The expression of uncertainty in non-linear parameter estimation

Balsamo, Alessandro; Mana, Giovanni; Pennecchi, Francesca

doi:10.1088/0026-1394/43/5/009

Cited by 21 publications

(21 citation statements)

References 4 publications

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“…We used MATLAB to analyze data by nonlinear least squares parameter fitting (Supplementary Material, see Additional File 2 for codebase). Uncertainties of parameters were measured according to the method of Balsamo et al 17 To disaggregate mean study group values to individual subjects, we used Monte Carlo sampling of the immune state. The immune trajectories were calculated individually for each sampled subject and finally aggregated back to their respective synthetic study groups to compare predicted to observed outcomes.…”

Section: Methodsmentioning

confidence: 99%

A quantitative survey of the literature on poliovirus infection and immunity

Behrend

Nigmatulina

et al. 2014

International Journal of Infectious Diseases

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Section: Methodsmentioning

confidence: 99%

A quantitative survey of the literature on poliovirus infection and immunity

Behrend

Nigmatulina

et al. 2014

International Journal of Infectious Diseases

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“…Since the explicit solution is only available for very special cases, the parameters of the calibration function are usually determined by iterative numerical procedures that minimise the criterion function (8) based on the total sum of the weighted squares of the residues.…”

Section: Linear Comparative Calibration Modelmentioning

confidence: 99%

“…[13], [21], [26], [23], [22], [24], and [9]. The estimated covariance matrix is usually based on the information matrices or their observed version based on the calculated Hessian matrix, although simplifications are possible, see for example [8] and [17] for a detailed discussion of the available approaches and comparisons in nonlinear measurement models.…”

Section: Linear Comparative Calibration Modelmentioning

confidence: 99%

ISO Linear Calibration and Measurement Uncertainty of the Result Obtained With the Calibrated Instrument

Palenčár

Chytil

et al. 2022

Measurement Science Review

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We address the problem of linear comparative calibration, a special case of linear calibration where both variables are measured with errors, and the analysis of the uncertainty of the measurement results obtained with the calibrated instrument. The concept is explained in detail using the calibration experiment of the pressure transducer and the subsequent analysis of the measurement uncertainties. In this context, the calibration and the measurements with the calibrated instrument are performed according to ISO Technical Specification 28037:2010 (here referred to as ISO linear calibration), based on the approximate linear calibration model and the application of the law of propagation of uncertainty (LPU) in this approximate model. Alternatively, estimates of the calibration line parameters, their standard uncertainties, the coverage intervals and the associated probability distributions are obtained using the Monte Carlo method (MCM) based on the law of propagation of distributions (LPD). Here we also obtain the probability distributions and the coverage interval for the quantities measured with the calibrated instrument. Furthermore, motivated by the model structure of this particular example, we conducted a simulation study that presents the empirical coverage probabilities of the ISO and MCM coverage intervals and investigates the influence of the sample size, i.e. the number of calibration points in the measurement range, and the different combinations of measurement uncertainties. The study generally confirms the good properties and validity of the ISO technical specification within the considered (limited) framework of experimental designs motivated by real-world application, with small uncertainties in relation to the measurement range. We also point out the potential weaknesses of this method that require increased user attention and emphasise the need for further research in this area.

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“…Validation of measuring methods is one of fastest growing fields of metrology with important applications in production engineering and, in a broader sense, the production of various machines and devices. According to [2,[4][5][6][7][8][9], there is a pressing need to develop, especially in the field of coordinate metrology, new measuring methods with the mandatory assessment of their accuracy and, above all, an effective model for their validation. Such model would call for the development of an algorithm used for validation of measuring and calibration methods, both at calibration and research laboratories, as well as industrial laboratories supervising production processes.…”

Section: Introductionmentioning

confidence: 99%

Determination of validation threshold for coordinate measuring methods using a metrological compatibility model

Gromczak¹,

Gąska²,

Kowalski³

et al. 2016

Meas. Sci. Technol.

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The following paper presents a practical approach to the validation process of coordinate measuring methods at an accredited laboratory, using a statistical model of metrological compatibility. The statistical analysis of measurement results obtained using a highly accurate system was intended to determine the permissible validation threshold values. The threshold value constitutes the primary criterion for the acceptance or rejection of the validated method, and depends on both the differences between measurement results with corresponding uncertainties and the individual correlation coefficient. The article specifies and explains the types of measuring methods that were subject to validation and defines the criterion value governing their acceptance or rejection in the validation process.

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The expression of uncertainty in non-linear parameter estimation

Cited by 21 publications

References 4 publications

A quantitative survey of the literature on poliovirus infection and immunity

A quantitative survey of the literature on poliovirus infection and immunity

ISO Linear Calibration and Measurement Uncertainty of the Result Obtained With the Calibrated Instrument

Determination of validation threshold for coordinate measuring methods using a metrological compatibility model

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