Difficulties arising from the representation of the measurand by a probability distribution

The way metrologists conceive of measurement has undergone a major shift in the last two decades. This shift can in great part be traced to a change in the statistical methods used to deal with the expression of measurement results, and, more particularly, with the calculation of measurement uncertainties. Indeed, as we show, the incapacity of the frequentist approach to the calculus of uncertainty to deal with systematic errors has prompted the replacement of the customary frequentist methods by fully Bayesian procedures. The epistemological ramifications of the Bayesian approach merge with a deep empiricist mood tantamount to an "epistemic turn": measurement results are analysed in terms of degrees of belief, and central concepts such as error and accuracy are called into question. We challenge the perspective entailed by this epistemic turn: we insist on the centrality of the concepts of error and accuracy by underlining the intentional character of measurement that is intimately linked to the process of correction of experimental data. We further circumvent the difficulties posed by the classical analysis of measurement by stressing the social rather than the epistemic dimension of measurement activities.

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“…12 See, for instance, Willink (2010a). 13 This does not mean that the agent is entirely driven by psychological factors.…”

Section: The Philosophical Ramifications Of the Bayesian Approach And The "Epistemic Turn" Of Metrologymentioning

confidence: 99%

The evaluation of measurement uncertainties and its epistemological ramifications

Courtenay

Grégis

2017

Studies in History and Philosophy of Science Part A

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“…Consider again the measurement problem described in Example 1, where the complex reflection coefficient Γ is measured using (15). We no longer assume that the denominator of that equation can be approximated by 1 + 0i, so we progress from an analysis with m = 2 to an analysis in which m = 5, where Γ is estimated by…”

Section: Examplementioning

confidence: 99%

“…The first two supplements to the Guide[14,13] adopt a Bayesian-like view of analysis in assigning probability distributions to fixed unknown quantities[15]. If a Bayesian approach to uncertainty analysis had been intended at the time the Guide was written then the W-S formula would not have been theoretically appropriate.…”

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confidence: 99%

An extension to GUM methodology: degrees-of-freedom calculations for correlated multidimensional estimates

Willink¹,

Hall²

2013

Preprint

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The Guide to the Expression of Uncertainty in Measurement advocates the use of an 'effective number of degrees of freedom' for the calculation of an interval of measurement uncertainty. However, it does not describe how this number is to be calculated when (i) the measurand is a vector quantity or (ii) when the errors in the estimates of the quantities defining the measurand (the 'input quantities') are not incurred independently. An appropriate analysis for a vector-valued measurand has been described (Metrologia 39 (2002) 361-9), and a method for a one-dimensional measurand with dependent errors has also been given (Metrologia 44 (2007) 340-9). This paper builds on those analyses to present a method for the situation where the problem is multidimensional and involves correlated errors. The result is an explicit general procedure that reduces to simpler procedures where appropriate. The example studied is from the field of radio-frequency metrology, where measured quantities are often complex-valued and can be regarded as vectors of two elements.

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“…In effect, the constant X i is represented in the mathematical analysis as if it were a random variable. For brevity, we shall call this a distributedmeasurand approach [20].…”

Section: The Distributed-measurand Approach: Assigning a Probability ...mentioning

confidence: 99%

On the validity of methods of uncertainty evaluation

Willink¹

2009

Metrologia

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This paper continues a discussion generated by a recent paper of Hall (2008 Metrologia 45 L5-8) regarding the performance of methods of uncertainty evaluation. The 'validity' of a method of generating intervals of measurement uncertainty is identified principally with the frequency with which these intervals contain the measurand. Two approaches to the evaluation of such intervals are described, and their performances are compared for the simple measurement function appearing in Hall's paper. The first is a Bayesian approach, which is consistent with the numerical method described in Supplement 1 to the Guide to the Expression of Uncertainty in Measurement. The second is an approach based on frequentist principles. Simulations with fixed values of the unknown parameters are conducted to find the rate at which the methods generate intervals containing the value of the measurand and to find the mean widths of the intervals produced. The results show that the standard Bayesian procedure and its modifications can perform poorly. In contrast, the frequentist procedure achieves the required rate of 0.95 while generating intervals of similar width.

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Difficulties arising from the representation of the measurand by a probability distribution

Cited by 12 publications

References 16 publications

The evaluation of measurement uncertainties and its epistemological ramifications

The evaluation of measurement uncertainties and its epistemological ramifications

An extension to GUM methodology: degrees-of-freedom calculations for correlated multidimensional estimates

On the validity of methods of uncertainty evaluation

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