Bayesian Theory

Within metrology the evaluation of measurement uncertainty plays a special and very important role. In the past the generally accepted procedure for establishing the uncertainty was the so-called error analysis. Within this procedure probability is interpreted strictly in the statistical (frequentist) sense. Since the available information needed to infer the measurand almost never consists of only observed statistical data, the inference on the basis of error analysis showed difficulties that in 1993 were overcome by an international recommendation to apply, at least within the various branches of metrology, Bayesian Statistics to measurement data. But the price to pay for the resulting consistent and satisfying evaluation procedure is to change one's view of probability and to accept the consequences. This needs guidance, particularly for those educated in frequency-based statistics.