An MCMC algorithm based on GUM Supplement 1 for uncertainty evaluation

• Published in: Measurement : journal of the International Measurement Confederation Vol. 45; no. 5; pp. 1188 - 1199
• Main Author: Forbes, A.B.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2012
• Subjects: Algorithms; Bayesian analysis; Bayesian inference; Bayesian theory; Computer programs; computer software; Markov chain; Markov chain Monte Carlo; Mathematical models; measurement; Measurement equation; Measurement uncertainty; Monte Carlo method; Monte Carlo methods; Observation equation; Post-processing; Software; Uncertainty; Measurement equation; Bayesian inference; Measurement uncertainty; Observation equation; Markov chain Monte Carlo
• ISSN: 0263-2241; 1873-412X
• DOI: 10.1016/j.measurement.2012.01.018

► Bayesian inference specifies a posterior distribution for a measurand. ► GUM Supplement 1 uses a specific prior for the measurand. ► We describe an MCMC scheme based on a GUMS1 sample. ► The scheme outputs a sample from the desired posterior distribution. This paper describes a simple Markov chain Monte Carlo algorithm for evaluating measurement uncertainty according to Bayesian principles. The algorithm has two phases, the first coinciding with the Monte Carlo method described in GUM Supplement 1 (GUMS1), the second a simple Metropolis–Hastings algorithm. The second phase can be regarded as a post-processing add-on to the GUMS1 calculation and can be used whenever a GUMS1 approach is adopted. The algorithm allows users freedom to choose their preferred prior distribution for the measurand, rather than that implicitly assigned in the GUMS1 approach, thereby avoiding some of the problems that can arise when applying GUMS1 to certain types of measurement model. The post-processing can be implemented in a few lines of software, so that many of the practical difficulties in implementing Bayesian approaches to measurement uncertainty evaluation are largely removed.