Rejection sampling for Bayesian uncertainty evaluation using the Monte Carlo techniques of GUM-S1

Abstract

Abstract Supplement 1 to the GUM (GUM-S1) extends the GUM uncertainty framework to non-linear functions and non-Gaussian distributions. For this purpose, it employs a Monte Carlo method that yields a probability density function for the measurand. This Monte Carlo method has been successfully applied in numerous applications throughout metrology. However, considerable criticism has been raised against the type A uncertainty evaluation of GUM-S1. Most of the criticism could be addressed by including prior information about the measurand which, however, is beyond the scope of GUM-S1. We propose an alternative Monte Carlo method that will allow prior information about the measurand to be included. The proposed method is based on a Bayesian uncertainty evaluation and applies a simple rejection sampling approach using the Monte Carlo techniques of GUM-S1. The range of applicability of the approach is explored theoretically and in terms of examples. The results are promising, leading us to conclude that many metrological applications could benefit from this approach. Software support is provided to ease its implementation.