Monte Carlo sampling bias in the microwave uncertainty framework

Uncertainty propagation software can have unknown, inadvertent biases introduced by various means. This work treats bias identification and reduction in one such software package, the microwave uncertainty framework (MUF). The MUF provides automated multivariate statistical uncertainty propagation and analysis on a Monte Carlo (MC) basis. Combine is a key module in the MUF, responsible for merging data, raw or transformed, to accurately reflect the variability in the data and in its central tendency. In this work the performance of Combine's MC replicates is analytically compared against its stated design goals. An alternative construction is proposed for Combine's MC replicates and its performance is compared, too, against Combine's design goals. These comparisons reveal that Combine's MC uncertainty results with the current construction method are biased except under restrictive conditions. The bias with the proposed alternative construction, by contrast, is, without restriction, asymptotically zero (in the large MC sample size limit), and this construction is recommended.