Uncertainties in parameter estimation: the inverse problem

Fadale, Tushar D.; Ненарокомов, А. В.; Emery, A. F.

doi:10.1016/0017-9310(94)00175-u

Cited by 45 publications

(30 citation statements)

References 3 publications

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“…As H 1 ðp 1 , q 1 Þ = 2 y 1 ½ , the couple ðp 1 , q 1 Þ obtained through classical least-square minimization is not consistent with the interval datum [ y 1 ]. This result can be confirmed using the algorithm SIVIAP that computes an outer approximation of the set AEðq 1 Þ defined by (15). In 2.5 s for " ¼ 0.02 SIVIAP indicates that AEðq 1 Þ ¼ ;, proving that AEðq 1 Þ is empty : there exists no p in P that is consistent with y ½ under the hypothesis q ¼ q 1 .…”

Section: Nuisance Parameters With Known Valuesmentioning

confidence: 62%

“…First, the uncertainty associated with the value q 1 has been neglected. In order to take into account this disturbance, Fadale [15] has proposed an extended maximum-likelihood estimator in which the above nuisance parameters are modeled as normal random variables with known variance. The uncertainty associated with the identified parameters is then derived from the asymptotic variance of the estimator.…”

Section: Nuisance Parametersmentioning

confidence: 99%

“…Outer enclosure. To provide a guaranteed estimation of a set V that may be either AEðq Ã Þ defined by (15) or Å defined by (18), two sets V and V such that V & V & V are computed. Thus, any value of p that belongs to the inner approximation V of V is proved to be consistent with the experimental data, while any value that lies outside the outer approximation V is proved to be inconsistent.…”

Section: 5mentioning

confidence: 99%

See 2 more Smart Citations

Guaranteed characterization of thermal conductivity and diffusivity in presence of model uncertainty

Braems

Ramdani

Kieffer

et al. 2007

Inverse Problems in Science and Engineering

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A crucial problem that occurs when estimating physical parameters from experimental data is the computation of reliable uncertainty bounds for the estimated parameters, while accounting for uncertainty in the model and data. We introduce a new numerical method that contributes to the solution of this problem. We show how to deal with uncertain nuisance parameters located within prior intervals. The method advocated in this article makes it possible to detect the absence of solution when the model hypotheses are inconsistent with the data. An analysis of the sensitivity of estimated uncertainty bounds to the nuisance parameters is also conducted. These features are illustrated with actual data collected on a thermal device used to estimate simultaneously the conductivity and diffusivity of materials.

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Section: Nuisance Parameters With Known Valuesmentioning

confidence: 62%

Section: Nuisance Parametersmentioning

confidence: 99%

Section: 5mentioning

confidence: 99%

See 1 more Smart Citation

Guaranteed characterization of thermal conductivity and diffusivity in presence of model uncertainty

Braems

Ramdani

Kieffer

et al. 2007

Inverse Problems in Science and Engineering

View full text Add to dashboard Cite

show abstract

“…The traditional CRB method can be extended when dealing with stochastic uncertain model parameters b, see (Fadale et al, 1995a), (Emery et al, 2000) with an unbiased estimator u. The forward problem becomes now Φ(u, b)+e n .…”

Section: Stochastic Cramér-rao Bound Methods (Scrb)mentioning

confidence: 99%

“…Therefore, the use of the Cramér-Rao bound method (CRB) is proposed for quantifying the possible uncertainties on the identified unknown parameter values u. CRB is widely-used in many engineering applications; heat transfer applications (Fadale et al, 1995a), biomedical engineering applications (Radich & Buckley, 1995), and signal analysis applications (Stoica & Nehorai, 1989).…”

Section: Error Estimation In the Inverse Problem Solutionsmentioning

confidence: 99%

Magnetic Material Characterization Using an Inverse Problem Approach

Abdallh¹,

Dupré²

2012

Advanced Magnetic Materials

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Fast Bayesian approach for parameter estimation

Jin

2008

Numerical Meth Engineering

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SUMMARYThis paper presents two techniques, i.e. the proper orthogonal decomposition (POD) and the stochastic collocation method (SCM), for constructing surrogate models to accelerate the Bayesian inference approach for parameter estimation problems associated with partial differential equations. POD is a model reduction technique that derives reduced-order models using an optimal problem-adapted basis to effect significant reduction of the problem size and hence computational cost. SCM is an uncertainty propagation technique that approximates the parameterized solution and reduces further forward solves to function evaluations. The utility of the techniques is assessed on the non-linear inverse problem of probabilistically calibrating scalar Robin coefficients from boundary measurements arising in the quenching process and non-destructive evaluation. A hierarchical Bayesian model that handles flexibly the regularization parameter and the noise level is employed, and the posterior state space is explored by the Markov chain Monte Carlo. The numerical results indicate that significant computational gains can be realized without sacrificing the accuracy.

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Uncertainties in parameter estimation: the inverse problem

Cited by 45 publications

References 3 publications

Guaranteed characterization of thermal conductivity and diffusivity in presence of model uncertainty

Guaranteed characterization of thermal conductivity and diffusivity in presence of model uncertainty

Magnetic Material Characterization Using an Inverse Problem Approach

Fast Bayesian approach for parameter estimation

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