Utilizing prior knowledge about the measurement process for uncertainty evaluation through plain Monte Carlo sampling

Abstract

Type A uncertainty evaluation can significantly benefit from incorporating prior knowledge about the precision of an employed measurement device, which allows for reliable uncertainty assessments with limited observations. The Bayesian framework, employing Bayes theorem and Markov Chain Monte Carlo (MCMC), is recommended to incorporate such prior knowledge in a statistically rigorous way. While MCMC is recommended, metrologists are usually well-familiar with plain Monte Carlo sampling and previous work demonstrated the integration of similar prior knowledge into an uncertainty evaluation framework following the plain Monte Carlo sampling of JCGM 101–the Supplement 1 to the GUM. In this work, we explore the potential and limitations of such an approach, presenting classes of data distributions for informative Type A uncertainty evaluations. Our work justifies an informative extension of the JCGM 101 Type A uncertainty evaluation from a statistical perspective, providing theoretical insight and practical guidance. Explicit distributions are proposed for input quantities in Type A scenarios, aligning with Bayesian uncertainty evaluations. In addition, inherent limitations of the JCGM 101 Monte Carlo approach are discussed concerning general Bayesian inference. Metrological examples support the theoretical findings, significantly expanding the applicability of the JCGM 101 Monte Carlo technique from a Bayesian perspective.