Monte Carlo Methods for the Propagation of Uncertainties

Stephen Crowder, Collin Delker, Eric Forrest and Nevin Martin ()
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Stephen Crowder: Sandia National Laboratories
Collin Delker: Sandia National Laboratories
Eric Forrest: Sandia National Laboratories
Nevin Martin: Sandia National Laboratories

Chapter Chapter 8 in Introduction to Statistics in Metrology, 2020, pp 153-180 from Springer

Abstract: Abstract This chapter introduces Monte Carlo methods for calculating uncertainty in indirect measurements. In the Monte Carlo method, each input variable to the measurement model equation is randomly sampled from an appropriate probability distribution many times, and the output of the model equation calculated many times. Uncertainty can then be estimated by statistical analysis of the resulting output distribution. Unlike the GUM method, Monte Carlo uncertainty propagation makes no assumptions about normality of the input distributions or the linearity of the measurement model. This chapter begins with a discussion of requirements for a suitable random number generator for Monte Carlo analysis and how random variates can be sampled from different probability distributions. Then, techniques for using Monte Carlo in the uncertainty propagation problem are discussed, followed with suggestions for validating the results and a full comparison to the traditional GUM method. Finally, several case studies are presented demonstrating Monte Carlo for uncertainty propagation.

Date: 2020
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DOI: 10.1007/978-3-030-53329-8_8

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