Measurement data subject only to random effects can be evaluated within the frameworks of conventional as well as Bayesian statistical theory. In this paper, both viewpoints are presented and examples including Gaussian, uniform and Poisson statistics are discussed. The cases of data produced by different observers, and of quantities expressed by measurement models involving systematic effects, are also briefly touched upon. It is shown that, although in most practical cases the uncertainty intervals obtained from repeated measurements using either theory may be similar, their interpretation is completely different. Since the Bayesian approach treats random and systematic effects in the same way, the authors claim that it is more flexible and better adapted to practice than conventional theory.
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