Comment on the book review: Evaluating the Measurement Uncertainty, Fundamentals and Practical Guidance

Abstract

Commenting on the `Bayesian flavour' of my book [1], the reviewer [2] writes that ``a strict application of Bayesian principles ... (to the evaluation of uncertainty) ... in the case of n repeated measurements, which is readily dealt with by using the usual frequentist approach ... leads to the condition that n > 3 in order for the standard uncertainty to exist. Perhaps some comment on this seemingly unphysical consequence of the Bayesian approach would have been desirable''. From a careful reading of book [1], however, one should discover that there is nothing `unphysical' in this situation. What happens is that in the commented case the resulting probability density function (pdf) for the linear transformation of the variable that represents the measurand is a Student's-t with n - 1 degrees of freedom. For this pdf the variance is (n - 1)/(n - 3), and it exists only in the case n > 3. Therefore, it is true that for just two or three repeated measurements one cannot find a standard uncertainty (which is defined as the square root of the variance); nevertheless an uncertainty region about the expectation of the measurand that is expected to contain its value can always be computed with any given probability, whatever the value of n. In any case, according to the viewpoint expounded in [1] the uncertainty is hardly a `physical' concept; it is just a mathematical way of communicating one's state of knowledge regarding the value of the measurand. For a fuller discussion about this point, see [3]. Ignacio Lira Pontificia Universidad Cat�lica de Chile References [1] Lira I 2002 Evaluating the Measurement Uncertainty. Fundamentals and Practical Guidance (Bristol: Institute of Physics Publishing) [2] Book Review: Evaluating the Measurement Uncertainty. Fundamentals and Practical Guidance Meas. Sci. Technol. 13 1502 (IOP Article) [3] Lira I and W�ger W 2001 Bayesian evaluation of the standard uncertainty and coverage probability in a simple measurement model Meas. Sci. Technol. 12 1172-9 (IOP Article)