Calculation of uncertainty in the presence of prior knowledge
Abstract
The Guide to the Expression of Uncertainty in Measurement (GUM) applies to the generic situation that a model is available which relates the quantity of interest to input quantities and that information on the input quantities is given in terms of estimates and uncertainties. Within this framework, the GUM specifies how to calculate an estimate of the quantity of interest and the uncertainty associated with this estimate as well as a coverage interval for the quantity according to a stipulated coverage probability.
In this paper the case is considered that additional prior knowledge about the quantity of interest is available. For instance, the quantity of interest could be known to be positive or some prior estimate and its associated uncertainty may be given. This case is treated using probability density functions which encode the information on the input quantities as well as the prior knowledge about the quantity of interest. In general, numerical techniques have to be employed and an easy-to-apply Monte Carlo method is proposed. For the particular case of a linear (or linearized) model relation and Gaussian probability density functions an analytic solution is derived and discussed. Finally, the proposed treatment, its numerical implementation and the possible benefit of taking into account prior knowledge are illustrated by an example.- Publication:
-
Metrologia
- Pub Date:
- April 2007
- DOI:
- 10.1088/0026-1394/44/2/002
- Bibcode:
- 2007Metro..44..111E