Quantifying the Measurement Uncertainty Using Bayesian Inference

In this paper we describe the use of Bayesian inference for the evaluation of measurement uncertainty. The performance of the proposed approach is tested in a multivariate non linear measurement model in which the measurand is the ratio between two quantities: the first one being the sum of constant systematic effects and experimental indications, while the second one is referred to a measurement standard. By assuming that the information about the input quantities are in form of prior joint probability density functions and a series of direct measurement data are available by experiment, the Bayes ' theorem is applied to evaluate the posterior expectation (estimate), the posterior standard uncertainty and the posterior coverage probability concerning the measurand. Numerical results are reported to asses the validity of the proposed analysis.