Approaches to evaluating measurement uncertainty

The Guide to the expression of measurement uncertainty, (GUM, JCGM 100) and its Supplement 1: propagation of distributions by a Monte Carlo method, (GUMS1, JCGM 101) are two of the most widely used documents concerning measurement uncertainty evaluation in metrology. Both documents describe three phases (a) the construction of a measurement model, (b) the assignment of probability distributions to quantities, and (c) a computational phase that specifies the distribution for the quantity of interest, the measurand. The two approaches described in these two documents agree in the first two phases but employ different computational approaches, with the GUM using linearisations to simplify the calculations. Recent years have seen an increasing interest in using Bayesian approaches to evaluating measurement uncertainty. The Bayesian approach in general differs in the assignment of the probability distributions and its computational phase usually requires Markov chain Monte Carlo (MCMC) approaches. In this paper, we summarise the three approaches to evaluating measurement uncertainty and show how we can regard the GUM and GUMS1 as providing approximate solutions to the Bayesian approach. These approximations can be used to design effective MCMC algorithms