Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Monte Carlo Sampling Bias in the Microwave Uncertainty Framework



Michael R. Frey, Benjamin Jamroz, Amanda Koepke, Jake Rezac, Dylan Williams


The Microwave Uncertainty Framework (MUF) is a software suite created, supported, and made publicly available by the Radio Frequency Division of the U.S. National Institute of Standards and Technology. The general purpose of the MUF is to provide 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 their performance is compared, too, against Combine's design goals. These comparisons are made within an archetypal two-stage scenario in which received data are first transformed in conjunction with shared systematic error and then combined to produce summary information. These comparisons reveal the limited conditions under which Combine's uncertainty results are unbiased and the extent of these biases when these conditions are dropped. For small MC sample sizes neither construction, current or alternative, fully meets Combine's design goals, nor does either construction consistently outperform the other. However, for large MC sample sizes the bias in the proposed alternative construction is asymptotically zero, and this construction is recommended.
Computational Statistics


Monte-Carlo, Microwave Uncertainty Framework, uncertainty, statistics


Frey, M. , Jamroz, B. , Koepke, A. , Rezac, J. and Williams, D. (2019), Monte Carlo Sampling Bias in the Microwave Uncertainty Framework, Computational Statistics (Accessed June 12, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created June 26, 2019, Updated October 12, 2021