Objective Bayes models for compatibility assessment and bias estimation

•The paper derives a class of non-informative, probability matching priors.•These distributions are useful to get a Bayesian model in the situation where one has to assess compatibility.•The latter is then interpreted as the parameter assignment for measurand's normal distribution.•The explicit Bayes rules arising from these prior distributions are compared.

The paper derives a class of non-informative, probability matching priors and of default, data-dependent priors for the difference in two normal means when the variance(s) are unknown. These distributions are useful to get a Bayesian model in the situation where one has to assess compatibility of data obtained by a laboratory with the specified values and uncertainty estimate given in the certificate of analysis. The latter is then interpreted as the parameter assignment for measurand's normal distribution. The Bayes rules arising from these prior distributions are compared via the frequentist coverage probability of corresponding credible intervals for lab's bias.