Evaluating the Measurement Uncertainty: Fundamentals and practical guidance

If you search the web for `measurement uncertainty', you will obtain a list of some 14500 items. This confirms, if necessary, the pervasiveness of this concept. Curiously, I am not aware of a scientific book specifically devoted to the evaluation of the measurement uncertainty. Therefore, this book certainly deserves careful consideration. If you go through it, you quickly realize that it is a multi-faceted book. It is an introduction to metrology, especially in chapter 1, due to T J Quinn, FRS, Director of the Bureau International des Poids et Mesures. It is an introductory course on uncertainty, largely but not exclusively based on the reference document, the Guide to the Expression of Uncertainty in Measurement (GUM), issued in 1995 by the seven leading organizations involved in measurement, such as the BIPM, the IUPAC, the IUPAP and so on. It is also a rich collection of examples and sometimes of curiosities (see Peelle's Pertinent Puzzle) taken from a wide spectrum of specialized applications. Furthermore, it contains an overview of one of the developments under consideration by the Joint Committee for Guides in Metrology (the body currently in charge of the GUM); namely, the treatment of the case of more than one measurand, which gives the author an occasion for an excursus on least squares and their application in metrology. From this viewpoint, the reader will find an answer to a very large number of possible questions concerning the routine uncertainty evaluation in, say, a calibration laboratory. However, in my opinion the distinctive feature of the book is the Bayesian flavour that one can perceive here and there from the first few chapters and which really begins in chapter 6, Bayesian Inference, the longest of the book. As a matter of fact, this book is essentially a manifesto of Bayesian principles applied to measurement uncertainty, and as such the title could be somewhat misleading to the unprepared reader. The application of Bayesian techniques to measurement is largely due to German scientists, with whom the author has cooperated. This approach is attractive, in that it provides a natural way to combine fresh data from the current experiment with prior knowledge such as, for example, values coming from previous calibrations. However, Bayesian techniques are far from being universally accepted within the metrologist community. If you search the web by crossing `measurement uncertainty' with `Bayes' you get only 350 items. There are essentially two reasons for this scarce acceptance. The first has to do with a supposed amount of subjectivity unavoidable in some cases in the assignment of the prior distribution, although the Bayesian theory can provide a sufficiently convincing motivation. The second reason is more practical: a strict application of Bayesian principles leads, even for comparatively simple cases, to complicated expressions which in most cases must be solved numerically. In addition, application to the case of n repeated measurements, which is readily dealt with by using the usual frequentist approach (which, incidentally, is severely criticized by Bayesians) 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. Overall, however, despite a notation that I found sometimes heavy and pedantic, the book represents a good tool for anybody wishing to understand better the topic of measurement uncertainty. The (dominating) section on Bayesian inference is interesting and collects a series of results that were widely scattered in the literature. Also the references reflect to some extent the bias of the author towards Bayesian principles, but, provided that you are aware of this bias, I warmly recommend you to read and consider the contents of this book. Walter Bich