Autoregressive parameter estimation from noisy data

2000 ◽  
Vol 47 (1) ◽  
pp. 71-75 ◽  
Author(s):  
Wei Xing Zheng
Keyword(s):  
Parameter Estimation ◽  
Noisy Data ◽  
Autoregressive Parameter

scholarly journals Parameter Estimation by Picard-Iteration for Biochemical Networks with Noisy Data

2018 ◽  
Vol 51 (19) ◽  
pp. 64-67
Author(s):  
Maike Naber ◽  
Friedrich von Haeseler ◽  
Nadine Rudolph ◽  
Heinrich J. Huber ◽  
Rolf Findeisen
Keyword(s):  
Parameter Estimation ◽  
Noisy Data ◽  
Biochemical Networks ◽  
Picard Iteration

Parameter estimation of linear systems with input-output noisy data: A generalized lp norm approach

1994 ◽  
Vol 37 (3) ◽  
pp. 345-356 ◽  
Author(s):  
Jeng-Ming Chen ◽  
Bor-Sen Chen ◽  
Wei-Sheng Chang
Keyword(s):  
Parameter Estimation ◽  
Linear Systems ◽  
Noisy Data ◽  
Input Output ◽  
Lp Norm

scholarly journals Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data

2019 ◽  
Vol 26 (3) ◽  
pp. 227-250 ◽  
Author(s):  
Fei Lu ◽  
Nils Weitzel ◽  
Adam H. Monahan
Keyword(s):  
Parameter Estimation ◽  
Energy Balance ◽  
Noisy Data ◽  
State Parameter ◽  
Energy Balance Model ◽  
Balance Model ◽  
Spatiotemporal Modeling ◽  
Mcmc Method ◽  
Physical Constraints ◽  
Observation Noise

Abstract. While nonlinear stochastic partial differential equations arise naturally in spatiotemporal modeling, inference for such systems often faces two major challenges: sparse noisy data and ill-posedness of the inverse problem of parameter estimation. To overcome the challenges, we introduce a strongly regularized posterior by normalizing the likelihood and by imposing physical constraints through priors of the parameters and states. We investigate joint parameter-state estimation by the regularized posterior in a physically motivated nonlinear stochastic energy balance model (SEBM) for paleoclimate reconstruction. The high-dimensional posterior is sampled by a particle Gibbs sampler that combines a Markov chain Monte Carlo (MCMC) method with an optimal particle filter exploiting the structure of the SEBM. In tests using either Gaussian or uniform priors based on the physical range of parameters, the regularized posteriors overcome the ill-posedness and lead to samples within physical ranges, quantifying the uncertainty in estimation. Due to the ill-posedness and the regularization, the posterior of parameters presents a relatively large uncertainty, and consequently, the maximum of the posterior, which is the minimizer in a variational approach, can have a large variation. In contrast, the posterior of states generally concentrates near the truth, substantially filtering out observation noise and reducing uncertainty in the unconstrained SEBM.

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