Bayesian statistics for determination of the reference value and degree of equivalence of inconsistent comparison data

Three methods for the determination of the key comparison reference value (KCRV) and degree of equivalence of inconsistent comparison data are proposed in this study. These methods are, respectively, based on the premises of (1) unknown biases of individual measurement values, (2) underestimated uncertainties of individual participants or (3) additional and common uncertainty. Bayesian statistics were employed for the analysis using locally uniform priors. In the case of the first premise, Procedure B in the CIPM guidelines (2002 Metrologia 39 589?95) can be derived in the Bayesian context. In the case of the second and the third premises, the weighted mean is a possible candidate for the KCRV. These methods are exemplified using the key comparison data of CIPM CCM.FF-K3 and APMP.L-K1. Markov chain Monte Carlo simulations were conducted for calculations based on the latter two premises. From the results obtained, it is considered that, in addition to Procedure B in the CIPM guidelines, the method based on the second premise is also a robust method for the estimation of the KCRV.

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