Assignment of a non-informative prior when using a calibration function

The evaluation of measurement uncertainty associated with the use of calibration functions was addressed in a talk at the 19th IMEKO World Congress 2009 in Lisbon (Proceedings, pp 2346-51). Therein, an example involving a cubic function was analysed by a Bayesian approach and by the Monte Carlo method described in Supplement 1 to the 'Guide to the Expression of Uncertainty in Measurement'. Results were found to be discrepant. In this paper we examine a simplified version of the example and show that the reported discrepancy is caused by the choice of the prior in the Bayesian analysis, which does not conform to formal rules for encoding the absence of prior knowledge. Two options for assigning a non-informative prior free from this shortcoming are considered; they are shown to be equivalent.