Assessment of measurement uncertainty via observation equations

According to the Guide to the Expression of Uncertainty in Measurement (GUM) (1995, Geneva, Switzerland: International Organization for Standardization (ISO)), the uncertainty in an estimate of the value of a measurand is assessed by propagating the uncertainty in estimates of values of input quantities, based on a measurement equation that expresses the former value as a known function of the latter values. However, in measurement situations where some of the input quantities in turn depend on the measurand, this approach is circuitous and ultimately impracticable. An alternative approach starts from the observation equation, which relates the experimental data to the measurand: this allows a uniform treatment of the most diverse metrological problems, and, once it is used in the context of Bayesian inference, also facilitates the exploitation of any information that may pre-exist about the measurand, alongside the information that fresh experimental data provide about it. The widest applicability of the observation equation approach is illustrated with detailed examples concerning the lifetime of mechanical parts, the measurement of mass, the calibration of a non-linear model in biochemistry and the estimation of a consensus value for arsenic concentration in a sample measured by multiple laboratories.