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Informative Bayesian Type A uncertainty evaluation for a small number of observations.

Cox, M G; Shirono, K* (2017) Informative Bayesian Type A uncertainty evaluation for a small number of observations. Metrologia, 54 (5). pp. 642-652.

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Abstract

A criticism levelled at the Guide to the expression of uncertainty (GUM) is that it is based on a mixture of frequentist and Bayesian thinking. In contrast, making the GUM fully Bayesian implies, among other things, that a (conventional) Bayesian approach to the Type A standard uncertainty evaluation for a small number n of observations leads to the unpalatable consequence that n must be at least equal to 4, which presents a difficulty for many metrologists. This paper presents a Bayesian analysis of Type A uncertainty evaluation that applies for all n = 2, as in the frequentist analysis in the current GUM. The analysis is based on assuming that the observations are drawn from a normal distribution (as in the conventional Bayesian analysis), but uses an informative prior based on lower and upper bounds for the variance of the quantity under consideration. The main outcome of the analysis is a closed-form mathematical expression for the factor by which the standard deviation of the mean observation should be multiplied to calculate the required standard uncertainty. Metrological examples are used to illustrate the approach, which is straightforward to apply using a formula or look-up table.

Item Type: Article
Keywords: Uncertainty, Type A, Bayes, Small
Subjects: Mathematics and Scientific Computing
Mathematics and Scientific Computing > Numerical Computation
Divisions: Data Science
Identification number/DOI: 10.1088/1681-7575/aa787f
Last Modified: 09 Feb 2018 11:56
URI: http://eprintspublications.npl.co.uk/id/eprint/7658

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