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Analyzing inconsistent measurement data


Adjusting inconsistent measurement data plays an important role in metrology, for example, to determine reference values when analyzing interlaboratory comparison measurements or when determining values for fundamental constants. The figure shows the example of current values measured for the Planck constant. The data are inconsistent with respect to the quoted uncertainties. Simple application of the weighted mean of the measured values would not be advisable, since this could lead to unreliable results. In such cases, metrology often resorts to the so-called "Birge ratio" method, in which all measurement uncertainties are enlarged in the same way such that consistency of the measurement data is achieved. This procedure is, however, only admissible on the basis of a very specific statistical model. If this – very restrictive – assumption is, however, violated, the Birge ratio method might yield unreliable results.

A new procedure based on Bayesian statistics has been developed at PTB; it allows inconsistent measurement data to be adjusted under considerably weaker assumptions about the underlying statistical model. The procedure is based on a more general class of statistical models, the so-called elliptically contoured distributions. It was possible to demonstrate that the results obtained with the new procedure are better and more robust than those obtained with alternative procedures and, especially, that the uncertainties determined by the new method are more reliable. The figure illustrates the application of the method. The result obtained is a probability distribution for the value of the Planck constant, from which an estimate and its associated uncertainty can be determined.

Olha Bodnar
Department 8.4 Mathematical Modelling and Data Analysis
Phone: +49 (0)30 3481-7414
E-mail: olha.bodnar(at)ptb.de

Scientific publication
O. Bodnar, A. Link, C. Elster: Objective Bayesian inference for a generalized marginal random effects model. Bayesian Analysis (2015, currently in press)



Data measured for the Planck constant (left from the dashed line). The error bars show standard uncertainties. As the result of the new adjustment method, the probability distribution for the value of the Planck constant is shown, together with the derived estimate and the corresponding standard uncertainty (right from the dashed line).