Comparison of three approaches for computing measurement uncertainties

Huang, Hening

doi:10.1016/j.measurement.2020.107923

Cited by 19 publications

(14 citation statements)

References 64 publications

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“…It should be mentioned that there are some confusion and misunderstanding about the concept of true values in the literature. Huang (2020a) recently clarifies that the concept of true values is a common ground among the three approaches for computing measurement uncertainties: GUM's confidence interval based, Bayesian, and probability interval based (i.e. the unified theory of measurement errors and uncertainties (Huang 2018a)).…”

Section: Transformation Between the Frequentist View And Bayesian Viewmentioning

confidence: 99%

“…For Case 2, two frequentist methods: LCD-based (LCD stands for the law of combination of distributions) and least squares, give the same results: 𝜇̂ = inverse-variance weighted-average of the prior mean and the sample mean, and SU = square root of the combined variance (Huang 2020b) (see table 1). Note: 𝑥̅ = observed sample mean, 𝑠 = observed sample standard deviation, n = sample size (number of observations), 𝑥 = prior mean, 𝜎 = prior variance, 𝑐 = bias correction factor, prior knowledge (represented by prior distribution) with current knowledge (represented by likelihood function) about the unknown parameters through Bayes Theorem to obtain the updated knowledge (represented by posterior distribution) (Huang 2020a). The mean of the marginal posterior distribution of µ is taken as 𝜇̂ and the standard deviation is the SU of 𝜇.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the use of the Bayesian Type A SU in the law of propagation of uncertainty (LPU) does not resolve the wellknown Ballico paradox (Huang 2018a). Therefore, the Bayesian Type A SU is essentially invalid and should be abandoned (Huang 2020a).…”

Section: Introductionmentioning

confidence: 99%

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A new modified Bayesian method for measurement uncertainty analysis and the unification of frequentist and Bayesian inference

Huang¹

2022

JPSS

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This paper proposes a new modification of the traditional Bayesian method for measurement uncertainty analysis. The new modified Bayesian method is derived from the law of aggregation of information (LAI) and the rule of transformation between the frequentist view and Bayesian view. It can also be derived from the original Bayes Theorem in continuous form. We focus on a problem that is often encountered in measurement science: a measurement gives a series of observations. We consider two cases: (1) there is no genuine prior information about the measurand, so the uncertainty evaluation is purely Type A, and (2) prior information is available and is represented by a normal distribution. The traditional Bayesian method (also known as the reformulated Bayes Theorem) fails to provide a valid estimate of standard uncertainty in either case. The new modified Bayesian method provides the same solutions to these two cases as its frequentist counterparts. The differences between the new modified Bayesian method and the traditional Bayesian method are discussed. This paper reveals that the traditional Bayesian method is not a self-consistent operation, so it may lead to incorrect inferences in some cases, such as the two cases considered. In the light of the frequentist-Bayesian transformation rule and the law of aggregation of information (LAI), the frequentist and Bayesian inference are virtually equivalent, so they can be unified, at least in measurement uncertainty analysis. The unification is of considerable interest because it may resolve the long-standing debate between frequentists and Bayesians. The unification may also lead to an indisputable, uniform revision of the GUM (Evaluation of measurement data - Guide to the expression of uncertainty in measurement (JCGM 2008)).

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Section: Transformation Between the Frequentist View And Bayesian Viewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A new modified Bayesian method for measurement uncertainty analysis and the unification of frequentist and Bayesian inference

Huang¹

2022

JPSS

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“…The experimental investigations are necessary for the complete assessment of any method's reliability. In order to evaluate quantitative characteristics of method accuracy, a systematic error of the experimental values from conventional true value has to be estimated [41], [42]. Equipment of different complexity can be used for the realization of different methods.…”

Section: B Experimental Verificationmentioning

confidence: 99%

The Methodology for the Reliability Evaluation of the Signal Processing Methods Used for the Dispersion Estimation of Lamb Waves

Draudvilienė

Meškuotienė

2022

IEEE Trans. Instrum. Meas.

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The applications of ultrasonic Lamb waves are becoming more and more frequent and diverse in industrial fields. These waves are used in non-destructive testing (NDT), structural health monitoring (SHM), for the assessment of the quality of materials, etc. However, due to the unusual properties of these waves, new or adapted signal processing methods are necessary to use for the analysis of such wave signals. Based on the requirements of ISO 17025, the work presents the methodology for verification of the signal processing methods used to reconstruct the dispersion curves of the phase and group velocities of Lamb waves. The key sequence of the mathematical and experimental stages, which must be passed to evaluate the reliability of the methods are developed. The present methodology includes the algorithm to optimally quantify the uncertainty, as to avoid additional testing, saving cost and time. The main characteristics and sources of the uncertainties, that mainly affect the accuracy of the obtained results are identified, analyzed, and presented. New standards for certification testing, inspection, and monitoring can be developed more easily and quickly based on the provided methodology in the future.

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“…We apply the model and the calculated metric to the problem of ultimate achievable precision when measuring the studied variable. One of the most original reviews of the advantages and disadvantages of statistical methods used to analyze experimental results is presented in [4], in which the extended uncertainty is used to analyze data on the uncertainties inherent in model variables and the uncertainties of experimental results conducted by various laboratories with different measurement methods. However, the presented approach plays by different rules than the standard statistical analysis of theoretical and experimental data with expert evaluation and measurement theory, the principles of which will be true forever and ever.…”

Section: Introductionmentioning

confidence: 99%

Information Content of the Model for Calculating the Finite Precision of Measurements

Menin¹

2020

PSIJ

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Aims: We argue that the choice of a specific qualitative–quantitative set of variables in a model by a conscious observer fundamentally limits the achievable accuracy of the measurement process. Place and Duration of Study: Mechanical & Refrigeration Consultation Expert, between January 2020 and July 2020. Methodology: Using the concept of “finite information quantities” introduced by Gisin, we try to present it as a practical tool in science and engineering in calculating the proximity indicator of a model to the phenomenon being studied. Results: The formulated metric (comparative uncertainty) allows us to set the optimal achievable uncertainty of the model and to confirm the impossibility of implementing the principle of infinite precision. Conclusion: Any attempt to search for a universal physical theory must consider the uncertainty caused by the observer’s vision and the working of the human brain.

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Comparison of three approaches for computing measurement uncertainties

Cited by 19 publications

References 64 publications

A new modified Bayesian method for measurement uncertainty analysis and the unification of frequentist and Bayesian inference

A new modified Bayesian method for measurement uncertainty analysis and the unification of frequentist and Bayesian inference

The Methodology for the Reliability Evaluation of the Signal Processing Methods Used for the Dispersion Estimation of Lamb Waves

Information Content of the Model for Calculating the Finite Precision of Measurements

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