Harris, P M; Matthews, C E; Cox, M G; Forbes, A B
(2014)
*Summarising the output of a Monte Carlo method for uncertainty evaluation.*
Metrologia, 51 (3).
pp. 243-252.

## Abstract

The `Guide to the expression of uncertainty in measurement' (GUM) requires that the way a measurement uncertainty is expressed should be transferable. It should be possible to use directly the uncertainty evaluated for one measurement as a component in evaluating the uncertainty for another measurement that depends on the first. Although the method for uncertainty evaluation described in the GUM meets this requirement of transferability, it is less clear how this requirement is to be achieved for Monte Carlo and Markov chain Monte Carlo methods, which are increasingly applied in practice. Such methods provide a sample composed of many values drawn randomly from the probability distribution for the measurand, which does not constitute a convenient way of communicating knowledge about the measurand. In this paper consideration is given to obtaining a compact summary of such a sample that preserves information about the measurand contained in the sample and can be used in a subsequent uncertainty calculation.

It has recently been shown that a quantile function in the form of an extended lambda distribution could provide adequate approximations in a number of cases. This distribution is defined by a fixed number of adjustable parameters determined, for example, by matching the moments of the distribution to those calculated in terms of the sample of values. In this paper that work is further developed by proposing alternative models for the quantile function and alternative methods for determining a quantile function from a sample of values. Examples show that the use of the proposed models and estimation methods can lead to improvements in the approximations obtained.

Item Type: | Article |
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Subjects: | Mathematics and Scientific Computing Mathematics and Scientific Computing > Measurement Uncertainties |

Identification number/DOI: | 10.1088/0026-1394/51/3/243 |

Last Modified: | 02 Feb 2018 13:13 |

URI: | http://eprintspublications.npl.co.uk/id/eprint/6215 |

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