Reassessment of a calibration model by bayesian reference analysis. http://dx.doi.org/10.1088/0026-1394/48/1/L02

Abstract

The Bayesian analysis of a simple calibration model is reconsidered. Observed values are at hand that conform to a Gaussian probability distribution of unknown standard deviation S. The mean of this distribution is given by a polynomial function of the measurand Y . For the coefficients P of this polynomial a state-of-knowledge distribution is available, whereas no prior information about Y and S exists. A conditional reference prior for (Y, S) given P is derived. It shows no functional dependence on the measurand in the case that the calibration function is linear, but depends non-trivially on the measurand otherwise. This prior is compared with other priors that have been used in the literature to analyse the same calibration model. It leads to a different posterior distribution than the application of Supplement 1 to the ‘Guide to the Expression of Uncertainty in Measurement’. An example illustrates differences of results founded on the various non-informative priors.