Bayesian decision threshold, detection limit and confidence limits in ionising-radiation measurement

Abstract

Based on Bayesian statistics and the Bayesian theory of measurement uncertainty, characteristic limits such as the decision threshold, detection limit and limits of a confidence interval can be calculated taking into account all sources of uncertainty. This approach consists of the complete evaluation of a measurement according to the ISO Guide to the Expression of Uncertainty in Measurement (GUM) and the successive determination of the characteristic limits by using the standard uncertainty obtained from the evaluation. This procedure is elaborated here for several particular models of evaluation. It is, however, so general that it allows for a large variety of applications to similar measurements. It is proposed for the revision of those parts of DIN 25482 and ISO 11929 that are still based on conventional statistics and, therefore, do not allow to take completely into account all the components of measurement uncertainty in the calculation of the characteristic limits.