: 99%

A two-stage ensemble Kalman filter for smooth data assimilation

Johns

Mandel

2007

Environ Ecol Stat

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“…Geweke and Tanizaki (2000) suggest four proposal distributions for nonlinear state space models. They conclude that the proposal distribution p(α t |α t−1 ) advocated by Carlin, Polson and Stoffer (1992) is the best choice among the four. Although existing methods have been demonstrated to work in some cases, there are at least two problems that have remained unsolved.…”

Section: Introductionmentioning

confidence: 94%

“…Tanizaki (2004) presents a review of relevant computational methods applied to state space models. Carlin, Polson and Stoffer (1992) and Geweke and Tanizaki (2000) apply single-move samplers, which sample the possibly highly correlated α t individually from p(α t |α −t , y), to create draws from p(α|y). Under assumptions (A1) and (A2), the above full conditional distribution can be written as p(α t |α −t , y) ∝ p(α t+1 |α t ) p(α t |α t−1 ) p(y t |α t ), (t = 2, .…”

Section: Introductionmentioning

confidence: 99%

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Bayesian analysis of nonlinear and non-Gaussian state space models via multiple-try sampling methods

2006

Stat Comput

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We develop in this paper three multiple-try blocking schemes for Bayesian analysis of nonlinear and nonGaussian state space models. To reduce the correlations between successive iterates and to avoid getting trapped in a local maximum, we construct Markov chains by drawing state variables in blocks with multiple trial points. The first and second methods adopt autoregressive and independent kernels to produce the trial points, while the third method uses samples along suitable directions. Using the time series structure of the state space models, the three sampling schemes can be implemented efficiently. In our multimodal examples, the three multiple-try samplers are able to generate the desired posterior sample, whereas existing methods fail to do so.

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“…Whereas off-line analysis through Gibbs sampling (Carlin et al, 1992;Fahrmeir et al, 1992) and iterative Gauss-Newton and Fisher-scoring methods (Fahrmeir and Kaufmann, 1991) leads to accurate estimates of the smoothing densities of the state vector and of smoothed posterior modes and curvature, respectively, exact sequential filtering schemes for on-line analysis still seem infeasible. The method of Kitagawa (1987) who used crude numerical integration over the state space by piecewise linear approximation is undoubtedly limited to models with a univariate or at most a bivariate state vector.…”

Section: Introductionmentioning

confidence: 99%

Applied state space modelling of non-Gaussian time series using integration-based Kalman filtering

Frühwirth‐Schnatter

1994

Stat Comput

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The main topic of the paper is on-line filtering for non-Gaussian dynamic (state space) models by approximate computation of the first two posterior moments using efficient numerical integration. Based on approximating the prior of the state vector by a normal density, we prove that the posterior moments of the state vector are related to the posterior moments of the linear predictor in a simple way. For the linear predictor Gauss-Hermite integration is carried out with automatic reparametrization based on an approximate posterior mode filter. We illustrate how further topics in applied state space modelling, such as estimating hyperparameters, computing model likelihoods and predictive residuals, are managed by integrationbased Kalman-filtering. The methodology derived in the paper is applied to on-line monitoring of ecological time series and filtering for small count data.

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A Monte Carlo Approach to Nonnormal and Nonlinear State-Space Modeling

Cited by 376 publications

References 22 publications

A two-stage ensemble Kalman filter for smooth data assimilation

A two-stage ensemble Kalman filter for smooth data assimilation

Bayesian analysis of nonlinear and non-Gaussian state space models via multiple-try sampling methods

Applied state space modelling of non-Gaussian time series using integration-based Kalman filtering

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