A two-stage procedure for determining the number of trials in the application of a Monte Carlo method for uncertainty evaluation

Abstract

Adaptive Monte Carlo schemes can be used to determine the number of Monte Carlo trials (the number of evaluations of the measurement model) necessary for the evaluation of uncertainty according to Supplement 1 to the GUM (GUM S1). The goal is to reach a prescribed numerical accuracy of the Monte Carlo results (the estimate, associated standard uncertainty and coverage interval endpoints) for a chosen confidence level. It is shown that simple sequential adaptive Monte Carlo schemes may not perform well in this regard and an alternative method based on a two-stage procedure due to Stein is proposed. The implementation of this two-stage scheme for GUM S1 is described, and its performance and robustness are demonstrated in terms of simulation results.