It is a long-accepted tenet of scientific practice that every measurement result ought to include a statement of uncertainty associated with the measured value. Such uncertainty should also be propagated to functions of the measured values. It is also widely recognized that probability distributions are well suited to express measurement uncertainty and that statistical methods are the choice vehicles to produce uncertainty assessments incorporating information in empirical data as well as other relevant information, either about the quantity that is the object of measurement or about the techniques or apparatuses used in measurement.
Statistical models and methods of statistical inference provide the technical machinery necessary to evaluate and propagate measurement uncertainty. Some of these models and methods are illustrated in five examples: (i) measurement of the refractive index of a glass prism (employing a venerable formula due to Gauss, as well as contemporary Monte Carlo methods); (ii) measurement of the mass fraction of arsenic in oyster tissue using data from an inter-laboratory study (introducing a Bayesian hierarchical model with adaptive tail heaviness); (iii) measurement of the relative viscosity increment of a solution of sucrose in water (using a copula); (iv) mapping measurements of radioactivity in the area of Fukushima, Japan (via both local regression and kriging, and explaining how model uncertainty may be evaluated); and (v) combining expert opinions about the flow rate of oil during the Deepwater Horizon oil spill into the Gulf of Mexico (via linear or logarithmic pooling). Copyright © 2012 John Wiley & Sons, Ltd.