State and Parameter Estimation from Observed Signal Increments

Nüsken, Nikolas; Reich, Sebastian; Rozdeba, Paul J.

doi:10.3390/e21050505

Cited by 15 publications

(33 citation statements)

References 36 publications

(94 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An extension to nonlinear and non-Gaussian estimation problems for SPDEs and different types of observation processes can be envisioned through nonlinear extensions of the Kalman-Bucy mean-field equations. See, for example, [15]. Furthermore, our results can be combined with those from [9] to study the coverage probabilities of Bayesian credible sets in a non-asymptotic regime.…”

mentioning

confidence: 85%

“…More recently, the Kalman-Bucy filter has been reformulated as a set of mean-field equations termed the ensemble Kalman-Bucy filter. See, for example [2,6,15]. These mean-field equations allow for a concise formulation of our time-dependent estimation problem.…”

mentioning

confidence: 99%

“…We emphasize that this joint posterior distribution is Gaussian due to the linearity of (4) and (6), respectively. We next reformulate this Bayesian inference problem in terms of pairs of new random variables (U t (k), F t (k)), k ≥ 1, which satisfy the mean-field Kalman-Bucy equations [6,15] dU…”

mentioning

confidence: 99%

See 2 more Smart Citations

Posterior contraction rates for non-parametric state and drift estimation

Reich¹,

Rozdeba²

2020

Foundations of Data Science

Self Cite

View full text Add to dashboard Cite

We consider a combined state and drift estimation problem for the linear stochastic heat equation. The infinite-dimensional Bayesian inference problem is formulated in terms of the Kalman-Bucy filter over an extended state space, and its long-time asymptotic properties are studied. Asymptotic posterior contraction rates in the unknown drift function are the main contribution of this paper. Such rates have been studied before for stationary non-parametric Bayesian inverse problems, and here we demonstrate the consistency of our time-dependent formulation with these previous results building upon scale separation and a slow manifold approximation.

show abstract

mentioning

confidence: 85%

mentioning

confidence: 99%

See 1 more Smart Citation

Posterior contraction rates for non-parametric state and drift estimation

Reich¹,

Rozdeba²

2020

Foundations of Data Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…We also note that the feedback particle formulation (4.19) can be extended to systems for which the measurement and model errors are correlated. See Nüsken, Reich and Rozdeba (2019) for more details.…”

Section: Da For Continuous-time Datamentioning

confidence: 99%

Data assimilation: The Schrödinger perspective

Reich

2019

Acta Numerica

Self Cite

View full text Add to dashboard Cite

Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using probabilistic particle-based algorithms. In addition to surveying recent developments for discrete-and continuous-time data assimilation, both in terms of mathematical foundations and algorithmic implementations, we also provide a unifying framework from the perspective of coupling of measures, and Schrödinger's boundary value problem for stochastic processes in particular.

show abstract

“…This approach is advantageous in that it avoids the strong nonlinearity arising from the integration of the dynamic system, but the disadvantage is that it requires high-frequency sampling of full-state data. For systems whose measurement values are partially missing or whose states are not all measurable, the state distribution at each time point can be recursively estimated through filtering and expectation-maximization followed by model parameter estimation through a state recursion equation [ 12 , 13 ]. However, this algorithm ensures convergence only when the initial estimates of parameters are relatively accurate.…”

mentioning

confidence: 99%

Constrained Parameter Estimation for a Mechanistic Kinetic Model of Cobalt–Hydrogen Electrochemical Competition during a Cobalt Removal Process

Liang

Zhang

2021

Entropy

View full text Add to dashboard Cite

A mechanistic kinetic model of cobalt–hydrogen electrochemical competition for the cobalt removal process in zinc hydrometallurgical was proposed. In addition, to overcome the parameter estimation difficulties arising from the model nonlinearities and the lack of information on the possible value ranges of parameters to be estimated, a constrained guided parameter estimation scheme was derived based on model equations and experimental data. The proposed model and the parameter estimation scheme have two advantages: (i) The model reflected for the first time the mechanism of the electrochemical competition between cobalt and hydrogen ions in the process of cobalt removal in zinc hydrometallurgy; (ii) The proposed constrained parameter estimation scheme did not depend on the information of the possible value ranges of parameters to be estimated; (iii) the constraint conditions provided in that scheme directly linked the experimental phenomenon metrics to the model parameters thereby providing deeper insights into the model parameters for model users. Numerical experiments showed that the proposed constrained parameter estimation algorithm significantly improved the estimation efficiency. Meanwhile, the proposed cobalt–hydrogen electrochemical competition model allowed for accurate simulation of the impact of hydrogen ions on cobalt removal rate as well as simulation of the trend of hydrogen ion concentration, which would be helpful for the actual cobalt removal process in zinc hydrometallurgy.

show abstract

State and Parameter Estimation from Observed Signal Increments

Cited by 15 publications

References 36 publications

Posterior contraction rates for non-parametric state and drift estimation

Posterior contraction rates for non-parametric state and drift estimation

Data assimilation: The Schrödinger perspective

Constrained Parameter Estimation for a Mechanistic Kinetic Model of Cobalt–Hydrogen Electrochemical Competition during a Cobalt Removal Process

Contact Info

Product

Resources

About